From: "Morgan L. Owens" Subject: (fractint) And we _missed it_! Date: 02 Apr 2000 01:59:15 +1200 You know what just occurred to me? Benoit Mandelbrot discovered the set that now bears his name 20 years ago _last month_. March 1980. I'm chagrined that I forgot. But at least here's a recreation of a scene first seen by human eyes a month later. Belated happy birthday... April1980 { reset=2000 type=mandellambda passes=1 corners=2.963/2.971/0.263/0.271 params=0/0 float=y maxiter=1023 inside=255 outside=15 periodicity=0 viewwindows=1/1/yes/0/0 colors=@default.map } Morgan L. Owens "I wonder how long it originally took to render?" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Les St Clair" Subject: Re: (fractint) Attn Les St Clair Date: 01 Apr 2000 17:32:11 +0100 Hello James, > Have you updated your par listings lately?< Sorry, I've been preoccupied with various other things lately. I'll endeavour to get the parameter collections up to date in the near future. In fact I haven't even had time to keep up with the mail on this, and other, fractal lists. Thanks to Lee Skinner for pointing this message out to me. My web sites at CompuServe and Prestel will soon be migrating to BTinternet. I'll let folks know when the updated collections are available. (this goes for the FOTD par collection, requested elsewhere). Cheers, Les Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Les St Clair" Subject: Re: (fractint) ftod v4? Date: 01 Apr 2000 17:46:29 +0100 Hi folks, > well, it's been just about a year since the last archive of jim muth's fotd < > was done. is anyone working on an archive of this years .pars? < Hmmm. There's something odd going on here (obviously my own fault), but I updated the collection back in December. I just logged onto my web site (which I don't normally visit myself) and found that the page is still the old one from April '99!! I've uploaded the corrected page and files now. The third anniversary of Jim's FOTD is due on 12 April. I'll commence the compilation of Vol.4 after that date. I confess that vol.3 is a little out of date (missing Dec.'99 onward), but I plan to address this problem very soon. I'll post a message here when the collection is updated. Meanwhile Vol.1 - Vol.3 are still available from: http://ourworld.compuserve.com/homepages/Les_StClair/pars.htm cheers, Les Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: (fractint) Fractal Census 2000 Date: 01 Apr 2000 23:26:49 -0600 Greetings, It has been about two weeks since the request for the "Fractal Census" was made, and still receiving an occasional email. I have been compiling this information into a Microsoft Excel spreadsheet, and was only entering the basic stats that was requested. But, decided to expand with additional information (web sites, email addresses, physical addresses, telephone numbers, birthdates, spouses and family members, etc.). It has gotten so large, that it now resembles a small database. I have only taken six of the key fields: Names Various Products Used Qty. Best or Most Used Email Addresses Web Sites to use in the creation of a web page: http://home.att.net/~Paul.N.Lee/Fractal_Census.html This is not the completed census data, which will take a few more hours (or may be days) to finish. But I thought I would publish what I have gathered so for. If someone finds the information for them inaccurate or incomplete, then please reply to the following email address: MAILTO:ABPF_Bot@hotmail.com Sincerely, P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 02-04-00 (Fractal Saturday [6]) (c) Date: 02 Apr 2000 03:59:11 -0400 (EDT) FOTD -- April 02, 2000 (Rating 6) Fractal visionaries and enthusiasts: Today's offering is another example of getting something from nothing. The nothing is the formula Z^(-1)+Z^(-2)+1/C, which when combined with a bailout radius of 10^100 gives a blank black screen at today's coordinates. Since blank screens make very poor fractals, I tried the different inside fills on today's blank screen, which is actually all inside. I found that several options give interesting results, with the bof61 being the best. My first impulse was to name the picture something like "Icy Cool", but I finally decided on "Fractal Saturday" to keep the string of weekday names going. The image, which is all inside fill and uses no periodicity checking, is a slow one, taking an hour to complete on an average Pentium. A download is far more efficient. That download may be found at: and at: The weather, (fractal weather that is), was sunny and 69F (20C) -- perfect conditions for the cats, (fractal cats that is), who spent the entire afternoon on the porch, watching the birds, (common starlings), build their nest in a hole in a tree. Unfortunately, we've come to the end of the day's FOTD. Until next time, take care, and don't take life too seriously. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Fractal_Saturday { ; time=0:59:24.88, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=-1.81391589229417800/+2.27623397785069900\ /1.02028e+009/1/-172.5 params=1/-1/1/-2/0/1e+100 float=y maxiter=1400 bailout=25 inside=bof61 logmap=226 symmetry=none periodicity=0 colors=000000i`V`NuiQiiLqdKn`IkWHhRHfNGcIE`EEZADW6BT\ 1BR0AO09L09K0BT0E`0Hh0Ko0Nx0Qz0Tz0Yz4`z9czEhzIkzNnzT\ szYvzayzhzzlzzqzz000kzzdtzRdsQGzODzOBzO9zOQzO6zN2z<2\ >N0zl0zL0z<4>L0zO0zR0zV2zYAz`GzcLzfTzzZzldzokz`axNVh\ 9NT0GE0EI0EL0EQ1DT2D04D`6Bc7Bh9BkABnEDBIEhNEdRGc<3>i\ ITzIQsKOxKLzLIzLHzZqzVisQanLV<3>T71KLEDZQ6la2tY0zT0z\ Q0zT0zV1zW<2>6x`7ta9scAodBnfDlhEiiGhkHdlIcnK`oLZqNWs\ OVtQTvOQxOOxNLyNKyLIzLGzKEzKDzIAzI9zH7zH4zG2zG1zE0zE\ 0zD0zD0zB0zB0zD0z<12>E0zE0zE0z<3>E0zYsH`qEcoBfnAil7l\ l6ok2<2>yf0zf0zd0zc0za0za0z`0zZ0zZ0zY0zW0zW0zV0zT1zT\ 2zR4yQ7xQ9vOAvNBtNEsLGqKHqKInNL<4>fVTdWVaYW<4>VdcTfd\ Qhf<3>KnlIonHqoHsnHtnHtnHvnHvnHxl<3>HzlHzkHzkHzkHzkH\ zkHzi<3>HziIzdKs`LkWNcTOWO<3>V29kv1kq9kkG } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 03-04-00 (Fractal Convergence [5]) (c) Date: 03 Apr 2000 00:48:34 -0400 (EDT) FOTD -- April 03, 2000 (Rating 5) Fractal visionaries and enthusiasts: Today's Fractal of the Day is named "Fractal Convergence". I gave it this name when I noticed the surrounding elements converging on the always-present midget at the center. Of course almost all Mandeloid midgets are surrounded by converging elements, but those in today's picture struck me as particularly impressive. The not-very-spectacular formula behind the image is (Z^0.8)+(Z^2.6)+C, an expression that would arouse the interest of but few math buffs. Fractal formulae are deceiving however, and today's modest formula exceeds itself in the fractal images it produces. As is the case with the images drawn by many combined formulas, the outside area of today's picture is filled with holes, giving it a particularly delicate appearance. Closer to the midget these holes form a distinctive texture, which is curious but not interesting enough to warrant a FOTD. The parameter file attached at the bottom of this discussion takes over six minutes to render. The JPEG image file takes under two minutes to download from: or from: The choice of how to view the image is up to you. If you run the parameter file, the .GIF image that results can be further investigated. If you download the image, you will have a JPEG file with no fractal data embedded, which can be viewed but not worked with. The weather today was cloudy and mild with periods of light rain totalling all of 0.1cm. The fractal cats enjoyed the temperature of 68F (20C) while it was dry, but came indoors when the rain began. Until next time, take care, stay dry, and see you soon. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ FractalConvergence { ; time=0:06:14.40, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.0606150317/0.0484140988/2441454/1/110 params=1/0.8/1/2.6/0/0 float=y maxiter=3600 inside=0 logmap=80 symmetry=none periodicity=10 colors=0004G90F1<3>KR6PU7TW8<3>eiLhmOkpRnsUqcVuRW<3>\ aegXhjSlmOkk_YijGBu_9a1RlBZwLe<3>Rf`Jk_BpZqKZ<4>fcFg\ eHigJNZT<3>fRh<2>iMYjWVtaSnOT_FUHDV8BW<4>SnjWulNCe<3\ >hUSnYPsaMxeJ<3>sph<3>rDqr3sk7r<3>KNnERmMOo<3>qGw<3>\ D4a31X22Z<3>16b17c8GVEPNLYERf6<3>egaigilgq7RXPZYfeY<\ 2>5ls<3>`07<2>8vohdvdbX`a8<2>1Xv<2>ASPNNO_JO<3>q9ju6\ py4uYSr6npNmecmW<2>ey4YvPQth<2>UVEaZahax<3>k17<3>UUi\ Q`rXTm<2>o7_<3>eAdcAeWMlOXsHgzJhuLiq<3>GmuFmvEmwDmw<\ 3>CmpCmoImq<3>emukmvjmt<3>fmmemkemj<3>_mWZmSXmPWmLVm\ I<3>jmNnmPrmQvmRzmS`mKCmDVmY<3>bmq<2>smc<3>amaXmaTma\ Pma<3>am`dm_gm_jm_mm_<2>XmYRmYKmfLmg<2>8mI } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: (fractint) Re: What's our population Date: 03 Apr 2000 13:16:54 GMT Did you know: If you send the command "who fractint" to majordomo@lists.xmission.com you get a list of the email addresses of everybody on the list? All 294 of us? (I just got one *big* email!) ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Fliguer, Miguel" Subject: (fractint) Franktal Gallery - Update Date: 03 Apr 2000 13:09:12 -0300 Hi ! A new iteration of the Franktal Gallery is on the usual site for your visual and aural pleasure. The maitre d' suggests : - Ray-Traced fractals : What happens inside a stack of mirrored balls ? - Fractal Babe #1 : By popular request..... - A small animation which uses the new 'lake' feature from v20.0.6 - Gallery V - Y2K compliant fractals : Miscellaneous pictures I know there are some minor thumbnail misplacements, I'll try to fix them ASAP Anyway, I encourage you to send me your feedback (positive/negative/real/complex). Enjoy !!! PS: Please could a kind soul forward this to the fractal art list ? Thank you. Miguel Fliguer Franktal Gallery http://members.xoom.com/fliguer/franktal.html mailto:franktal@hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Tim Wegner Subject: (fractint) list archive Date: 03 Apr 2000 20:13:54 -0600 Discussion of list management issues is officially off topic except for me, the benevolent dictator :-) If anyone has an opinion on the issue mentioned below, please *email me* (but don't post to the list). I would like to get opinions, but not clutter the list with discussion on this topic. Some of you may be aware that the archive of the digest version of this list is publically visible at: http://www.xmission.com/pub/lists/fractint/archive/ It is possible that automatic webcrawlers can scavange email addresses from the archive. I have no evidence that this actually happens, and I have heard a point of view that web crawlers probably don't check ftp files, which is what the archive consists of. I could make the archive inaccessible to the public. SHould I? Pro: This might reduce the exposure of your email to potential spammers. Con: Availablilty of the archive is useful for folks who are returning to the list after an absence or want to search for a topic, so we'd lose this capability if the archive were not public. If you have an opinion, email me. I'm leaning toward the status quo. Tim Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jason Hine" Subject: (fractint) Amy Grant uses Fractint? Date: 03 Apr 2000 20:43:33 -0700 Folks, You know that rather unmistakable three-note sound that Fractint uses to indicate image completion? Well, take a listen to the title track (#6) from Amy Grant's somewhat recent album, "Behind the Eyes". I've put a 15-second clip in MP3 format out at: http://tumnus.home.mindspring.com/sounds/ The file is called fractint_1.mp3. The position of the fractint sound is indicated in the lyrics below: Who can trace the path of time? Not you or me. The twisting road we call our lives We cannot see... It would calm my nerves considerably if someone would take a listen and tell me that I'm not just hearing things, which of course, I am... but you know what I mean. Talk about fractal music... sheesh! Jason Hine Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Damien M. Jones" Subject: Re: (fractint) Amy Grant uses Fractint? Date: 04 Apr 2000 12:10:11 -0400 Jason, - You know that rather unmistakable three-note sound that Fractint uses - to indicate image completion? [...] - - It would calm my nerves considerably if someone would take a listen - and tell me that I'm not just hearing things, which of course, I am... Sorry, can't oblige you there. :-) I downloaded the clip, I've listened to it quite carefully, and I hear the sound you're talking about, I don't think it's from FractInt at all. It's just the way it ends up sounding right there. Damien M. Jones \\ dmj@fractalus.com \\ Fractalus Galleries & Info: \\ http://www.fractalus.com/ Please do not post my e-mail address on a web site or in a newsgroup. Thank you. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Angela Wilczynski" Subject: Re: (fractint) Amy Grant uses Fractint? Date: 03 Apr 2000 21:54:25 -0700 Who is Amy Grant? Has she posted any fractals? Are they any good?????? wizzle "Damien M. Jones" wrote: > > Jason, > > - You know that rather unmistakable three-note sound that Fractint uses > - to indicate image completion? [...] > - > - It would calm my nerves considerably if someone would take a listen > - and tell me that I'm not just hearing things, which of course, I am... > > Sorry, can't oblige you there. :-) I downloaded the clip, I've listened to > it quite carefully, and I hear the sound you're talking about, I don't > think it's from FractInt at all. It's just the way it ends up sounding > right there. > > Damien M. Jones \\ > dmj@fractalus.com \\ Fractalus Galleries & Info: > \\ http://www.fractalus.com/ > > Please do not post my e-mail address on a web site or > in a newsgroup. Thank you. > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 04-04-00 (Catkins [4]) (c) Date: 04 Apr 2000 01:46:39 -0400 (EDT) FOTD -- April 04, 2000 (Rating 4) Fractal visionaries and enthusiasts: When I first saw today's squirmy image, it reminded me of something that I could not quite identify. Then a few minutes later I remembered that the poplar trees down the street are covered with dangling bronze catkins. The spiral elements in today's picture resemble those catkins so closely that the name "Catkins" was a natural choice. The formula behind the image is 999Z^(-0.9)-999Z^(-0.9999)+C, another non-notable expression that does more than it should. The unusual effect in the picture is due to the fact that the image consists entirely of bof60 inside fill. This fill tends to produce bubble-like effects in the inside areas of fractals. Since today's image is all inside, it is filled with the bubbles. I have colored the scene with a near-monochrome palette of tints of red and blue. And yes, I did liven the colors a bit in a graphic program. The parameter file runs in a rather tardy 18+ minutes. For quick relief, the JPEG image can be downloaded far more efficiently from either: or from: The fractal weather today was partly cloudy and 75F (19C), with a thunder-shower in the evening. The cats loved the warm afternoon, but our local baseball team failed to take advantage of the unexpectedly fine conditions. They lost the opening game of the season 4-to-1. For now, we've come to the end of another FOTD. But have no fear, I'll return in 24 hours or so with another glorious fractal and some not quite so glorious words. Until then, keep the fractal faith. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Catkins { ; time=0:18:15.88, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=mandelbrotmix4 function=ident passes=1 center-mag=-35.3855307227961/+0.122906688853536/2.20\ 181e+007/1/57.5 params=1/-0.9/-1/-0.9999/999/1e+020 float=y maxiter=3000 bailout=25 inside=bof60 symmetry=none periodicity=10 colors=000`Bc<3>_Af_Af_Ah<2>_Aj_Aj_Al_AlZ9mZ9o<2>Z9q\ Z9qZ9sZ9sZ9tY8v<2>Y8wY8xY8zY8zY8zY7z<3>Y8zY8zY8z<2>Y\ 8zY8zW8zV8xU8xT9xR9wQ9vP9tO9q<3>J9lI9jG9h<3>FAcFAaFA\ `<8>FA_FB_FB_FBY<3>FBYFBYFBX<2>FBXFBXFDX<4>FDWFDWFDV\ <3>FDVGEWFDVFDVFDVEBV<3>DAVDAVCAT<3>B8TB8TA8T<4>D6SE\ 6SE6SF6SG5SG5SI5SJ4SJ4QK4Q<2>L3QL3QK2QK2QK2QJ0PK1QK1\ QK2QL2SL3VL3WM4XM4YM5`O5aO6cO6dP7eP7hP8iQ8jQ9lQ9oRAo\ RAoRBoTBoTDp<4>VFqVGqVGqWIqWIsWJsYJs<3>ZLtZMtZMv_Ov<\ 3>`Qw`QwbRwbRwbSxcSxcUxcUxdVxdVzdWzfWzfXzgXziZz<3>n`\ zo`zqbz<3>vdzxdzydzoczccz`bwYbvU`sR`qO_oK_mIZjEZiBXh\ 8Xe5Wd2Wa0V`0VY0UX0UV0ST0SS0RQ<10>0RP0RP0RO<3>0RObDV\ <3>bDXbDYbDY`B_`B``B``Ba`Bc } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Tony \(Anthony\) Hanmer" Subject: (fractint) Time for some more L-Systems, 1 Date: 04 Apr 2000 11:16:10 GEST Here are some more sets of L-Systems. This one and the next one should be combined into one file called horizons.l If there are any long lines which have been cut into 2, you should restore these to single lines in a text editor. Tony Hanmer README { ; These l-systems, which I have called "Horizons", are all based on Angle 8 ; a horizontal line of length 2-5 segments, with a"growth" up off Axiom f ; it, which usually retraces itself to return to the horizon. f=f ; Anthony Hanmer 2000 } ADH231 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+f+f++++f+f+f } ADH231a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+f+f++++f+f+f } ADH232 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+f+ff++++ff+f+f } ADH232a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+f+ff++++ff+f+f } ADH233 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+f+ff++++f++f++++f++f+f+f } ADH233a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+f+ff++++f++f++++f++f+f+f } ADH237 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=ff+f+f++f+f++f+f++f+f+f } ADH237a { ; Anthony Hanmer 2000 Angle 4 ; Axiom +f++f f=ff+f+f++f+f++f+f++f+f+f } ADH238 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=ff+ff+f++ff++f+ff+f } ADH238a { ; Anthony Hanmer 2000 Angle 4 ; Axiom +f++f f=ff+ff+f++ff++f+ff+f } ADH239 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=ff+ff+f++ff++f+ff+ff } ADH246 { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f++f+f++++f++f++++f+f++ff } ADH247 { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f++f+f++++f++ff++++ff+f++f } ADH248 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f+f++++f++ff++++ff+f++ff } ADH248a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++f+f++++f++ff++++ff+f++ff } ADH249 { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=ff++f+f++++f++ff++++ff+f++ff } ADH250 { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff+f++++f++f++++f+ff++ff } ADH251 { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff+f++++f++ff++++ff+ff++ff } ADH252 { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=ff++ff+f++++f++ff++++ff+ff++f } ADH253 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+f++f++f++f+ff } ADH253a { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++f++f++f++++f--f--f--f f=f+f++f++f++f+ff } ADH253b { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++++h f=f+f++f++f++f+ff h=ff+f++f++f++f+f } ADH254 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=f+f+f++f+f+ff } ADH255 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=f+f+ff++f+ff+ff } ADH256 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+f++f+ff } ADH256a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f+f+f+f++f-f-f-f f=f+f++f+ff } ADH257 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=f+f+f+++f-f++ff } ADH257a { ; Anthony Hanmer 2000 Angle 6 ; Axiom f+++f f=f+f+f+++f-f++ff } ADH258 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=ff++f++f++fff } ADH258a { ; Anthony Hanmer 2000 Angle 6 ; Axiom f++f++f+++f--f--f f=ff++f++f++fff } ADH259 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff++ff+ff } ADH259a { ; Anthony Hanmer 2000 Angle 4 ; Axiom +f++f f=f+ff++ff+ff } ADH259b { ; Anthony Hanmer 2000 Angle 4 ; Axiom f+f+f+f++f-f-f-f f=f+ff++ff+ff } ADH260 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f+f++++f-f++ff } ADH260a { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f++f+f++++f-f++ff } ADH261 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=f+f+f+f+++f-f-f++ff } ADH261a { ; Anthony Hanmer 2000 Angle 6 ; Axiom +f+++f f=f+f+f+f+++f-f-f++ff } ADH262 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=ff+f+f+f+++f-f-f++f } ADH262a { ; Anthony Hanmer 2000 Angle 6 ; Axiom -f+++f f=ff+f+f+f+++f-f-f++f } ADH264 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+++f++++f+++f++++f+++f++++f+++ff } ADH264a { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++++f f=f+++f++++f+++f++++f+++f++++f+++ff } ADH264b { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++f++f++f++++f--f--f--f f=f+++f++++f+++f++++f+++f++++f+++ff } ADH265 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+++ff++++ff+++f++++f+++ff++++ff+++ff } ADH265a { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++++f f=f+++ff++++ff+++f++++f+++ff++++ff+++ff } ADH265b { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++f++f++f++++f--f--f--f f=f+++ff++++ff+++f++++f+++ff++++ff+++ff } ADH266 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+++f++++f+++ff++++ff+++f++++f+++ff } ADH266a { ; Anthony Hanmer 2000 Angle 8 ; Axiom --f++++f f=f+++f++++f+++ff++++ff+++f++++f+++ff } ADH266b { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++f++f++f++++f--f--f--f f=f+++f++++f+++ff++++ff+++f++++f+++ff } ADH267 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+++ff++++ff+++fff++++fff+++f++++f+++ff } ADH267a { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f+++ff++++ff+++fff++++fff+++f++++f+++ff } ADH267b { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++f++f++f++++f--f--f--f f=f+++ff++++ff+++fff++++fff+++f++++f+++ff } ADH268 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+++ff++++ff+++f++++f+++fff++++fff+++f } ADH269 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f++++f+++f++++f+++ff } ADH269a { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++++f f=f++f++++f+++f++++f+++ff } ADH269b { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++f++f++f++++f--f--f--f f=f++f++++f+++f++++f+++ff } ADH270 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff++++ff+++f++++f+++ff } ADH270a { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f++ff++++ff+++f++++f+++ff } ADH270b { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++f++f++f++++f--f--f--f f=f++ff++++ff+++f++++f+++ff } ADH274 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+++f-f++++f+f+ff } ADH274a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+++f-f++++f+f+ff } ADH275 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+++ff-f++++f+ff+ff } ADH275a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+++ff-f++++f+ff+ff } ADH276 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=ff+++ff-f++++f+ff+f } ADH276a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=ff+++ff-f++++f+ff+f } ADH277 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=ff+++ff-f++++f+ff+ff } ADH277a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=ff+++ff-f++++f+ff+ff } ADH278 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=f++f-f+++f+f+ff } ADH278a { ; Anthony Hanmer 2000 Angle 6 ; Axiom f+++f f=f++f-f+++f+f+ff } ADH279 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=f++ff-f+++f+ff+ff } ADH279a { ; Anthony Hanmer 2000 Angle 6 ; Axiom +f+++f f=f++ff-f+++f+ff+ff } ADH280 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+fff+f++f+f++f+f++f+fff+ff } ADH280a { ; Anthony Hanmer 2000 Angle 4 ; Axiom +f++f f=f+fff+f++f+f++f+f++f+fff+ff } ADH281 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff+f++++f+++f++++f+f++++f+++ff++ff } ADH281a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff+f++++f+++f++++f+f++++f+++ff++ff } ADH283 { ; Anthony Hanmer 2000 Angle 8 ; Looking to William McWorter's Maze09 Axiom f f=ff+++f-f++++f+f--f+f++++f-f-f } ADH284 { ; Anthony Hanmer 2000 Angle 8 ; Looking to William McWorter's Maze09 Axiom f f=ff+++f-f++++f+f--f+f++++f-f-ff } ADH285 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+++f--f++++f++f+ff } ADH285a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+++f--f++++f++f+ff } ADH286 { ; Anthony Hanmer 2000 Angle 8 ; The Wave Axiom f f=f+f++f++++f--f+++f } ADH286a { ; Anthony Hanmer 2000 Angle 8 ; The Wave, doubled Axiom f++++f f=f+f++f++++f--f+++f } ADH286b { ; Anthony Hanmer 2000 Angle 8 ; The Wave, square Axiom f--f--f--f f=f+f++f++++f--f+++f } ADH290 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+f-f++f+f+f } ADH291 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+f-f++f+f+ff } ADH291a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f++f f=f+f-f++f+f+ff } ADH291b { ; Anthony Hanmer 2000 Angle 4 ; Axiom f+f+f+f++f-f-f-f f=f+f-f++f+f+ff } ADH292 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff-f++f+ff+ff } ADH292a { ; Anthony Hanmer 2000 Angle 4 ; Axiom +f++f f=f+ff-f++f+ff+ff } ADH293 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff-ff++ff+ff+fff } ADH293a { ; Anthony Hanmer 2000 Angle 4 ; Axiom +f++f f=f+ff-ff++ff+ff+fff } ADH294 { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f f=f+f++f++++f+++f--f++++f---f++++f+f-f+++f } ADH294a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+f++f++++f+++f--f++++f---f++++f+f-f+++f } ADH295 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+f++f++++f+++f--f++++f---f++++f+f-f+++ff } ADH295a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+f++f++++f+++f--f++++f---f++++f+f-f+++ff } ADH296 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+ff++f++++f+++f--f++++f---f++++f+f-ff+++ff } ADH296a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+ff++f++++f+++f--f++++f---f++++f+f-ff+++ff } ADH297 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f-f---f++++f+++f+f++ff } ADH297a { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++++f f=f++f-f---f++++f+++f+f++ff } ADH298 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff-f---f++++f+++f+ff++ff } ADH298a { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++++f f=f++ff-f---f++++f+++f+ff++ff } ADH299 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f--f+f++++f-f++f++f } ADH299a { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f++f--f+f++++f-f++f++f } ADH300 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f--f+f++++f-f++f++ff } ADH300a { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f++f--f+f++++f-f++f++ff } ADH301 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff--f+f++++f-f++ff++ff } ADH301a { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f++ff--f+f++++f-f++ff++ff } ADH302 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f--f+++f++++f---f++f++f } ADH302a { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f++f--f+++f++++f---f++f++f } ADH303 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f--f+++f++++f---f++f++ff } ADH303a { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f++f--f+++f++++f---f++f++ff } ADH304 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff--f+++f++++f---f++ff++ff } ADH304a { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f++ff--f+++f++++f---f++ff++ff } ADH306 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=f+ff+f++f++f--ff++ff } ADH306a { ; Anthony Hanmer 2000 Angle 6 ; Axiom f+++f f=f+ff+f++f++f--ff++ff } ADH308 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=f+ff++f++f-f++f } ADH309 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=f+ff++f++f-f++ff } ADH309a { ; Anthony Hanmer 2000 Angle 6 ; Axiom f+++f f=f+ff++f++f-f++ff } ADH310 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f+++f---f++++f+++f---f++ff } ADH310a { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++++f f=f++f+++f---f++++f+++f---f++ff } ADH311 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff+++f---f++++f+++f---ff++ff } ADH311a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff+++f---f++++f+++f---ff++ff } ADH312 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+f+f-f++f+ff++f+f+ff } ADH312a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f++f f=f+f+f-f++f+ff++f+f+ff } ADH313 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff+f-f++f+ff++f+ff+ff } ADH313a { ; Anthony Hanmer 2000 Angle 4 ; Axiom +f++f f=f+ff+f-f++f+ff++f+ff+ff } ADH314 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f--f+++f--f++++f++f---f++f++f } ADH315 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f--f+++f--f++++f++f---f++f++ff } ADH315a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++f--f+++f--f++++f++f---f++f++ff } ADH316 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff--f+++f--f++++f++f---f++ff++ff } ADH316a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff--f+++f--f++++f++f---f++ff++ff } ADH317 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+f+ff++++f++f++++f++f+f+ff } ADH317a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+f+ff++++f++f++++f++f+f+ff } ADH318 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+f+f++f++++f--f+f+f } ADH318a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+f+f++f++++f--f+f+f } ADH319 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+f+f++f++++f--f+f+ff } ADH319a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+f+f++f++++f--f+f+ff } ADH320 { ; Anthony Hanmer 2000 Angle 4 ; Axiom d d=dd\90d\80d\180dd\180d\100d\90d } ADH320a { ; Anthony Hanmer 2000 Angle 4 ; Axiom d\180d d=dd\90d\80d\180dd\180d\100d\90d } ADH321 { ; Anthony Hanmer 2000 Angle 4 ; Axiom d d=dd\80d\90d\180d\90d\180d\90d\180d\90d\100d } ADH321a { ; Anthony Hanmer 2000 Angle 4 ; Axiom \90d\180d d=dd\80d\90d\180d\90d\180d\90d\180d\90d\100d } ADH322 { ; Anthony Hanmer 2000 Angle 4 ; Axiom d d=dd\90d\60d\180dd\180d\120d\90d } ADH322a { ; Anthony Hanmer 2000 Angle 4 ; Axiom \90d\180d d=dd\90d\60d\180dd\180d\120d\90d } ADH323 { ; Anthony Hanmer 2000 Angle 4 ; Axiom d d=dd\60d\90d\180d\90d\180d\90d\180d\90d\120d } ADH323a { ; Anthony Hanmer 2000 Angle 4 ; Axiom \110d\180d d=dd\60d\90d\180d\90d\180d\90d\180d\90d\120d } ADH326 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff+++f+++ff++++f++f++ff } ADH326a { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++++f f=f++ff+++f+++ff++++f++f++ff } ADH327 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff+f+f+ff++f+f+f+f } ADH328 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+ff+++f++++f---ff+++ff } ADH329 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+ff+f+++f+f-f+++f } ADH330 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+ff+f+++f+f-f+++ff } ADH330a { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f+ff+f+++f+f-f+++ff } ADH331 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+ff++f++++f--ff+++ff } ADH331a { ; Anthony Hanmer 2000 Angle 8 ; Axiom ++f++++f f=f+ff++f++++f--ff+++ff } ADH332 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff+f+f++ff-f++f+f+f-ff+fff } ADH332a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f++f f=f+ff+f+f++ff-f++f+f+f-ff+fff } ADH333 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff+f+f++ff++f+f-ff+fff } ADH333a { ; Anthony Hanmer 2000 Angle 4 ; Axiom +f++f f=f+ff+f+f++ff++f+f-ff+fff } ADH334 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff++f---f++++f+++f--ff++ff } ADH334a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff++f---f++++f+++f--ff++ff } ADH335 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff++f---f---f++++f+++f+++f--ff++ff } ADH335a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff++f---f---f++++f+++f+++f--ff++ff } ADH336 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff++f---ff---f++++f+++ff+++f--ff++fff } ADH336a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff++f---ff---f++++f+++ff+++f--ff++fff } ADH337 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f++f---ff---f++++f+++ff+++f--f++ff } ADH338 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f++f---ff--f++++f++ff+++f--f++ff } ADH338a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++f++f---ff--f++++f++ff+++f--f++ff } ADH339 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++f++f---ff-f++++f+ff+++f--f++ff } ADH339a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++f++f---ff-f++++f+ff+++f--f++ff } ADH340 { ; Anthony Hanmer 2000 Angle 12 ; Axiom f f=f+++f++f++++++f++f++++++f++f+++ff } ADH340a { ; Anthony Hanmer 2000 Angle 12 ; Axiom +f++++++f f=f+++f++f++++++f++f++++++f++f+++ff } ADH341 { ; Anthony Hanmer 2000 Angle 12 ; Axiom f f=f+++f++f++++++f+f++++++f+++f+++ff } ADH341a { ; Anthony Hanmer 2000 Angle 12 ; Axiom +f++++++f f=f+++f++f++++++f+f++++++f+++f+++ff } ADH342 { ; Anthony Hanmer 2000 Angle 12 ; Axiom f f=f+++f++f++++++f+@.8f++++++f+++@1.25f+++ff } ADH342a { ; Anthony Hanmer 2000 Angle 12 ; Axiom +f++++++f f=f+++f++f++++++f+@.8f++++++f+++@1.25f+++ff } ADH343 { ; Anthony Hanmer 2000 Angle 12 ; Axiom f f=f+++f++f++++++ff++++++f++++f+++ff } ADH343a { ; Anthony Hanmer 2000 Angle 12 ; Axiom +f++++++f f=f+++f++f++++++ff++++++f++++f+++ff } ADH344 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=f++f++f+++f--f+f } ADH345 { ; Anthony Hanmer 2000 Angle 6 ; Axiom f f=f++f++@.8f+++f--@1.25f+f } ADH346 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+f+f+f-f-f++++f+f+f-f-f+++ff } ADH346a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+f+f+f-f-f++++f+f+f-f-f+++ff } ADH347 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=ff+f+f+f-f-f++++f+f+f-f-f+++ff } ADH347a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=ff+f+f+f-f-f++++f+f+f-f-f+++ff } ADH348 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+f+f+f+f-f-f-f++++f+f+f+f-f-f-f+++fff } ADH348a { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++++f f=f+f+f+f+f-f-f-f++++f+f+f+f-f-f-f+++fff } ADH351 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+f+f-f++f+f-f+ff } ADH351a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f++f f=f+f+f-f++f+f-f+ff } ADH352 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=ff+f+f-f++f+f-f+ff } ADH352a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f++f f=ff+f+f-f++f+f-f+ff } ADH353 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff+f-f++f+f-ff+ff } ADH353a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f++f f=f+ff+f-f++f+f-ff+ff } ADH354 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+f+f-f-f++f+f+f-f+ff } ADH354a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f++f f=f+f+f-f-f++f+f+f-f+ff } ADH355 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff+f++f+f++f+ff++ff+ff+fff } ADH355a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f++f f=f+ff+f++f+f++f+ff++ff+ff+fff } ADH356 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff+f++f+f++f+ff++ff+ff+ff } ADH357 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=ff+ff+f++f+f++f+ff++ff+ff+ff } ADH357a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f++f f=ff+ff+f++f+f++f+ff++ff+ff+ff } ADH359 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+f++ff--f--f--ff++f+ff } ADH359a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+f++ff--f--f--ff++f+ff } ADH360 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=ff+f++ff--f--f--ff++f+ff } ADH361 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=ff+ff+ff+f+f+f++f-f-f-ff-ff+ff } ADH361a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f++f f=ff+ff+ff+f+f+f++f-f-f-ff-ff+ff } ADH362 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=ff+ff+ff+f+f++f-f-ff-ff+ff } ADH362a { ; Anthony Hanmer 2000 Angle 4 ; Axiom f++f f=ff+ff+ff+f+f++f-f-ff-ff+ff } ADH363 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff+ff+f+f++f-f-ff-ff+ff } ADH364 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f+ff++f++f++++f--f--ff+++ff } ADH364a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f+ff++f++f++++f--f--ff+++ff } ADH365 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff+++ff++++ff--f++++f+++ff++ff } ADH365a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff+++ff++++ff--f++++f+++ff++ff } ADH366 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff+++ff++++ff--ff++++ff+++ff++ff } ADH366a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff+++ff++++ff--ff++++ff+++ff++ff } ADH367 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff+++f++++f--f++++f+++ff++ff } ADH367a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff+++f++++f--f++++f+++ff++ff } ADH368 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff+++f++++f--ff++++ff+++ff++ff } ADH368a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++ff+++f++++f--ff++++ff+++ff++ff } ADH369 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++fff+++f++++f--f++++f+++fff++ff } ADH369a { ; Anthony Hanmer 2000 Angle 8 ; Axiom +f++++f f=f++fff+++f++++f--f++++f+++fff++ff } ADH370 { ; Anthony Hanmer 2000 Angle 8 ; Axiom f f=f++ff++f-f++++f+ff-f++++f+f++ff++ff } ADH370a { ; Anthony Hanmer 2000 Angle 8 ; Axiom f++++f f=f++ff++f-f++++f+ff-f++++f+f++ff++ff } ADH371 { ; Anthony Hanmer 2000 Angle 8 ; Axiom d d=d\80d\20d/180d/20d\100dd } ADH371a { ; Anthony Hanmer 2000 Angle 8 ; Axiom \30d\180d d=d\80d\20d/180d/20d\100dd } ADH372 { ; Anthony Hanmer 2000 Angle 8 ; Axiom d d=d\30dd\90d/180d/90dd\150dd } ADH372a { ; Anthony Hanmer 2000 Angle 8 ; Axiom d\180d d=d\30dd\90d/180d/90dd\150dd } ADH373 { ; Anthony Hanmer 2000 Angle 8 ; Axiom /30d\180d d=d\30dd\90dd/180dd/90dd\150dd } ADH373a { ; Anthony Hanmer 2000 Angle 8 ; Axiom /30d\180d d=d\30dd\90dd/180dd/90dd\150dd } ADH374 { ; Anthony Hanmer 2000 Angle 8 ; Axiom d d=d\50dd\90dd/180dd/90dd\130dd } ADH374a { ; Anthony Hanmer 2000 Angle 8 ; Axiom \30d\180d d=d\50dd\90dd/180dd/90dd\130dd } ADH375 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+fff-f-f+f+f++f-f-f+f+fff+ff } ADH376 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff-f-f+f+f++f-f-f+f+ff+fff } ADH376a { ; Anthony Hanmer 2000 Angle 4 ; Axiom +f++f f=f+ff-f-f+f+f++f-f-f+f+ff+fff } ADH377 { ; Anthony Hanmer 2000 Angle 4 ; Axiom f f=f+ff-f-f+f+ff++ff-f-f+f+ff+fff } ADH377a { ; Anthony Hanmer 2000 Angle 4 ; Axiom +f++f f=f+ff-f-f+f+ff++ff-f-f+f+ff+fff } ADH378 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+@q2f+++@iq2f++f++f } ADH378a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f+@q2f+++@iq2f++f++f } ADH379 { ; Anthony Hanmer 2000 Angle 5 Axiom f f=+f--f--f--f--f++ff } ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Tony \(Anthony\) Hanmer" Subject: (fractint) Time for some more L-Systems, 2 Date: 04 Apr 2000 11:19:33 GEST Add these to the previous posting and call it all horizons.l Tony Hanmer ADH380 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+f-f++f+f+ff } ADH380a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+f-f++f+f+ff } ADH381 { ; Anthony Hanmer 2000 Angle 4 Axiom ++f f=+f+f++ff++f+f+ff } ADH382 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=+f++f++f+ff } ADH382a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=+f++f++f+ff } ADH382b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=+f++f++f+ff } ADH382c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=+f++f++f+ff } ADH382d { ; Anthony Hanmer 2000 Angle 6 Axiom f--f--f f=+f++f++f+ff } ADH383 { ; Anthony Hanmer 2000 Angle 12 Axiom f f=+++ff++f++++++f++f++++++f++ff+++fff } ADH383a { ; Anthony Hanmer 2000 Angle 12 Axiom +f++++++f f=+++ff++f++++++f++f++++++f++ff+++fff } ADH384 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++@q2f+++@iq2f++f+f } ADH384a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f++@q2f+++@iq2f++f+f } ADH385 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++@q2f+++@iq2f++f+ff } ADH386 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++@q2f+++@iq2f++f++++f--f---@q2f++@iq2ff } ADH386a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++@q2f+++@iq2f++f++++f--f---@q2f++@iq2ff } ADH387 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=+f+f++f+f+ff } ADH388 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f+ff++f++@.8f+++f--@1.25f--ff++ff } ADH388a { ; Anthony Hanmer 2000 Angle 6 Axiom f+f+f+f+f+f f=f+ff++f++@.8f+++f--@1.25f--ff++ff } ADH389 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f+ff++f++@.8f+++f@1.25f+++f+f--ff++ff } ADH389a { ; Anthony Hanmer 2000 Angle 6 Axiom +f+++f f=f+ff++f++@.8f+++f@1.25f+++f+f--ff++ff } ADH390 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff-f+ } ADH391 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f--ff+f } ADH392 { ; Anthony Hanmer 2000 Angle 3 Axiom f f=f+ff+f-ff+f } ADH395 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f+f++f+f++f+ff+fff } ADH395a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f++f+f++f+f++f+ff+fff } ADH396 { ; Anthony Hanmer 2000 Angle 16 Axiom f f=+++f++f++++++++f--f+++++ff } ADH396a { ; Anthony Hanmer 2000 Angle 16 Axiom ++f++++++++f f=+++f++f++++++++f--f+++++ff } ADH397 { ; Anthony Hanmer 2000 Angle 16 Axiom f f=+++f++f++++++++f--f+++++fff } ADH397a { ; Anthony Hanmer 2000 Angle 16 Axiom ++f++++++++f f=+++f++f++++++++f--f+++++fff } ADH397b { ; Anthony Hanmer 2000 Angle 16 Axiom f++++f++++f++++f++++++++f----f----f----f f=+++f++f++++++++f--f+++++fff } ADH397c { ; Anthony Hanmer 2000 Angle 16 Axiom c09f++c12f++c09f++c12f++c09f++c12f++c09f++c12f++++++++c09f--c12f--c09f--c12f--c09f--c12f--c09f--c12f f=+++f++f++++++++f--f+++++fff } ADH398 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff-ff++ff+ff+ff+f+f++f-f+ff } ADH398a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff-ff++ff+ff+ff+f+f++f-f+ff } ADH399 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff-ff++ff+ff+ff+f+f++f-f+f } ADH399a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff-ff++ff+ff+ff+f+f++f-f+f } ADH400 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff-ff++ff+ff+ff+f+f++f-f+ff } ADH400a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+ff-ff++ff+ff+ff+f+f++f-f+ff } ADH401 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+f++++f+++f+++f++++f+f } ADH401a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+f++++f+++f+++f++++f+f } ADH402 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++ff+++f+++f++++f+f } ADH402a { ; Anthony Hanmer 2000 Angle 8 Axiom -f++++f f=f+ff++++ff+++f+++f++++f+f } ADH403 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++ff+++f+++ff++++ff+f } ADH403a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f+ff++++ff+++f+++ff++++ff+f } ADH404 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+f++++f+++f+++ff++++ff+f } ADH404a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+f++++f+++f+++ff++++ff+f } ADH405 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff++++ff+++f+++f++++f+ff } ADH405a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+ff++++ff+++f+++f++++f+ff } ADH406 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff++++ff+++f+++ff++++ff+ff } ADH406a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+ff++++ff+++f+++ff++++ff+ff } ADH407 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+f++++f+++f+++ff++++ff+ff } ADH407a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+f++++f+++f+++ff++++ff+ff } ADH408 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+fff++++fff+++f+++ff++++ff+ff } ADH408a { ; Anthony Hanmer 2000 Angle 8 Axiom -f++++f f=f+fff++++fff+++f+++ff++++ff+ff } ADH409 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++ff+++f+++fff++++fff+ff } ADH409a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+ff++++ff+++f+++fff++++fff+ff } ADH410 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+fff++++fff+++f+++fff++++fff+ff } ADH410a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+fff++++fff+++f+++fff++++fff+ff } ADH411 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff++++ff+++f+++fff++++fff+ff } ADH411a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+ff++++ff+++f+++fff++++fff+ff } ADH412 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f-f-f++f+f+f+fff } ADH412a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+f-f-f++f+f+f+fff } ADH413 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f++f-f+f++f+f+ff } ADH413a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f++f-f+f++f+f+ff } ADH414 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f-f+f++f+f+fff } ADH414a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff+f++f-f+f++f+f+fff } ADH415 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f++f-f+f++f+f+fff } ADH415a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+ff+f++f-f+f++f+f+fff } ADH416 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f++f+f+ff } ADH416a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff++f+f++f+f+ff } ADH417 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f++f+f+fff } ADH417a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff++f+f++f+f+fff } ADH418 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+fff++f+f++f+ff+fff } ADH418a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+fff++f+f++f+ff+fff } ADH419 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff---f++++f+++f+++ff } ADH419a { ; Anthony Hanmer 2000 Angle 8 Axiom f++f++f++f f=+ff---f++++f+++f+++ff } ADH419b { ; Anthony Hanmer 2000 Angle 8 Axiom f--f--f--f f=+ff---f++++f+++f+++ff } ADH419c { ; Anthony Hanmer 2000 Angle 8 Axiom f++f++f++f++++f--f--f--f f=+ff---f++++f+++f+++ff } ADH420 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff---ff++++ff+++ff+++fff } ADH420a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+ff---ff++++ff+++ff+++fff } ADH421 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f+f++ff++f+f+f+fff } ADH421a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff++f+f+f++ff++f+f+f+fff } ADH422 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff++f+f+f++ff++f+f+f+ffff } ADH422a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+ff++f+f+f++ff++f+f+f+ffff } ADH423 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f+f++ff++f+f+f+ffff } ADH423a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff++f+f+f++ff++f+f+f+ffff } ADH424 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f+f++fff++ff+f+f+ffff } ADH424a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff++f+f+f++fff++ff+f+f+ffff } ADH425 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff++f+f+f++fff++ff+f+f+ffff } ADH425a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+ff++f+f+f++fff++ff+f+f+ffff } ADH426 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+fff++ff+f+f++ff++f+f+f+fff } ADH426a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+fff++ff+f+f++ff++f+f+f+fff } ADH427 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f+ff++fff++f+f+f+fff } ADH427a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff++f+f+ff++fff++f+f+f+fff } ADH428 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff++ff+f+f++ff++f+f+f+fff } ADH428a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff++ff+f+f++ff++f+f+f+fff } ADH429 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff++f+f+ff++fff++f+f+f+fff } ADH429a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff++f+f+ff++fff++f+f+f+fff } ADH430 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f-f+f+f++ff++f+f+f+ffff } ADH430a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff+f++f-f+f+f++ff++f+f+f+ffff } ADH431 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f-f+f+ff++fff++f+f+f+ffff } ADH431a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f++f-f+f+ff++fff++f+f+f+ffff } ADH432 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f-f+f+f++ff++f+f+f+fff } ADH432a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff+f++f-f+f+f++ff++f+f+f+fff } ADH433 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f-f+f+ff++fff++f+f+f+fff } ADH433a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f++f-f+f+ff++fff++f+f+f+fff } ADH434 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff++ff+f+ff++fff++f+f+f+fff } ADH434a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff++ff+f+ff++fff++f+f+f+fff } ADH435 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+fff++ff+f+ff++fff++f+f+f+ffff } ADH435a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+fff++ff+f+ff++fff++f+f+f+ffff } ADH436 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff+f++f-ff+f+ff++fff++f+f+f+fff } ADH436a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff+f++f-ff+f+ff++fff++f+f+f+fff } ADH437 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff++ff+f+ff++fff++f+f+f+ffff } ADH437a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff++ff+f+ff++fff++f+f+f+ffff } ADH438 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff+f++f-ff+f+ff++fff++f+f+f+ffff } ADH438a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff+f++f-ff+f+ff++fff++f+f+f+ffff } ADH439 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f---f+++f++++f---f+++f++ff } ADH439a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=f++f---f+++f++++f---f+++f++ff } ADH440 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++f---f+++f++++f---f+++f++ff } ADH440a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=++f---f+++f++++f---f+++f++ff } ADH441 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f---f+++ff++++ff---f+++f++fff } ADH441a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++f---f+++ff++++ff---f+++f++fff } ADH442 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++f---f+++f++++f---f+++f++fff } ADH442a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=++f---f+++f++++f---f+++f++fff } ADH443 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++f-f++++f---f+++ff } ADH443a { ; Anthony Hanmer 2000 Angle 8 Axiom -f++++f f=f+ff++++f-f++++f---f+++ff } ADH444 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++f-ff++++ff---f+++fff } ADH444a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=f+ff++++f-ff++++ff---f+++fff } ADH445 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff++++f-ff++++ff---f+++ff } ADH445a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=+ff++++f-ff++++ff---f+++ff } ADH446 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++f-ff++++ff---f+++fff } ADH446a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=f+ff++++f-ff++++ff---f+++fff } ADH447 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++f--f++++f--f+++ff } ADH447a { ; Anthony Hanmer 2000 Angle 8 Axiom -f++++f f=f+ff++++f--f++++f--f+++ff } ADH448 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++f--ff++++ff--f+++fff } ADH448a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+ff++++f--ff++++ff--f+++fff } ADH449 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff++++f--f++++f--f+++fff } ADH449a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+ff++++f--f++++f--f+++fff } ADH450 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+f+f++f+f+f++f-f+f+f++ff++f+f+f+fff } ADH450a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+f+f++f+f+f++f-f+f+f++ff++f+f+f+fff } ADH451 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+f++f+f+f++f-f+f+f++ff++f+f+f+fff } ADH451a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+f+f++f+f+f++f-f+f+f++ff++f+f+f+fff } ADH452 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+f+f++f+f+f++f-f+f+ff++fff++f+f+f+fff } ADH452a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+f+f++f+f+f++f-f+f+ff++fff++f+f+f+fff } ADH453 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+f++f+f+f++f-f+f+ff++fff++f+f+f+fff } ADH453a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+f+f++f+f+f++f-f+f+ff++fff++f+f+f+fff } ADH454 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f+f++ff++f+ff+f++ff++f+f+ff+fff } ADH454a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f+f++ff++f+ff+f++ff++f+f+ff+fff } ADH455 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++ff++f+ff+f++ff++f+f+ff+fff } ADH455a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++ff++f+ff+f++ff++f+f+ff+fff } ADH456 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++fff++ff+ff+f++ff++f+f+ff+fff } ADH456a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++fff++ff+ff+f++ff++f+f+ff+fff } ADH457 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f+f++fff++ff+ff+f++ff++f+f+ff+fff } ADH457a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f+f++fff++ff+ff+f++ff++f+f+ff+fff } ADH458 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++fff++ff+ff+f++ff++f+f+ff+ffff } ADH458a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++fff++ff+ff+f++ff++f+f+ff+ffff } ADH459 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++ff++f+ff+ff++fff++f+f+ff+fff } ADH459a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++ff++f+ff+ff++fff++f+f+ff+fff } ADH460 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f+f++ff++f+ff+ff++fff++f+f+ff+ffff } ADH460a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f+f++ff++f+ff+ff++fff++f+f+ff+ffff } ADH461 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++fff++ff+ff+ff++fff++f+f+ff+ffff } ADH461a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++fff++ff+ff+ff++fff++f+f+ff+ffff } ADH462 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+f--f--f--f+f++ff } ADH462a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f++f+f--f--f--f+f++ff } ADH463 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++f+f--f--f--f+f++ff } ADH463a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=++f+f--f--f--f+f++ff } ADH464 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+f--f--f--f+f++fff } ADH464a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f++f+f--f--f--f+f++fff } ADH465 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f+f+f+++f+f+f+++f+f+++f+f+f++ffff } ADH465a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=f+f+f+++f+f+f+++f+f+++f+f+f++ffff } ADH466 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=+f+f+++f+f+f+++f+f+++f+f+f++fff } ADH466a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=+f+f+++f+f+f+++f+f+++f+f+f++fff } ADH467 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=+f+f+++f+f+f+++f+f+++f+f+f++ffff } ADH467a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=+f+f+++f+f+f+++f+f+++f+f+f++ffff } ADH468 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+++f--ff++f+++@q2ff++@iq2ff } ADH468a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+++f--ff++f+++@q2ff++@iq2ff } ADH469 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+++f--ff++f+++@q2ff++@iq2fff } ADH469a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+++f--ff++f+++@q2ff++@iq2fff } ADH470 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+++f--ff++++ff+++f+f++++f++f++++f+f+++f+fff } ADH470a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+++f--ff++++ff+++f+f++++f++f++++f+f+++f+fff } ADH471 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+++f--ff++++ff+++f+f++++f++f++++f+f+++f+fff } ADH471a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+++f--ff++++ff+++f+f++++f++f++++f+f+++f+fff } ADH472 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f++ff--f+++f++ff+ff } ADH472a { ; Anthony Hanmer 2000 Angle 6 Axiom +f+++f f=f++ff--f+++f++ff+ff } ADH473 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f+f+f+++f+f+++f+f++fff } ADH473a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=f+f+f+++f+f+++f+f++fff } ADH474 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=+f+f+++f+f+++f+f++fff } ADH474a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=+f+f+++f+f+++f+f++fff } ADH475 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f+f+f+++f+f+++f+f++ff } ADH475a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=f+f+f+++f+f+++f+f++ff } ADH476 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f+f+ff+++ff+f+++f+f++ff } ADH476a { ; Anthony Hanmer 2000 Angle 6 Axiom +f+++f f=f+f+ff+++ff+f+++f+f++ff } ADH477 { ; Anthony Hanmer 2000 Angle 12 Axiom f f=+++f++f++++++f++f++++++f++f+++fff } ADH477a { ; Anthony Hanmer 2000 Angle 12 Axiom f++++++f f=+++f++f++++++f++f++++++f++f+++fff } ADH478 { ; Anthony Hanmer 2000 Angle 12 Axiom f f=f+++f++f++++++f++f++++++f++f+++ff } ADH478a { ; Anthony Hanmer 2000 Angle 12 Axiom +f++++++f f=f+++f++f++++++f++f++++++f++f+++ff } ADH479 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f++f+f+++f+f+++f+f+ff } ADH479a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=f++f+f+++f+f+++f+f+ff } ADH480 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=++f+f+++f+f+++f+f+ff } ADH481 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=ff+ff+ff+++ff+ff+++ff+ff++ffff } ADH481a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=ff+ff+ff+++ff+ff+++ff+ff++ffff } ADH482 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=++ff+ff+++ff+ff+++ff+ff+ffff } ADH482a { ; Anthony Hanmer 2000 Angle 6 Axiom +f+++f f=++ff+ff+++ff+ff+++ff+ff+ffff } ADH483 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=ff+ff+ff+++ff+ff+++ff+ff++fff } ADH483a { ; Anthony Hanmer 2000 Angle 6 Axiom +f+++f f=ff+ff+ff+++ff+ff+++ff+ff++fff } ADH484 { ; Anthony Hanmer 2000 Angle 6 Axiom d d=d\60d\58d/178d\58d/178d\60d\120dd } ADH484a { ; Anthony Hanmer 2000 Angle 6 Axiom \60d/180d d=d\60d\58d/178d\58d/178d\60d\120dd } ADH485 { ; Anthony Hanmer 2000 Angle 6 Axiom d d=d\60d\58@.5d/178d\58@2sd/178d\60d\120dd } ADH485a { ; Anthony Hanmer 2000 Angle 6 Axiom d/180d d=d\60d\58@.5d/178d\58@2sd/178d\60d\120dd } ADH486 { ; Anthony Hanmer 2000 Angle 6 Axiom d d=d\60@.5d\58@2d/178d\58d/178d\60@.5d\120@2dd } ADH486a { ; Anthony Hanmer 2000 Angle 6 Axiom d/180d d=d\60@.5d\58@2d/178d\58d/178d\60@.5d\120@2dd } ADH487 { ; Anthony Hanmer 2000 Angle 6 Axiom d d=d\60d\58d/178d\58@.5d/178d\60@2d\120dd } ADH487a { ; Anthony Hanmer 2000 Angle 6 Axiom \60d/180d d=d\60d\58d/178d\58@.5d/178d\60@2d\120dd } ADH488 { ; Anthony Hanmer 2000 Angle 6 Axiom d d=d\60d\58@.5d/178d\58d/178d\60@2d\120dd } ADH488a { ; Anthony Hanmer 2000 Angle 6 Axiom \60d/180d d=d\60d\58@.5d/178d\58d/178d\60@2d\120dd } ADH490 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+ff++ff+f++ff+ff } ADH490a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+f+ff++ff+f++ff+ff } ADH491 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f++f+f++fff+ff } ADH491a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f++f+f++fff+ff } ADH492 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+f++f+ff++fff+ff } ADH492a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+f+f++f+ff++fff+ff } ADH493 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+ff++ff+f++fff+ff } ADH493a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+ff++ff+f++fff+ff } ADH495 { ; Anthony Hanmer 2000 Angle 10 Axiom f f=f++f+f+++++f+f+++++f+f+++++f+f+++++f+f+++ff } ADH495a { ; Anthony Hanmer 2000 Angle 10 Axiom ++f+++++f f=f++f+f+++++f+f+++++f+f+++++f+f+++++f+f+++ff } ADH496 { ; Anthony Hanmer 2000 Angle 20 Axiom f f=f+++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++f+++++ff } ADH496a { ; Anthony Hanmer 2000 Angle 20 Axiom +++++f++++++++++f f=f+++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++f+++++ff } ADH497 { ; Anthony Hanmer 2000 Angle 20 Axiom f f=+++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++f+++++fff } ADH497a { ; Anthony Hanmer 2000 Angle 20 Axiom +++++f++++++++++f f=+++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++f+++++fff } ADH498 { ; Anthony Hanmer 2000 Angle 20 Axiom f f=f+++++ff++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++ff+++++fff } ADH498a { ; Anthony Hanmer 2000 Angle 20 Axiom +++++f++++++++++f f=f+++++ff++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++ff+++++fff } ADH499 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f+@.5f+@2f+++f+f+++f+@.5f++@2ff } ADH499a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=f+@.5f+@2f+++f+f+++f+@.5f++@2ff } ADH499b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f+@.5f+@2f+++f+f+++f+@.5f++@2ff } ADH499c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f+@.5f+@2f+++f+f+++f+@.5f++@2ff } ADH500 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f+f+@.5f+++f+@2f+++f+f++ff } ADH500a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=f+f+@.5f+++f+@2f+++f+f++ff } ADH500b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f+f+@.5f+++f+@2f+++f+f++ff } ADH500c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f+f+@.5f+++f+@2f+++f+f++ff } ADH501 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f+f+f+++f+@.5f+++f+@2f++ff } ADH501a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=f+f+f+++f+@.5f+++f+@2f++ff } ADH501b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f+f+f+++f+@.5f+++f+@2f++ff } ADH501c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f+f+f+++f+@.5f+++f+@2f++ff } ADH502 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f+f+@.5f+++f+f+++f+@2f++ff } ADH502a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=f+f+@.5f+++f+f+++f+@2f++ff } ADH502b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f+f+@.5f+++f+f+++f+@2f++ff } ADH502c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f+f+@.5f+++f+f+++f+@2f++ff } ADH503 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f++f+@.5f+++f+@2f+++f+f+ff } ADH503a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=f++f+@.5f+++f+@2f+++f+f+ff } ADH503b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f++f+@.5f+++f+@2f+++f+f+ff } ADH503c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f++f+@.5f+++f+@2f+++f+f+ff } ADH504 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f++f+f+++f+@.5f+++f+@2f+ff } ADH504a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=f++f+f+++f+@.5f+++f+@2f+ff } ADH504b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f++f+f+++f+@.5f+++f+@2f+ff } ADH504c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f++f+f+++f+@.5f+++f+@2f+ff } ADH505 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f++f+@.5f+++f+f+++f+@2f+ff } ADH505a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=f++f+@.5f+++f+f+++f+@2f+ff } ADH505b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f++f+@.5f+++f+f+++f+@2f+ff } ADH505c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f++f+@.5f+++f+f+++f+@2f+ff } ADH506 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=++f+@.5f+++f+@2f+++f+f+ff } ADH506a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=++f+@.5f+++f+@2f+++f+f+ff } ADH506b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=++f+@.5f+++f+@2f+++f+f+ff } ADH506c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=++f+@.5f+++f+@2f+++f+f+ff } ADH507 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=++f+f+++f+@.5f+++f+@2f+ff } ADH507a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=++f+f+++f+@.5f+++f+@2f+ff } ADH507b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=++f+f+++f+@.5f+++f+@2f+ff } ADH507c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=++f+f+++f+@.5f+++f+@2f+ff } ADH508 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=++f+@.5f+++f+f+++f+@2f+ff } ADH508a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=++f+@.5f+++f+f+++f+@2f+ff } ADH508b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=++f+@.5f+++f+f+++f+@2f+ff } ADH508c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=++f+@.5f+++f+f+++f+@2f+ff } ADH509 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+f++@.5f+@2f++f+f+f++f+@.5f++@2f+f+ff } ADH509a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+f+f++@.5f+@2f++f+f+f++f+@.5f++@2f+f+ff } ADH510 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+f+f++@.5f+@2f++f+f+f++f+@.5f++@2f+f+fff } ADH510a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+f+f++@.5f+@2f++f+f+f++f+@.5f++@2f+f+fff } ADH511 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++f-ff-f++f+f+ff+fff } ADH511a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++f-ff-f++f+f+ff+fff } ADH512 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++ff---f+++f---f++++f+++f---f+++ff++ff } ADH512a { ; Anthony Hanmer 2000 Angle 8 Axiom -f++++f f=f++ff---f+++f---f++++f+++f---f+++ff++ff } ADH513 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f---f++f---f++++f+++f--f+++f++ff } ADH513a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=f++f---f++f---f++++f+++f--f+++f++ff } ADH514 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++f---f++f---f++++f+++f--f+++f++fff } ADH514a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=++f---f++f---f++++f+++f--f+++f++fff } ADH515 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++f---f+++f---f++++f+++f---f+++f++fff } ADH515a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=++f---f+++f---f++++f+++f---f+++f++fff } ADH516 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++ff+++f+++ff++++ff---f---ff++ff } ADH516a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f++ff+++f+++ff++++ff---f---ff++ff } ADH517 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+++f+++ff++++ff---f---f++ff } ADH517a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++f+++f+++ff++++ff---f---f++ff } ADH518 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+++f+++f++++f---f---f++ff } ADH518a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++f+++f+++f++++f---f---f++ff } ADH519 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f+ff-f++f+ff-f-f-ff+ff } ADH519a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f+ff-f++f+ff-f-f-ff+ff } ADH520 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=ff+ff+f+f+ff-f++f+ff-f-f-ff+fff } ADH520a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=ff+ff+f+f+ff-f++f+ff-f-f-ff+fff } ADH521 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff+f+f+ff-f++f+ff-f-f-fff+ff } ADH521a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff+f+f+ff-f++f+ff-f-f-fff+ff } ADH522 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f+f+ff-f++f+ff-f-f-ff+fff } ADH522a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f+f+ff-f++f+ff-f-f-ff+fff } ADH523 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=ff+fff+f+f+ff-f++f+ff-f-f-fff+fff } ADH523a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=ff+fff+f+f+ff-f++f+ff-f-f-fff+fff } ADH524 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f+ff++ff-f-f-ff+ff } ADH524a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f+ff++ff-f-f-ff+ff } ADH525 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff+f+f+ff++ff-f-f-fff+fff } ADH525a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff+f+f+ff++ff-f-f-fff+fff } ADH526 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f+f+ff++ff-f-f-ff+fff } ADH526a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff+f+f+ff++ff-f-f-ff+fff } ADH527 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff-f-f-ff++ff+f+f+fff+fff } ADH527a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff-f-f-ff++ff+f+f+fff+fff } ADH528 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+@.5f-@2f-f-f-@.5f+@2f++f-@.5f+@2f+f+f+@.5f-@2f+ff } ADH528a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+f+@.5f-@2f-f-f-@.5f+@2f++f-@.5f+@2f+f+f+@.5f-@2f+ff } ADH529 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+@.5f+f-@2f-f-f-@.5f+@2f++f-@.5f+@2f+f+f+@.5f-f+@2ff } ADH529a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+@.5f+f-@2f-f-f-@.5f+@2f++f-@.5f+@2f+f+f+@.5f-f+@2ff } ADH530 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+@.5f+f-@2f-f-f-@.5f+f++f-f+@2f+f+f+@.5f-f+@2ff } ADH530a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+@.5f+f-@2f-f-f-@.5f+f++f-f+@2f+f+f+@.5f-f+@2ff } ADH531 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++@.5f+f+f---f+f---f+f---f+f++++f-f+++f-f+++f-f+++f-f-f++@2ff } ADH531a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++@.5f+f+f---f+f---f+f---f+f++++f-f+++f-f+++f-f+++f-f-f++@2ff } ADH533 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+f++++f+++f-f++++f---f++++f+++f++++f+f---f++++f-f++ff } ADH533a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++f+f++++f+++f-f++++f---f++++f+++f++++f+f---f++++f-f++ff } ADH534 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+f++++f+++f-f++++f---f++++f+++f++++f+f---f++++f-f++fff } ADH534a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f++f+f++++f+++f-f++++f---f++++f+++f++++f+f---f++++f-f++fff } ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Tony \(Anthony\) Hanmer" Subject: (fractint) Time for some more L-Systems, 2 Date: 04 Apr 2000 11:22:05 GEST Add these to the previous posting and call it all horizons.l Tony Hanmer ADH380 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+f-f++f+f+ff } ADH380a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+f-f++f+f+ff } ADH381 { ; Anthony Hanmer 2000 Angle 4 Axiom ++f f=+f+f++ff++f+f+ff } ADH382 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=+f++f++f+ff } ADH382a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=+f++f++f+ff } ADH382b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=+f++f++f+ff } ADH382c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=+f++f++f+ff } ADH382d { ; Anthony Hanmer 2000 Angle 6 Axiom f--f--f f=+f++f++f+ff } ADH383 { ; Anthony Hanmer 2000 Angle 12 Axiom f f=+++ff++f++++++f++f++++++f++ff+++fff } ADH383a { ; Anthony Hanmer 2000 Angle 12 Axiom +f++++++f f=+++ff++f++++++f++f++++++f++ff+++fff } ADH384 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++@q2f+++@iq2f++f+f } ADH384a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f++@q2f+++@iq2f++f+f } ADH385 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++@q2f+++@iq2f++f+ff } ADH386 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++@q2f+++@iq2f++f++++f--f---@q2f++@iq2ff } ADH386a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++@q2f+++@iq2f++f++++f--f---@q2f++@iq2ff } ADH387 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=+f+f++f+f+ff } ADH388 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f+ff++f++@.8f+++f--@1.25f--ff++ff } ADH388a { ; Anthony Hanmer 2000 Angle 6 Axiom f+f+f+f+f+f f=f+ff++f++@.8f+++f--@1.25f--ff++ff } ADH389 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f+ff++f++@.8f+++f@1.25f+++f+f--ff++ff } ADH389a { ; Anthony Hanmer 2000 Angle 6 Axiom +f+++f f=f+ff++f++@.8f+++f@1.25f+++f+f--ff++ff } ADH390 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff-f+ } ADH391 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f--ff+f } ADH392 { ; Anthony Hanmer 2000 Angle 3 Axiom f f=f+ff+f-ff+f } ADH395 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f+f++f+f++f+ff+fff } ADH395a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f++f+f++f+f++f+ff+fff } ADH396 { ; Anthony Hanmer 2000 Angle 16 Axiom f f=+++f++f++++++++f--f+++++ff } ADH396a { ; Anthony Hanmer 2000 Angle 16 Axiom ++f++++++++f f=+++f++f++++++++f--f+++++ff } ADH397 { ; Anthony Hanmer 2000 Angle 16 Axiom f f=+++f++f++++++++f--f+++++fff } ADH397a { ; Anthony Hanmer 2000 Angle 16 Axiom ++f++++++++f f=+++f++f++++++++f--f+++++fff } ADH397b { ; Anthony Hanmer 2000 Angle 16 Axiom f++++f++++f++++f++++++++f----f----f----f f=+++f++f++++++++f--f+++++fff } ADH397c { ; Anthony Hanmer 2000 Angle 16 Axiom c09f++c12f++c09f++c12f++c09f++c12f++c09f++c12f++++++++c09f--c12f--c09f--c12f--c09f--c12f--c09f--c12f f=+++f++f++++++++f--f+++++fff } ADH398 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff-ff++ff+ff+ff+f+f++f-f+ff } ADH398a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff-ff++ff+ff+ff+f+f++f-f+ff } ADH399 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff-ff++ff+ff+ff+f+f++f-f+f } ADH399a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff-ff++ff+ff+ff+f+f++f-f+f } ADH400 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff-ff++ff+ff+ff+f+f++f-f+ff } ADH400a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+ff-ff++ff+ff+ff+f+f++f-f+ff } ADH401 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+f++++f+++f+++f++++f+f } ADH401a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+f++++f+++f+++f++++f+f } ADH402 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++ff+++f+++f++++f+f } ADH402a { ; Anthony Hanmer 2000 Angle 8 Axiom -f++++f f=f+ff++++ff+++f+++f++++f+f } ADH403 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++ff+++f+++ff++++ff+f } ADH403a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f+ff++++ff+++f+++ff++++ff+f } ADH404 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+f++++f+++f+++ff++++ff+f } ADH404a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+f++++f+++f+++ff++++ff+f } ADH405 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff++++ff+++f+++f++++f+ff } ADH405a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+ff++++ff+++f+++f++++f+ff } ADH406 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff++++ff+++f+++ff++++ff+ff } ADH406a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+ff++++ff+++f+++ff++++ff+ff } ADH407 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+f++++f+++f+++ff++++ff+ff } ADH407a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+f++++f+++f+++ff++++ff+ff } ADH408 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+fff++++fff+++f+++ff++++ff+ff } ADH408a { ; Anthony Hanmer 2000 Angle 8 Axiom -f++++f f=f+fff++++fff+++f+++ff++++ff+ff } ADH409 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++ff+++f+++fff++++fff+ff } ADH409a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+ff++++ff+++f+++fff++++fff+ff } ADH410 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+fff++++fff+++f+++fff++++fff+ff } ADH410a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+fff++++fff+++f+++fff++++fff+ff } ADH411 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff++++ff+++f+++fff++++fff+ff } ADH411a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+ff++++ff+++f+++fff++++fff+ff } ADH412 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f-f-f++f+f+f+fff } ADH412a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+f-f-f++f+f+f+fff } ADH413 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f++f-f+f++f+f+ff } ADH413a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f++f-f+f++f+f+ff } ADH414 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f-f+f++f+f+fff } ADH414a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff+f++f-f+f++f+f+fff } ADH415 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f++f-f+f++f+f+fff } ADH415a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+ff+f++f-f+f++f+f+fff } ADH416 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f++f+f+ff } ADH416a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff++f+f++f+f+ff } ADH417 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f++f+f+fff } ADH417a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff++f+f++f+f+fff } ADH418 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+fff++f+f++f+ff+fff } ADH418a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+fff++f+f++f+ff+fff } ADH419 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff---f++++f+++f+++ff } ADH419a { ; Anthony Hanmer 2000 Angle 8 Axiom f++f++f++f f=+ff---f++++f+++f+++ff } ADH419b { ; Anthony Hanmer 2000 Angle 8 Axiom f--f--f--f f=+ff---f++++f+++f+++ff } ADH419c { ; Anthony Hanmer 2000 Angle 8 Axiom f++f++f++f++++f--f--f--f f=+ff---f++++f+++f+++ff } ADH420 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff---ff++++ff+++ff+++fff } ADH420a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+ff---ff++++ff+++ff+++fff } ADH421 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f+f++ff++f+f+f+fff } ADH421a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff++f+f+f++ff++f+f+f+fff } ADH422 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff++f+f+f++ff++f+f+f+ffff } ADH422a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+ff++f+f+f++ff++f+f+f+ffff } ADH423 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f+f++ff++f+f+f+ffff } ADH423a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff++f+f+f++ff++f+f+f+ffff } ADH424 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f+f++fff++ff+f+f+ffff } ADH424a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff++f+f+f++fff++ff+f+f+ffff } ADH425 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff++f+f+f++fff++ff+f+f+ffff } ADH425a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+ff++f+f+f++fff++ff+f+f+ffff } ADH426 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+fff++ff+f+f++ff++f+f+f+fff } ADH426a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+fff++ff+f+f++ff++f+f+f+fff } ADH427 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff++f+f+ff++fff++f+f+f+fff } ADH427a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff++f+f+ff++fff++f+f+f+fff } ADH428 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff++ff+f+f++ff++f+f+f+fff } ADH428a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff++ff+f+f++ff++f+f+f+fff } ADH429 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff++f+f+ff++fff++f+f+f+fff } ADH429a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff++f+f+ff++fff++f+f+f+fff } ADH430 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f-f+f+f++ff++f+f+f+ffff } ADH430a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff+f++f-f+f+f++ff++f+f+f+ffff } ADH431 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f-f+f+ff++fff++f+f+f+ffff } ADH431a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f++f-f+f+ff++fff++f+f+f+ffff } ADH432 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f-f+f+f++ff++f+f+f+fff } ADH432a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff+f++f-f+f+f++ff++f+f+f+fff } ADH433 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f++f-f+f+ff++fff++f+f+f+fff } ADH433a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f++f-f+f+ff++fff++f+f+f+fff } ADH434 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff++ff+f+ff++fff++f+f+f+fff } ADH434a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff++ff+f+ff++fff++f+f+f+fff } ADH435 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+fff++ff+f+ff++fff++f+f+f+ffff } ADH435a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+fff++ff+f+ff++fff++f+f+f+ffff } ADH436 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff+f++f-ff+f+ff++fff++f+f+f+fff } ADH436a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff+f++f-ff+f+ff++fff++f+f+f+fff } ADH437 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff++ff+f+ff++fff++f+f+f+ffff } ADH437a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff++ff+f+ff++fff++f+f+f+ffff } ADH438 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff+f++f-ff+f+ff++fff++f+f+f+ffff } ADH438a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff+f++f-ff+f+ff++fff++f+f+f+ffff } ADH439 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f---f+++f++++f---f+++f++ff } ADH439a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=f++f---f+++f++++f---f+++f++ff } ADH440 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++f---f+++f++++f---f+++f++ff } ADH440a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=++f---f+++f++++f---f+++f++ff } ADH441 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f---f+++ff++++ff---f+++f++fff } ADH441a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++f---f+++ff++++ff---f+++f++fff } ADH442 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++f---f+++f++++f---f+++f++fff } ADH442a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=++f---f+++f++++f---f+++f++fff } ADH443 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++f-f++++f---f+++ff } ADH443a { ; Anthony Hanmer 2000 Angle 8 Axiom -f++++f f=f+ff++++f-f++++f---f+++ff } ADH444 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++f-ff++++ff---f+++fff } ADH444a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=f+ff++++f-ff++++ff---f+++fff } ADH445 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff++++f-ff++++ff---f+++ff } ADH445a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=+ff++++f-ff++++ff---f+++ff } ADH446 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++f-ff++++ff---f+++fff } ADH446a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=f+ff++++f-ff++++ff---f+++fff } ADH447 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++f--f++++f--f+++ff } ADH447a { ; Anthony Hanmer 2000 Angle 8 Axiom -f++++f f=f+ff++++f--f++++f--f+++ff } ADH448 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+ff++++f--ff++++ff--f+++fff } ADH448a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+ff++++f--ff++++ff--f+++fff } ADH449 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+ff++++f--f++++f--f+++fff } ADH449a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+ff++++f--f++++f--f+++fff } ADH450 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+f+f++f+f+f++f-f+f+f++ff++f+f+f+fff } ADH450a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+f+f++f+f+f++f-f+f+f++ff++f+f+f+fff } ADH451 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+f++f+f+f++f-f+f+f++ff++f+f+f+fff } ADH451a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+f+f++f+f+f++f-f+f+f++ff++f+f+f+fff } ADH452 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+f+f++f+f+f++f-f+f+ff++fff++f+f+f+fff } ADH452a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+f+f++f+f+f++f-f+f+ff++fff++f+f+f+fff } ADH453 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+f++f+f+f++f-f+f+ff++fff++f+f+f+fff } ADH453a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+f+f++f+f+f++f-f+f+ff++fff++f+f+f+fff } ADH454 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f+f++ff++f+ff+f++ff++f+f+ff+fff } ADH454a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f+f++ff++f+ff+f++ff++f+f+ff+fff } ADH455 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++ff++f+ff+f++ff++f+f+ff+fff } ADH455a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++ff++f+ff+f++ff++f+f+ff+fff } ADH456 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++fff++ff+ff+f++ff++f+f+ff+fff } ADH456a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++fff++ff+ff+f++ff++f+f+ff+fff } ADH457 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f+f++fff++ff+ff+f++ff++f+f+ff+fff } ADH457a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f+f++fff++ff+ff+f++ff++f+f+ff+fff } ADH458 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++fff++ff+ff+f++ff++f+f+ff+ffff } ADH458a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++fff++ff+ff+f++ff++f+f+ff+ffff } ADH459 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++ff++f+ff+ff++fff++f+f+ff+fff } ADH459a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++ff++f+ff+ff++fff++f+f+ff+fff } ADH460 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f+f++ff++f+ff+ff++fff++f+f+ff+ffff } ADH460a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f+f++ff++f+ff+ff++fff++f+f+ff+ffff } ADH461 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++fff++ff+ff+ff++fff++f+f+ff+ffff } ADH461a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++fff++ff+ff+ff++fff++f+f+ff+ffff } ADH462 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+f--f--f--f+f++ff } ADH462a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f++f+f--f--f--f+f++ff } ADH463 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++f+f--f--f--f+f++ff } ADH463a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=++f+f--f--f--f+f++ff } ADH464 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+f--f--f--f+f++fff } ADH464a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f++f+f--f--f--f+f++fff } ADH465 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f+f+f+++f+f+f+++f+f+++f+f+f++ffff } ADH465a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=f+f+f+++f+f+f+++f+f+++f+f+f++ffff } ADH466 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=+f+f+++f+f+f+++f+f+++f+f+f++fff } ADH466a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=+f+f+++f+f+f+++f+f+++f+f+f++fff } ADH467 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=+f+f+++f+f+f+++f+f+++f+f+f++ffff } ADH467a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=+f+f+++f+f+f+++f+f+++f+f+f++ffff } ADH468 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+++f--ff++f+++@q2ff++@iq2ff } ADH468a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+++f--ff++f+++@q2ff++@iq2ff } ADH469 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+++f--ff++f+++@q2ff++@iq2fff } ADH469a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+++f--ff++f+++@q2ff++@iq2fff } ADH470 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f+++f--ff++++ff+++f+f++++f++f++++f+f+++f+fff } ADH470a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f+++f--ff++++ff+++f+f++++f++f++++f+f+++f+fff } ADH471 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=+++f--ff++++ff+++f+f++++f++f++++f+f+++f+fff } ADH471a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=+++f--ff++++ff+++f+f++++f++f++++f+f+++f+fff } ADH472 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f++ff--f+++f++ff+ff } ADH472a { ; Anthony Hanmer 2000 Angle 6 Axiom +f+++f f=f++ff--f+++f++ff+ff } ADH473 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f+f+f+++f+f+++f+f++fff } ADH473a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=f+f+f+++f+f+++f+f++fff } ADH474 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=+f+f+++f+f+++f+f++fff } ADH474a { ; Anthony Hanmer 2000 Angle 6 Axiom f+++f f=+f+f+++f+f+++f+f++fff } ADH475 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f+f+f+++f+f+++f+f++ff } ADH475a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=f+f+f+++f+f+++f+f++ff } ADH476 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=f+f+ff+++ff+f+++f+f++ff } ADH476a { ; Anthony Hanmer 2000 Angle 6 Axiom +f+++f f=f+f+ff+++ff+f+++f+f++ff } ADH477 { ; Anthony Hanmer 2000 Angle 12 Axiom f f=+++f++f++++++f++f++++++f++f+++fff } ADH477a { ; Anthony Hanmer 2000 Angle 12 Axiom f++++++f f=+++f++f++++++f++f++++++f++f+++fff } ADH478 { ; Anthony Hanmer 2000 Angle 12 Axiom f f=f+++f++f++++++f++f++++++f++f+++ff } ADH478a { ; Anthony Hanmer 2000 Angle 12 Axiom +f++++++f f=f+++f++f++++++f++f++++++f++f+++ff } ADH479 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f++f+f+++f+f+++f+f+ff } ADH479a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=f++f+f+++f+f+++f+f+ff } ADH480 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=++f+f+++f+f+++f+f+ff } ADH481 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=ff+ff+ff+++ff+ff+++ff+ff++ffff } ADH481a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=ff+ff+ff+++ff+ff+++ff+ff++ffff } ADH482 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=++ff+ff+++ff+ff+++ff+ff+ffff } ADH482a { ; Anthony Hanmer 2000 Angle 6 Axiom +f+++f f=++ff+ff+++ff+ff+++ff+ff+ffff } ADH483 { ; Anthony Hanmer 2000 Angle 6 Axiom f f=ff+ff+ff+++ff+ff+++ff+ff++fff } ADH483a { ; Anthony Hanmer 2000 Angle 6 Axiom +f+++f f=ff+ff+ff+++ff+ff+++ff+ff++fff } ADH484 { ; Anthony Hanmer 2000 Angle 6 Axiom d d=d\60d\58d/178d\58d/178d\60d\120dd } ADH484a { ; Anthony Hanmer 2000 Angle 6 Axiom \60d/180d d=d\60d\58d/178d\58d/178d\60d\120dd } ADH485 { ; Anthony Hanmer 2000 Angle 6 Axiom d d=d\60d\58@.5d/178d\58@2sd/178d\60d\120dd } ADH485a { ; Anthony Hanmer 2000 Angle 6 Axiom d/180d d=d\60d\58@.5d/178d\58@2sd/178d\60d\120dd } ADH486 { ; Anthony Hanmer 2000 Angle 6 Axiom d d=d\60@.5d\58@2d/178d\58d/178d\60@.5d\120@2dd } ADH486a { ; Anthony Hanmer 2000 Angle 6 Axiom d/180d d=d\60@.5d\58@2d/178d\58d/178d\60@.5d\120@2dd } ADH487 { ; Anthony Hanmer 2000 Angle 6 Axiom d d=d\60d\58d/178d\58@.5d/178d\60@2d\120dd } ADH487a { ; Anthony Hanmer 2000 Angle 6 Axiom \60d/180d d=d\60d\58d/178d\58@.5d/178d\60@2d\120dd } ADH488 { ; Anthony Hanmer 2000 Angle 6 Axiom d d=d\60d\58@.5d/178d\58d/178d\60@2d\120dd } ADH488a { ; Anthony Hanmer 2000 Angle 6 Axiom \60d/180d d=d\60d\58@.5d/178d\58d/178d\60@2d\120dd } ADH490 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+ff++ff+f++ff+ff } ADH490a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=f+f+ff++ff+f++ff+ff } ADH491 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f++f+f++fff+ff } ADH491a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f++f+f++fff+ff } ADH492 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+f++f+ff++fff+ff } ADH492a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+f+f++f+ff++fff+ff } ADH493 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+ff++ff+f++fff+ff } ADH493a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+ff++ff+f++fff+ff } ADH495 { ; Anthony Hanmer 2000 Angle 10 Axiom f f=f++f+f+++++f+f+++++f+f+++++f+f+++++f+f+++ff } ADH495a { ; Anthony Hanmer 2000 Angle 10 Axiom ++f+++++f f=f++f+f+++++f+f+++++f+f+++++f+f+++++f+f+++ff } ADH496 { ; Anthony Hanmer 2000 Angle 20 Axiom f f=f+++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++f+++++ff } ADH496a { ; Anthony Hanmer 2000 Angle 20 Axiom +++++f++++++++++f f=f+++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++f+++++ff } ADH497 { ; Anthony Hanmer 2000 Angle 20 Axiom f f=+++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++f+++++fff } ADH497a { ; Anthony Hanmer 2000 Angle 20 Axiom +++++f++++++++++f f=+++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++f+++++fff } ADH498 { ; Anthony Hanmer 2000 Angle 20 Axiom f f=f+++++ff++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++ff+++++fff } ADH498a { ; Anthony Hanmer 2000 Angle 20 Axiom +++++f++++++++++f f=f+++++ff++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++f++++++++++f++++++++++ff+++++fff } ADH499 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f+@.5f+@2f+++f+f+++f+@.5f++@2ff } ADH499a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=f+@.5f+@2f+++f+f+++f+@.5f++@2ff } ADH499b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f+@.5f+@2f+++f+f+++f+@.5f++@2ff } ADH499c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f+@.5f+@2f+++f+f+++f+@.5f++@2ff } ADH500 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f+f+@.5f+++f+@2f+++f+f++ff } ADH500a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=f+f+@.5f+++f+@2f+++f+f++ff } ADH500b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f+f+@.5f+++f+@2f+++f+f++ff } ADH500c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f+f+@.5f+++f+@2f+++f+f++ff } ADH501 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f+f+f+++f+@.5f+++f+@2f++ff } ADH501a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=f+f+f+++f+@.5f+++f+@2f++ff } ADH501b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f+f+f+++f+@.5f+++f+@2f++ff } ADH501c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f+f+f+++f+@.5f+++f+@2f++ff } ADH502 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f+f+@.5f+++f+f+++f+@2f++ff } ADH502a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=f+f+@.5f+++f+f+++f+@2f++ff } ADH502b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f+f+@.5f+++f+f+++f+@2f++ff } ADH502c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f+f+@.5f+++f+f+++f+@2f++ff } ADH503 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f++f+@.5f+++f+@2f+++f+f+ff } ADH503a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=f++f+@.5f+++f+@2f+++f+f+ff } ADH503b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f++f+@.5f+++f+@2f+++f+f+ff } ADH503c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f++f+@.5f+++f+@2f+++f+f+ff } ADH504 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f++f+f+++f+@.5f+++f+@2f+ff } ADH504a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=f++f+f+++f+@.5f+++f+@2f+ff } ADH504b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f++f+f+++f+@.5f+++f+@2f+ff } ADH504c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f++f+f+++f+@.5f+++f+@2f+ff } ADH505 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=f++f+@.5f+++f+f+++f+@2f+ff } ADH505a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=f++f+@.5f+++f+f+++f+@2f+ff } ADH505b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=f++f+@.5f+++f+f+++f+@2f+ff } ADH505c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=f++f+@.5f+++f+f+++f+@2f+ff } ADH506 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=++f+@.5f+++f+@2f+++f+f+ff } ADH506a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=++f+@.5f+++f+@2f+++f+f+ff } ADH506b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=++f+@.5f+++f+@2f+++f+f+ff } ADH506c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=++f+@.5f+++f+@2f+++f+f+ff } ADH507 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=++f+f+++f+@.5f+++f+@2f+ff } ADH507a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f+++f ; though it does touch itself. f=++f+f+++f+@.5f+++f+@2f+ff } ADH507b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=++f+f+++f+@.5f+++f+@2f+ff } ADH507c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=++f+f+++f+@.5f+++f+@2f+ff } ADH508 { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom f ; though it does touch itself. f=++f+@.5f+++f+f+++f+@2f+ff } ADH508a { ; Anthony Hanmer 2000 Angle 6 ; This one doesn't seem to cross itself, Axiom +f+++f ; though it does touch itself. f=++f+@.5f+++f+f+++f+@2f+ff } ADH508b { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f f=++f+@.5f+++f+f+++f+@2f+ff } ADH508c { ; Anthony Hanmer 2000 Angle 6 Axiom f++f++f+++f--f--f f=++f+@.5f+++f+f+++f+@2f+ff } ADH509 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+f++@.5f+@2f++f+f+f++f+@.5f++@2f+f+ff } ADH509a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+f+f++@.5f+@2f++f+f+f++f+@.5f++@2f+f+ff } ADH510 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+f+f++@.5f+@2f++f+f+f++f+@.5f++@2f+f+fff } ADH510a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+f+f++@.5f+@2f++f+f+f++f+@.5f++@2f+f+fff } ADH511 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f++f-ff-f++f+f+ff+fff } ADH511a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f++f-ff-f++f+f+ff+fff } ADH512 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++ff---f+++f---f++++f+++f---f+++ff++ff } ADH512a { ; Anthony Hanmer 2000 Angle 8 Axiom -f++++f f=f++ff---f+++f---f++++f+++f---f+++ff++ff } ADH513 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f---f++f---f++++f+++f--f+++f++ff } ADH513a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=f++f---f++f---f++++f+++f--f+++f++ff } ADH514 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++f---f++f---f++++f+++f--f+++f++fff } ADH514a { ; Anthony Hanmer 2000 Angle 8 Axiom f++++f f=++f---f++f---f++++f+++f--f+++f++fff } ADH515 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=++f---f+++f---f++++f+++f---f+++f++fff } ADH515a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=++f---f+++f---f++++f+++f---f+++f++fff } ADH516 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++ff+++f+++ff++++ff---f---ff++ff } ADH516a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f++ff+++f+++ff++++ff---f---ff++ff } ADH517 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+++f+++ff++++ff---f---f++ff } ADH517a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++f+++f+++ff++++ff---f---f++ff } ADH518 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+++f+++f++++f---f---f++ff } ADH518a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++f+++f+++f++++f---f---f++ff } ADH519 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f+ff-f++f+ff-f-f-ff+ff } ADH519a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f+ff-f++f+ff-f-f-ff+ff } ADH520 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=ff+ff+f+f+ff-f++f+ff-f-f-ff+fff } ADH520a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=ff+ff+f+f+ff-f++f+ff-f-f-ff+fff } ADH521 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff+f+f+ff-f++f+ff-f-f-fff+ff } ADH521a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff+f+f+ff-f++f+ff-f-f-fff+ff } ADH522 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f+f+ff-f++f+ff-f-f-ff+fff } ADH522a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=+ff+f+f+ff-f++f+ff-f-f-ff+fff } ADH523 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=ff+fff+f+f+ff-f++f+ff-f-f-fff+fff } ADH523a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=ff+fff+f+f+ff-f++f+ff-f-f-fff+fff } ADH524 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+ff+f+f+ff++ff-f-f-ff+ff } ADH524a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+ff+f+f+ff++ff-f-f-ff+ff } ADH525 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff+f+f+ff++ff-f-f-fff+fff } ADH525a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff+f+f+ff++ff-f-f-fff+fff } ADH526 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=+ff+f+f+ff++ff-f-f-ff+fff } ADH526a { ; Anthony Hanmer 2000 Angle 4 Axiom f++f f=+ff+f+f+ff++ff-f-f-ff+fff } ADH527 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+fff-f-f-ff++ff+f+f+fff+fff } ADH527a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+fff-f-f-ff++ff+f+f+fff+fff } ADH528 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+f+@.5f-@2f-f-f-@.5f+@2f++f-@.5f+@2f+f+f+@.5f-@2f+ff } ADH528a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+f+@.5f-@2f-f-f-@.5f+@2f++f-@.5f+@2f+f+f+@.5f-@2f+ff } ADH529 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+@.5f+f-@2f-f-f-@.5f+@2f++f-@.5f+@2f+f+f+@.5f-f+@2ff } ADH529a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+@.5f+f-@2f-f-f-@.5f+@2f++f-@.5f+@2f+f+f+@.5f-f+@2ff } ADH530 { ; Anthony Hanmer 2000 Angle 4 Axiom f f=f+@.5f+f-@2f-f-f-@.5f+f++f-f+@2f+f+f+@.5f-f+@2ff } ADH530a { ; Anthony Hanmer 2000 Angle 4 Axiom +f++f f=f+@.5f+f-@2f-f-f-@.5f+f++f-f+@2f+f+f+@.5f-f+@2ff } ADH531 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++@.5f+f+f---f+f---f+f---f+f++++f-f+++f-f+++f-f+++f-f-f++@2ff } ADH531a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++@.5f+f+f---f+f---f+f---f+f++++f-f+++f-f+++f-f+++f-f-f++@2ff } ADH533 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+f++++f+++f-f++++f---f++++f+++f++++f+f---f++++f-f++ff } ADH533a { ; Anthony Hanmer 2000 Angle 8 Axiom +f++++f f=f++f+f++++f+++f-f++++f---f++++f+++f++++f+f---f++++f-f++ff } ADH534 { ; Anthony Hanmer 2000 Angle 8 Axiom f f=f++f+f++++f+++f-f++++f---f++++f+++f++++f+f---f++++f-f++fff } ADH534a { ; Anthony Hanmer 2000 Angle 8 Axiom ++f++++f f=f++f+f++++f+++f-f++++f---f++++f+++f++++f+f---f++++f-f++fff } ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Tony \(Anthony\) Hanmer" Subject: (fractint) Time for some more L-Systems, 3 Date: 04 Apr 2000 11:26:47 GEST This file should be named edragons.l Tony Hanmer README { ; Anthony Hanmer 2000 Angle 4 ; These are all L-systems which tile part of a polygon - Axiom ; a square or equilateral triangle. So, putting 3 or 4 f=ff ; of them together fills the polygon completely. } ; (They're also a subset of Horizons.l.) ADH236a { ; Anthony Hanmer 2000 Angle 4 ; Escher's 1st Dragon (2 colours) Axiom c9f+c12f+c9f+c12f f=ff+f+f++ff++f+f+f } ADH236b { ; Anthony Hanmer 2000 Angle 4 ; Escher's 1st Dragon (4 colours) Axiom c9f+c10f+c12f+c14f f=ff+f+f++ff++f+f+f } ADH236c { ; Anthony Hanmer 2000 Angle 4 ; rectangle, 2 colours Axiom +c9f+c12f+c9f+c12ff+c9f+c12f+c9f-c12f-c9f-c12ff-c9f-c12f f=ff+f+f++ff++f+f+f } ADH236d { ; Anthony Hanmer 2000 Angle 4 ; equal-armed cross, 2 colours Axiom c9f+c12f++c12f+c9f++c9f+c12f++c12f+c9f f=ff+f+f++ff++f+f+f } ADH236e { ; Anthony Hanmer 2000 Angle 4 ; diamond, mono Axiom f+f+f+f++f-f-f-ff-f-f+f-f-f+f-f-f+f-f-f++f+f+f-f+f+f-f+f+f-f+f+f f=ff+f+f++ff++f+f+f } ADH236f { ; Anthony Hanmer 2000 Angle 4 ; diamond, 2 colours Axiom c9f+c12f+c9f+c12f++c12f-c9f-c12f-c9fc12f-c9f-c12f+c9f-c12f-c9f+c12f-c9f-c12f+c9f-c12f-c9f++c9f+c12f+c9f-c12f+c9f+c12f-c9f+c12f+c9f-c12f+c9f+c12f f=ff+f+f++ff++f+f+f } ADH271a { ; Anthony Hanmer 2000 Angle 6 ; Escher's 2nd Dragon (3 colours), Axiom c9f++c12f++c14f ; triangular tiling f=f+f+++f++f } ADH271b { ; Anthony Hanmer 2000 Angle 6 ; Axiom c9f++c12f++c14f+++c14f--c12f--c9f f=f+f+++f++f } ADH271c { ; Anthony Hanmer 2000 Angle 6 ; Hexagon 1 Axiom c9f++c14f++c12f---c9f++c14f++c12f---c9f++c14f++c12f---c9f++c14f++c12f---c9f++c14f++c12f---c9f++c14f++c12f f=f+f+++f++f } ADH271d { ; Anthony Hanmer 2000 Angle 6 ; Hexagon 2 Axiom c9f++c14f++c12f---c12f++c14f++c9f---c9f++c14f++c12f---c12f++c14f++c9f---c9f++c14f++c12f---c12f++c14f++c9f f=f+f+++f++f } ADH271e { ; Anthony Hanmer 2000 Angle 6 ; Hexagon 3 Axiom c14f+f+f+f+f+f+++f-f-f-f-f-f--c9f--c12f+++c12f--c9f+++c9f--c12f+++c12f--c9f+++c9f--c12f+++c12f--c9f f=f+f+++f++f } ADH489b { ; Anthony Hanmer 2000 Angle 4 ; Escher's 3rd Dragon, 2 colours Axiom c9f+c12f+c9f+c12f f=f+f+f++f+f++ff+ff } ADH489c { ; Anthony Hanmer 2000 Angle 4 ; Escher's 3rd Dragon, 4 colours Axiom c9f+c10f+c12f+c14f f=f+f+f++f+f++ff+ff } ADH489d { ; Anthony Hanmer 2000 Angle 4 ; ... further expansion, 2 colours Axiom c9f+c12f+c9f+c12f++c12f-c9f-c12f-c9f f=f+f+f++f+f++ff+ff } ADH489e { ; Anthony Hanmer 2000 Angle 4 ; rectangle, 2 colours Axiom +c9f+c12f+c9f+c12ff+c9f+c12f+c9f-c12f-c9f-c12ff-c9f-c12f f=f+f+f++f+f++ff+ff } ADH489f { ; Anthony Hanmer 2000 Angle 4 ; equal-armed cross, 2 colours Axiom c9f+c12f++c12f+c9f++c9f+c12f++c12f+c9f f=f+f+f++f+f++ff+ff } ADH489g { ; Anthony Hanmer 2000 Angle 4 ; diamond, mono Axiom f+f+f+f++f-f-f-ff-f-f+f-f-f+f-f-f+f-f-f++f+f+f-f+f+f-f+f+f-f+f+f f=f+f+f++f+f++ff+ff } ADH489h { ; Anthony Hanmer 2000 Angle 4 ; diamond, 2 colours Axiom c9f+c12f+c9f+c12f++c12f-c9f-c12f-c9fc12f-c9f-c12f+c9f-c12f-c9f+c12f-c9f-c12f+c9f-c12f-c9f++c9f+c12f+c9f-c12f+c9f+c12f-c9f+c12f+c9f-c12f+c9f+c12f f=f+f+f++f+f++ff+ff } ADH494a { ; Anthony Hanmer 2000 Angle 4 ; Escher's 4th Dragon, 2 colours Axiom c9f+c12f+c9f+c12f f=f+ff++ff+f+f++f+f } ADH494b { ; Anthony Hanmer 2000 Angle 4 ; Escher's 4th Dragon, 4 colours Axiom c9f+c10f+c12f+c14f f=f+ff++ff+f+f++f+f } ADH494c { ; Anthony Hanmer 2000 Angle 4 ; rectangle, 2 colours Axiom +c9f+c12f+c9f+c12ff+c9f+c12f+c9f-c12f-c9f-c12ff-c9f-c12f f=f+ff++ff+f+f++f+f } ADH494d { ; Anthony Hanmer 2000 Angle 4 ; equal-armed cross, 2 colours Axiom c9f+c12f++c12f+c9f++c9f+c12f++c12f+c9f f=f+ff++ff+f+f++f+f } ADH494e { ; Anthony Hanmer 2000 Angle 4 ; diamond, mono Axiom f+f+f+f++f-f-f-ff-f-f+f-f-f+f-f-f+f-f-f++f+f+f-f+f+f-f+f+f-f+f+f f=f+ff++ff+f+f++f+f } ADH494f { ; Anthony Hanmer 2000 Angle 4 ; diamond, 2 colours Axiom c9f+c12f+c9f+c12f++c12f-c9f-c12f-c9fc12f-c9f-c12f+c9f-c12f-c9f+c12f-c9f-c12f+c9f-c12f-c9f++c9f+c12f+c9f-c12f+c9f+c12f-c9f+c12f+c9f-c12f+c9f+c12f f=f+ff++ff+f+f++f+f } ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Tony \(Anthony\) Hanmer" Subject: (fractint) Time for some more L-Systems, 4 Date: 04 Apr 2000 11:29:29 GEST This last posting for now should be called Maze09.l (They're all variations on William McWorter's Maze09, and playing with only the top half gave me the inspiration for Horizons.) Tony Hanmer T184 { ; Anthony Hanmer 2000 Angle 8 ; Looking to William McWorter's Maze09 Axiom f f=f+f++f++f++ff--f--f--f-ff } T184a { ; Anthony Hanmer 2000 Angle 8 ; Looking to William McWorter's Maze09 Axiom f++f++f++f f=f+f++f++f++ff--f--f--f-ff } T186 { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f f=f+f+f++f+ff-f--f-f-ff } T186a { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f++f++f f=f+f+f++f+ff-f--f-f-ff } T187 { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f f=f+f+ff++f+fff-ff--f-ff-ff } T187a { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f++f++f f=f+f+ff++f+fff-ff--f-ff-ff } T188 { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f f=f+f+ff++f+fff-ff--f-ff-fff } T188a { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f++f++f f=f+f+ff++f+fff-ff--f-ff-fff } T189 { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f f=ff+f+ff++f+fff-ff--f-ff-ff } T196 { ; Anthony Hanmer 2000 Angle 4 ; Looking to William McWorter's Maze09 Axiom f f=f+f++ff++f-ff } T196a { ; Anthony Hanmer 2000 Angle 4 ; Looking to William McWorter's Maze09 Axiom f+f+f+f f=f+f++ff++f-ff } T196b { ; Anthony Hanmer 2000 Angle 4 ; Looking to William McWorter's Maze09 Axiom f++f f=f+f++ff++f-ff } T199 { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f f=f+f+f+++f-ff+f+++f-f-ff } T199a { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f++f++f f=f+f+f+++f-ff+f+++f-f-ff } T199b { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f--f--f f=f+f+f+++f-ff+f+++f-f-ff } T200 { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f f=ff++f++f+f++f-f } T200a { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f++f++f f=ff++f++f+f++f-f } T203 { ; Anthony Hanmer 2000 Angle 8 ; Looking to William McWorter's Maze09 Axiom f f=f++f+f++++f-ff-f++++f+f--ff } T204 { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f f=f+f+f+f+++f-f-f+f-f-f+++f+f+f--ff } T205 { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f f=ff+f+f+f+++f-f-f+f-f-f+++f+f+f--ff } T213 { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f f=ff+f+++f+f+++f--f } T213a { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f++f++f f=ff+f+++f+f+++f--f } T214 { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f f=ff++f+++f++++f+++f } T214a { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f++f++f f=ff++f+++f++++f+++f } T214b { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f--f--f f=ff++f+++f++++f+++f } T214c { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f+f+++f+f f=ff++f+++f++++f+++f } T215a { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f++f++f f=ff++f+++f+f+++f--f } T215b { ; Anthony Hanmer 2000 Angle 6 ; Looking to William McWorter's Maze09 Axiom f--f--f f=ff++f+++f+f+++f--f } T220 { ; Anthony Hanmer 2000 Angle 36 ; Looking to William McWorter's Maze09 Axiom f f=ff+++++++++f++++++++f++++++++++++++++++f--------ff--------f------------------f++++++++f---------ff } T221 { ; Anthony Hanmer 2000 Angle 36 ; Looking to William McWorter's Maze09 Axiom f f=f+++++++++f++++++++f++++++++++++++++++f--------ff--------f------------------f++++++++f---------ff } T222 { ; Anthony Hanmer 2000 Angle 36 ; Looking to William McWorter's Maze09 Axiom f f=ff+++++++++f++++++++f++++++++++++++++++f--------ff--------f------------------f++++++++f---------f } T228 { ; Anthony Hanmer 2000 Angle 4 ; Looking to William McWorter's Maze09 Axiom f f=ff+f+f++f-ff-f--f+f-f } T229 { ; Anthony Hanmer 2000 Angle 4 ; Looking to William McWorter's Maze09 Axiom f f=f+f+f++f-ff-f--f+f-ff } T230 { ; Anthony Hanmer 2000 Angle 4 ; Looking to William McWorter's Maze09 Axiom f f=ff+f+f++f-ff-f--f+f-ff } T283 { ; Anthony Hanmer 2000 Angle 8 ; Looking to William McWorter's Maze09 Axiom f f=ff+++f-f++++f+f--f+f++++f-f-f } T284 { ; Anthony Hanmer 2000 Angle 8 ; Looking to William McWorter's Maze09 Axiom f f=ff+++f-f++++f+f--f+f++++f-f-ff } ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: davides Subject: Re: (fractint) Amy Grant uses Fractint? Date: 04 Apr 2000 05:43:27 -0400 At 08:43 PM 4/3/2000 -0700, you wrote: (Amy Grant...) I downloaded the clip, listened a couple of times (nice voice, I haven't heard her), but I do not hear fractint in there. Sorry... :) OTOH, maybe I'll pick up that cd. :> davides@pipeline.com Back up my hard drive? How do I put it in reverse? Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "James R. McKenzie" Subject: Re: (fractint) list archive Date: 04 Apr 2000 06:25:53 -0400 For my $.02 it's not a big risk (so far as I can tell) so my vote (for now) is no. Leave it as is. T H A N K Y O U James R. McKenzie jimmckenzie@earthlink.net ----- Original Message ----- Sent: Monday, April 03, 2000 10:13 PM > Discussion of list management issues is officially off topic except > for me, the benevolent dictator :-) If anyone has an opinion on the > issue mentioned below, please *email me* (but don't post to the > list). I would like to get opinions, but not clutter the list with > discussion on this topic. > > Some of you may be aware that the archive of the digest version of > this list is publically visible at: > > http://www.xmission.com/pub/lists/fractint/archive/ > > It is possible that automatic webcrawlers can scavange email > addresses from the archive. I have no evidence that this actually > happens, and I have heard a point of view that web crawlers > probably don't check ftp files, which is what the archive consists of. > > I could make the archive inaccessible to the public. SHould I? > > Pro: This might reduce the exposure of your email to potential > spammers. > > Con: Availablilty of the archive is useful for folks who are returning > to the list after an absence or want to search for a topic, so we'd > lose this capability if the archive were not public. > > If you have an opinion, email me. I'm leaning toward the status quo. > > Tim > > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JWeaver285@aol.com Subject: (fractint) Blue Ribbon Fractal ~ Date: 04 Apr 2000 23:49:15 EDT Hi Everyone~ I submitted 2 fractal images in a judged spring showing at the Victoria Art League Center in Victoria,Tx., only because they happened to have a computer art category, along with oils, acrylics, charcoal, sculpting, etc., and was rewarded with 1st and 2nd place!! Not overall mind you, just for PC art (intermediate). This par is of the 1st place pic which was printed in portrait style and the other is a UF image which can be seen at .....members.aol.com/JimBeau549/jim3.htm title is...."LOVE IS..." Fractals are SOOO cool! Enjoy ~ Jim Weaver ________________________________ Ivory02.gif { ; image(c)2000 Jim Weaver reset=1960 type=formula formulafile=fractint.frm formulaname=prn_02 function=log/tanh/sqr passes=t center-mag=-12.4833/-2.13163e-014/0.04731381 params=-0.03624/0/0.4/0 float=y invert=1/0/0 periodicity=0 colors=000hoxksynvz<15>F8I<9>c_ffbiiellhookrrnu<17>LDD<13>yll<17>B5G<13>\ rcu<15>444<17>kkw<27>EJODIMCHLAFJBFK<29>zgz<15>13M<22>MCrAFp9Jp<6>05g<12\ >dlv } Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Paul DeCelle Subject: Re: (fractint) Blue Ribbon Fractal ~ Date: 05 Apr 2000 00:44:26 -0400 Hi, Jim-- > I submitted 2 fractal images in a judged spring showing at the Victoria Art > League Center in Victoria,Tx., only because they happened to have a computer > art category, along with oils, acrylics, charcoal, sculpting, etc., and was > rewarded with 1st and 2nd place!! Not overall mind you, just for PC art > (intermediate). This par is of the 1st place pic which was printed in > portrait style and the other is a UF image which can be seen at > .....members.aol.com/JimBeau549/jim3.htm title is...."LOVE IS..." > Fractals are SOOO cool! Congratulations - Very nice work! Regards, Paul Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jason Hine" Subject: (fractint) Re: Amy Grant uses Fractint? Date: 04 Apr 2000 22:41:55 -0700 Thanks to all those who took a listen... seems the general consensus is that I'm hearing things. Well, it's not the first time, that's for sure... Amy Grant, for those unfamiliar with her, writes contemporary secular Christian songs, and has been doing so for around the past 20 years. A quick web browse will tell you more if you're curious... ... and if anyone else listens to the clip and _does_ hear Fractint's sound in there, I'd be delighted to hear from you! Cheers, Jason Hine Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 05-04-00 (The Enclosed World [7]) (c) Date: 05 Apr 2000 01:48:53 -0400 (EDT) FOTD -- April 05, 2000 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal midget was generated by another apparently uninteresting formula. But the formula, 3.48(Z^0.7)-2.32(Z^0.5)+C, is uninteresting only on the surface. When iterated it draws a most unusual little Mandelbrot set with all the convolutions of the classic set. Today's scene is located in the area of the period-10 radical on the northeast shore of the main bay of the little M-set, deep in the spiral of a minor elephant trunk. I devoted a little extra effort the coloring, which accounts for the picture's rating of seven. At a rendering time of over seven minutes, running the parameter file is the slow way of seeing the image. A far better way is to download the pre-rendered JPEG file from: or from: The weather was rainy and muggy in the morning, and clearing and colder in the evening, with the temperature falling from 66F (19C) to 44F (6.5C) through the day. The fractal cats chose to stay indoors, where the temperature remained a relatively constant 69F (20.5C). Tomorrow I'll delve deeper into the world of fractals. For this evening the hour grows late, the cats are growing hungry and it's time to post this FOTD. Until next time, take care, and take life one fractal at a time. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ The_Enclosed_World { ; time=0:07:20.62, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=mandelbrotmix4 function=ident passes=1 center-mag=+0.1446730940127774/+0.01040684926964369/\ 3.308281e+010/1/-12.499 params=-0.4/0.5/0.6/0.7/4.8/0 float=y maxiter=1200 bailout=25 inside=0 logmap=140 symmetry=none periodicity=10 colors=000Qc2<2>Ri2Sk2Un1Xp1`r1cu1ex1WvAEr9DmCBhE9cG\ A_IBTKDNNEDFqKt<3>gFmeEkbDi`Bf<2>R8ZRCZTFa<3>hTnlXrn\ _s<3>xtyzzzsrznmyhlw<3>Ohr<9>jUflSdoRcqPbsOauN`<3>wG\ QwFOqEM<3>XEFREEMECHEB<3>WKKZMMbNO<3>pTWKyw<8>B_rAYq\ 9Vq<3>6Ko<2>lCQ<3>w2Uy0Vx1W<6>v7Xv8Xv9Y<3>uCY<3>YZjS\ cmMip<2>5yy<3>4ox4mx4kx4hx4fx4dx<6>IMfKKcMHa<3>U7S<5\ >iHVlJWoKW<3>yQY<3>cJeZHgTFi<3>89q<2>_44<3>P2FN2IK1L\ <2>C0TA0V95W<4>9SX8XY8`Y<3>8rZ<3>IvVKwUNxTPyT<3>ZzP`\ zObzO<9>UzKUzJTzJ<3>QzI<2>tz7Lz_<2>rzM<3>ezEbzD_zB<3\ >Oz4<4>Qz3 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: davides Subject: Re: (fractint) Blue Ribbon Fractal ~ Date: 05 Apr 2000 05:54:03 -0400 At 11:49 PM 4/4/2000 EDT, you wrote: > > Hi Everyone~ > > I submitted 2 fractal images in a judged spring showing at the Victoria Art >League Center in Victoria,Tx., Very nice! And congratulations on your winning! I'll have to cruise by your site and look at the UF image. David davides@pipeline.com Back up my hard drive? How do I put it in reverse? Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: BillatNY@aol.com Subject: Re: (fractint) Blue Ribbon Fractal ~ Date: 05 Apr 2000 17:07:31 EDT Jim, Congratulations! That's great news! Bill Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 06-04-00 (Protobud [5]) (c) Date: 06 Apr 2000 01:31:03 -0400 (EDT) FOTD -- April 06, 2000 (Rating 5) Fractal visionaries and enthusiasts: Where do Mandelbrot buds come from? . . . why, they come from protobuds. Today's rather striking image shows a protobud caught in the act of emerging from the universal sea of fractal protoplasm, but not yet fully formed into a mature Mandelbrot bud. Making this birth scene visible required extraordinary measures. To begin, the entire action takes place in the unreal world of totally trapped points. This required that a nonflat inside fill be applied to the image to make the invisible visible. Several inside fills did an acceptable job, but the atan fill worked the best. The formula behind the image is 999(Z^-0.26)-999(Z^-0.25)+1/C, another of my whimsical, very simple but very surprising concoctions. After a slight overall contrast boost in a graphic program, I named the final result "Protobud", a purely descrip- tive and at the same time poetic name. Since the image consists entirely of inside areas, and the periodicity has been turned off, the image is not a fast one. It requires 6-1/2 minutes on an average 200mhz Pentium. As always, the JPEG'd image file has been posted to: The image is also available at: The day's fractal weather was partly cloudy with a brisk wind and a chilly temperature of 54F (12C). The cats ventured out briefly, but asked to come indoors when a cloud obscured the sun. Until next time, take care. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Protobud { ; time=0:06:31.42, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=mandelbrotmix4 function=recip center-mag=0.0665663/0.0150862/2813.113/1/67.499 params=1/-0.25/-1/-0.26/-1000/100000 float=y maxiter=300 bailout=25 inside=atan logmap=yes symmetry=none periodicity=0 sound=off colors=000p_D<4>oSDoQCoPCmOC<3>lIClGClFClDCjCCjACj9C\ j6Aj7Ci7Cg7Cd7C<3>Y7CX7CT7C<4>L7CJ7CG7CF7CD7CA7C97C7\ 7C47C37C17C<2>07C07C09F0AI0CJ<2>0GQ0IT0IV<4>0Pf0Qi0Q\ j<2>0Vr0Xu0Yv0_y0_z0dz4iz<3>YzzXyzXyzVxyVxxTxuTvsSvp\ SvoSumQujQuiPsfPsdOsaOr`Or_MrXMpVLpSLpQJoOJoMJoMJlLd\ gV__fMQa7I`0D_0CY0F`0Ic0Md1Pg3Sj6Wl7_r9ctCewAcsA_rAX\ m9Sj9Og9Jd9Ga7C_77X73T60Q60O60L10J00I00G60FD0FJ0FP0D\ V0C_0Cd0Ai0Af09i07m07p16u36x34z43z63z71z40z71z94zA7z\ DAzFDzGGzIJzLMzMPzOSzPVzSYyT`xVcxYfv_iu`lsaosdrrfupg\ xoizpiyrVpsGioJflMcgP`dQ_aTXYXTV_QS`POcMLfJOgIIvI9zF\ CzIFzJIzLJzMMzOPzPSzQTzSXzT_zXazY<2>izalzcmzdpzfszgv\ zjxzlzzm<3>zzszzuzzvzzszzpzzmzzlzzi<2>xzauz_szYpzVoz\ SlzQjzOizLfzJdzGazD`zCYz9Xz6Tz4Sz1Pz0Oz0Lz0<2>Gz0Fz0\ Fy0Dy1Dy4Cx7Cx9AxCAvF9vIraDr`D } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Tom Conally Subject: (fractint) where oh where Date: 06 Apr 2000 08:35:29 -0400 Sorry but I can't find the address to get patch 9 of Fractint 20. Help me out please. Tom Conally In every boomerang there is a perfect throw. Your life, Grasshopper, is to practice till you find that throw and become one with that boomerang! http://fly.to/boomerangs " Flying Frog Boomerangs" http://www.vstore.com/vstorehardware/flyingfrogtools/ "Flying Frog Tools" http://www.netpath.net/~conally My greater internet index Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Scott D. Boyd" Subject: Re: (fractint) where oh where Date: 06 Apr 2000 11:17:02 -0500 On Thu, 06 Apr 2000, Tom wrote: > Sorry but I can't find the address to get patch 9 of Fractint 20. > Help me out please. > Tom Conally > http://www.fractint.org for the Development Team home page or ftp://ftp.fractint.org/2000p09.zip to download the file directly. Scott Boyd -- email: sdboyd@fastlane.net http://www.fastlane.net/~sdboyd/ Introducing Windows 2000 !! -- Reduced to only 65,000 bugs !! Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: comdotatdotcom@csi.com Subject: RE: (fractint) where oh where Date: 06 Apr 2000 17:24 0000 Hi Tom, >Sorry but I can't find the address to get patch 9 of Fractint 20. >Help me out please. Sure! check out: ftp://ftp.fractint.org/fractdev.zip this should always link to an executable at the latest patch level. To get the patch itself just knock the filename off the end of that path and take a look at what's there. Cheers, Robin. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Tom Conally Subject: Re: (fractint) where oh where Date: 06 Apr 2000 12:44:07 -0400 Thank you all, I have it now. At 11:17 AM 4/6/2000 -0500, you wrote: >On Thu, 06 Apr 2000, Tom wrote: >> Sorry but I can't find the address to get patch 9 of Fractint 20. >> Help me out please. >> Tom Conally >> >http://www.fractint.org for the Development Team home page or >ftp://ftp.fractint.org/2000p09.zip to download the file directly. > >Scott Boyd Tom Conally In every boomerang there is a perfect throw. Your life, Grasshopper, is to practice till you find that throw and become one with that boomerang! http://fly.to/boomerangs " Flying Frog Boomerangs" http://www.vstore.com/vstorehardware/flyingfrogtools/ "Flying Frog Tools" http://www.netpath.net/~conally My greater internet index Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 07-04-00 (Melismatic Midget [5]) (c) Date: 07 Apr 2000 02:08:28 -0400 (EDT) FOTD -- April 07, 2000 (Rating 5) Fractal visionaries and enthusiasts: We have a slight trace of northern lights visible here at Fractal Central this evening -- not an unheard-of event, but rare enough to call for a look at the northern horizon. We also have a melismatic midget. While searching for today's fractal, I was listening to middle- eastern music, which is filled with those decorative phrases known as melismas. For some reason, today's image with its intricate patterns reminded me of that music. I then named the picture "Melismatic Midget". The formula behind the scene is 6(Z^1.333)-6(Z^1.667)+C, a very simple expression, as are all expressions calculated by the MandelbrotMix4 formula, which outperforms its apparent potential by several orders of magnitude. The eight minutes required to run the parameter file can be avoided by downloading the pre-rendered JPEG file from Usenet at: or from the WWW at Paul Lee's web site at: The fractal weather today was unexpectedly warm and sunny, though the wind was a bit too brisk for the fractal cats, who grow cautious when the wind blows. The temperature of 79F (26C) was perfect for anything. Right now it's already time to shut down the fractal place for another evening and call it a day. Until next time, take care, keep your feet on the ground and your head in the stars. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Melismatic_Midget { ; time=0:08:19.44, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=mandelbrotmix4 function=ident passes=1 center-mag=+0.824444041338745/+0.000121906568368/8.2\ 94846e+008/1/79.999 params=-1/1.667/1/1.333/5/0 float=y maxiter=2200 bailout=25 inside=0 logmap=163 symmetry=none periodicity=10 colors=000_Sd_Sd<3>cWldXneYp<2>h`v<3>ld_meUnfOchMRkK\ 4kK3jM<3>2NS2HT2BU17N04H<4>M5TQ6WU6Y<3>j6f<6>ZFbXGaV\ Ha<3>PL_<3>o4x<5>fUYdYUcaP<3>Yr8<3>amMblQcjT<3>gff<3\ >mRRnNNoJJ<2>s87<9>`KO_LQYMS<2>SPXRQYOJ`<2>F1h<3>FQS\ FWOFaK<2>Fs8<2>qxZ<3>nyQmyOlyM<2>jyGjyEkuH<6>lZXlWZm\ T`<2>mJgmGioIe<3>sMT<3>PYTI_TPsz<3>RhjRefSbb<3>TTN<3\ >kNQpLRuKSyJS<9>oANnAMm9M<2>j6Kj6KkAM<3>nPSnTToUV<3>\ rU`rUasUctUdtUe<3>wYNxZIy_Ez`9za5<6>jh7hi7fj7<3>Zn7M\ oE9pL<3>EtYGu`Hvc<2>KylXzZ<5>OzdNzeLzf<3>Gzi<3>Sz_Oz\ pOzsNzi } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: (fractint) Branch Cuts Date: 07 Apr 2000 10:01:53 GMT Some time ago I mentioned that if you ask FractInt to render something like Z^2.5 + C you get a "fractured" image due to branch cuts in the formula... I wondered if it was possible to move these branch cuts... Anyway, I seem to have found out where these things originate from. A look at FractInt's trig identities confirms that FractInt calculates A^B by taking the natural logarithm of A, multiplying it by B, and then taking the natural antilogarithm of the product thus obtained. Now, the complex antilogarithm function *is* a "function", i.e. it produces a single value. But the logarithm function has multiple solutions; this is where the branch cuts are comming from. The FractInt docs don't make this very clear, but basically, to take the natural logarithm of a complex number Z, you calculate a new number K with Re(K) = e^(Mag(Z)) and Im(K) = Arg(Z). It's this second part that introduces the multiple possibilities. FractInt works out the argument of a complex number using C's atan2() function. This returns results +/- pi. By just adding 2pi on to the imaginary part of the result, you get a different, but still legal result. So I can move the branch cuts "one full circle"... but how do I move then by just, say, half a turn? Adding on a fraction of pi won't do it... then I'd just have nonsense answers. Any ideas? Anyone? ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Barry N Merenoff <110144.2274@compuserve.com> Subject: (fractint) Branch Cuts Date: 07 Apr 2000 10:42:43 -0400 You can multiply the number by some unitary complex number, take the logarithm, then subtract the logarithm of your multiplier. Sincerely, Collin Merenoff Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 08-04-00 (Midget with Pancake [3]) (c) Date: 08 Apr 2000 01:31:57 -0400 (EDT) FOTD -- April 08, 2000 (Rating 3) Fractal visionaries and enthusiasts: Today turned unexpectedly busy, cutting my fractal hunting time to the bare minimum. But despite the rush, I did find a fractal, and the fractal is worth being declared Fractal of the Day for April 08. The less-than-spectacular fractal reminds me of a midget in the center of a pancake, most likely covered with strawberry syrup. I named the picture "Midget with Pancake" when I noticed the resemblance. The formula that caused all the excitement is Z+2(1/Z)+C, a formula far too simple and uninteresting to do anything of value. But the formula doesn't know this, and produces interesting fractals anyway. Perhaps the worthless formula is the reason I rate the picture only a significantly-below-average 3 on my 1-to-10 scale of fractal worth. The image might not be gold or silver, or even bronze, but it is strawberry, and it is posted to: and to: The fractal weather today was a bit cooler than yesterday, but still pleasant. The temperature of 68F (20C) was perfect for the cats as well as the dogs. Until next time, take care, and take a brief fractal break. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Midget_withPancake { ; time=0:05:17.00, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-2.06274581089187400/+0.68669116186631770\ /1.940765e+011/1/147.502/-0.002 params=1/1/2/-1/0/0 float=y maxiter=1500 bailout=25 inside=0 logmap=106 symmetry=none periodicity=10 colors=000KC1A01A01A04A06<3>L0GO0JR0LU0NX0QZASa2V<3>\ l0c<9>gYPg`NfcM<3>epG<3>nfCqdBsbA<2>yW8<3>dYAZYBUZBP\ ZCKZC<7>SPDTODUND<3>YJD<6>KXUIZXG`Z<3>9gg<3>WaZ``Xf_\ VkZT<3>NdXHfYBgZ5hZ<3>RlQXlOamM<3>wpE<7>hYXfVZeT`<3>\ ZKiwxP<5>kwMivMgvL<2>avK`vKYuL<6>HsSFrTCrU<3>3qX<3>T\ QIZJFdCBj68<2>icjX8r<3>nePrmInnN<3>bne_njXnoUns<4>_c\ j``iaZg<3>eRa<5>mJcoIcpHc<3>uCd<3>`SOWVJRZF<2>Ci3Glq\ <6>Q`ZSZWTXT<3>YRJ<3>`gVakYao`bscbwebydHME<3>PI8RH6T\ G5VF3XF2<8>nNQpNTrOW<3>yRe<5>icCc_IYWN } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Tim Wegner Subject: Re: (fractint) Branch Cuts Date: 08 Apr 2000 11:43:43 -0600 Andrew wrote: > Now, the complex antilogarithm function *is* a "function", i.e. it produces > a single value. But the logarithm function has multiple solutions; this is > where the branch cuts are comming from. Exactly. So Fractint's logarithm formula (and any other complex valued logarithm formula) has to arbitrarily select from among the multiple values. This creates a discontinuity somewhere in the values. You cxan visualize the log function as an infinite corkscrew. A function has to be single valued, so only one 360 degree piece of the corkscrew is used by the function, so the corkscrew has to be cut somewhere. > > The FractInt docs don't make this very clear, but basically, to take the > natural logarithm of a complex number Z, you calculate a new number K with > Re(K) = e^(Mag(Z)) and Im(K) = Arg(Z). It's this second part that introduces > the multiple possibilities. Th docs give the formula for logarithm making it clear it has multiple values: log(x+iy) = (1/2)log(x^2 + y^2) + i(atan(y/x) + 2kPi) for k = 0, -1, 1, -2, 2, ... However the docs don't say anything about the visual discontinuity except that we know it is supposed to be there. The book Fractal Creations does discuss this. > So I can move the branch cuts "one full circle"... but how do I move then by > just, say, half a turn? Adding on a fraction of pi won't do it... then I'd > just have nonsense answers. Any ideas? Anyone? Hmmm, I don't know if this is worthwhile or not, but we could add the fraction of PI within fractint itself, effectively giving you alternate logarithm formulas. However you can do this yourself in the formula parser. Just add some multiple of 2*PI to the imaginary part of the log function in a formula and see what happens (see formula for log above). Let us know if you get any interesting results. Tim Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 09-04-00 (Branch Cuts [3]) (c) Date: 09 Apr 2000 10:20:09 -0400 (EDT) FOTD -- April 09, 2000 (Rating 3) Fractal visionaries and enthusiasts: The lateness is due to a short power failure and the fact that I fell asleep while waiting for the power to return. I recently noticed a few letters on the fractint list under the topic "branch cuts", which discussed the discontinuities in fractals that contain a fractional exponent in their formulas. It was correctly pointed out that because the complex logarithm function is multi-valued, these discontinuities must always appear. This discussion prompted me to bring out a formula that I wrote some time ago in an effort to investigate the multi- valued nature of the complex logarithm. The expression (x^x)^(1/x)=x, is true when x is a real number. But when x is a complex number, strange things happen due to the multi-valued nature of the complex log function. The basic iterated expression in the MultValLog2 formula is (Z^Z)^(1/Z), which appears as though it should equal Z, but doesn't. I'm not quite sure what the initial z=p1*(1e-100) was supposed to do, but p2 and p3 control the portions of (^Z) an (^1/Z). Since Z+C draws no fractal, the fractals created by this formula theoretically consist of only artifacts arbitrarily created by the parser as it decides which log value to use. I'm not sure whether the images can be considered fractals at all, but they certainly are fractured. And surprisingly, the fractals, which are unusually slow, contain midgets of an unusual kind, resembling sort of a cross between a quadratic midget and a midget of a high order. I don't know enough about this formula and its fractals to say much more, so I'll let it go at this, but I'll be further exploring this forgotten formula in the days to come. I named the image "Branch Cuts" after the topic line of the letters that led me to remember the formula. The artistic rating of today's effort is only a 3, though the mathematical interest may be a bit higher. The parameter file is a rather slow one, so a download is recommended. That download can be found on Usenet at: and on the WWW at: The weather today was sunny and 80F (26.5C). Tonight it is snowing. The fractal cats are totally confused by the rapid changes. The day's philosophy will have to wait until tomorrow's FOTD, much to the chagrin of those waiting for (IMO) enlightenment. But as I have often said, don't feel too disappointed. After all, one person's enlightenment is another person's nonsense. I see that it's time to end today's FOTD. So until next time, which will be in only 15 hours or so, take care, and brush the snow from your tulips. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Branch_Cuts { ; time=0:36:35.34, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=multival.frm formulaname=MultValLog2 passes=1 center-mag=-1.15934761779311800/-0.06686366463112242\ /4458813 params=0/0/-2.5/0/-2.5/0 float=y maxiter=12000 bailout=25 inside=0 logmap=328 symmetry=none periodicity=10 colors=000bJHlWL<8>nTCnSBnSA<2>oR7oR6pS5<37>i8Ki8Ki7\ Ki7Li6L<72>PsnPtnPuo<2>OwpOwpNuo<3>LpojlUcUoXcoJko<3\ 2>37k26k25k<2>01k00k11j<66>LTK } frm:MultValLog2 {; Jim Muth z=p1+(1e-100), c=pixel: z=(p2*(z^z))^(p3*(1/z))+c, |z| <= 100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 10-04-00 (Semi-Spiral Scene [6]) (c) Date: 10 Apr 2000 01:42:20 -0400 (EDT) FOTD -- April 10, 2000 (Rating 6) Fractal visionaries and enthusiasts: With no power failure today, I'm writing the FOTD discussion on time. The fractal in question is an improvement over the past two days' offerings, which rated only a three. Today's FOTD, which not surprisingly was found with the MandelbrotMix4 formula, rates a somewhat-above-average 6 on my scale of fractal quality. The exact fractal formula being iterated in today's image is -1(Z^2.5)-Z+C, another uninteresting expression that holds quite a few surprises. I named the picture "Semi-Spiral Scene" because I couldn't decide whether I was looking at a series of spirals or an octagon. I finally decided on the spiral theme, since the apparent octagon is an artifact of coloring. The parameter file runs slowly enough to make a download the better choice. That download may be found at: or at: The fractal weather today was partly sunny but blustery and chilly. The 3cm of snow that fell overnight vanished by midday, but the temperature, which remained in the high 40's (around 9C) was too chilly for the cats, who passed the day eating and sleeping. And sleeping is what I'll be doing before much longer, preparing myself for what promises to be an active week, both in the work and the fractal departments. Until next time, take care, and there's no such thing as a bad fractal. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Semi-Spiral_Scene { ; time=0:09:29.02, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.89728782155468800/-0.41895782132379090\ /5768086/1/-55 params=-1/2.5/-1/1/0/0 float=y maxiter=1200 bailout=25 inside=0 logmap=149 symmetry=none periodicity=10 colors=00070K80K90Kc0Kc1Nf3Qf4Tc5Wa6ZG7aH8dKJ`NTYMaJ\ <2>TcpSSlRGiS2g<8>DIaBK`9M_<3>3SY<3>hmi<3>LMGZERGG9<\ 2>eFCsFDzBFyFDuIBqLA<3>fZ4ca2ad1iaJpZ_ybw<2>sLdwGb<3\ >_GOUGKOGGIGCAC7<3>KRDNVEPYGSaHTcH<6>VeLVfMVfN<3>WgP\ UlQ<3>aTPcPPeKPhFPjAPn6PsANwQMnILmMKkQIjXHhcG<2>frCe\ wBezAdwD<3>acN`YP_VS<3>XJaWGcS9j<3>eMThQOkTK<2>ua7rQ\ NpEbjVUejL<3>gZJhWJhTJkOK<3>bXG`_FZaEXcDUk3<3>YP`ZKh\ WNj<4>JXoH_pEaq<3>4iu1pw<3>3_s3Vs3Rr<2>4Fp<3>8N`9PYA\ RU<3>DZF<3>aKVgHZmDbvBj<4>i7Sg6Od5K<3>W36<3>kAOp8Q<4\ >mNYmP_lS`<2>k`ekbfmbipclqdlren<3>QitGjv<4>UouXpu_qu\ <3>iuuXvvKwvJxsIyp`zFZz8 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: Re: (fractint) Branch Cuts Date: 10 Apr 2000 09:21:10 GMT >>The FractInt docs don't make this very clear, but basically, to >> take >>the natural logarithm of a complex number Z, you calculate a >> new number >>K with Re(K) = e^(Mag(Z)) and Im(K) = Arg(Z). It's this >> second part >>that introduces the multiple possibilities. > >The docs give the formula for logarithm making it clear it has >multiple values: > > log(x+iy) = (1/2)log(x^2 + y^2) + i(atan(y/x) + 2kPi) > for k = 0, -1, 1, -2, 2, ... > >However the docs don't say anything about the visual discontinuity >except that we know it is supposed to be there. The book Fractal >Creations does discuss this. No, I just ment that (unless you know about these things) it isn't all that clear that atan(y/x) is Arg(Z) and (1/2)log(x^2 + y^2) is Log(Mag(Z)). PS. Nice shortcut with the logarithm there actually... I would have taken the sqare root then the log, but your way *is* quicker! >Tim ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: (fractint) Branch Cuts Date: 10 Apr 2000 10:22:48 GMT So log(Z) is a cork screw, and you have to take a 360 degree slice of it. Hmmm... This formula (I think) varies the slice taken, but only by another 360 degrees. If k is below -3 then you get what the formula parser normally does. If you now raise k, you get a nice branch cut shift... until you reach +3, and thereafter there is no further change. Any ideas how to correct this? --BEGIN comment { Andrew Orphi Coppin, 10 May 2000AD } BrotBC = { ; Z^2.5 + C ; real(p1) = phase shift. p = real(p1) Z = C = Pixel: Z = log(Z) IF(imag(Z) > p) Z = Z + flip(2*PI) ENDIF Z = exp(2.5*Z) + C |Z| < 4 } --END ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Barry N Merenoff <110144.2274@compuserve.com> Subject: (fractint) Branch Cuts Date: 10 Apr 2000 08:31:09 -0400 Andrew, try this: p=3Dreal(p1)+PI q=3D2*PI*floor(p/(2*PI)) r=3Dreal(p1)-q Z=3DC=3DPixel: Z=3Dlog(Z) IF(imag(Z)>p) Z=3DZ+flip(2*PI) ENDIF Z=3Dexp(2.5*(Z+flip(q)))+C |Z|<4 } Note: I don't know if Fractint has a floor function, but it should have something equivalent to it. Sincerely, Collin Merenoff Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Kenneth Childress Subject: Re: (fractint) Branch Cuts Date: 10 Apr 2000 14:06:22 -0700 (PDT) Collin, > p=real(p1)+PI > q=2*PI*floor(p/(2*PI)) > r=real(p1)-q > Z=C=Pixel: > Z=log(Z) > IF(imag(Z)>p) Z=Z+flip(2*PI) ENDIF > Z=exp(2.5*(Z+flip(q)))+C > |Z|<4 > } > > Note: I don't know if Fractint has a floor function, but it should have > something equivalent to it. Is there a typo or mistake in the above? I notice that the assignment to r is never used. Ken... Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Barry N Merenoff <110144.2274@compuserve.com> Subject: Re: (fractint) Branch Cuts Date: 11 Apr 2000 01:17:41 -0400 OOPS!!! That should be IF (imag(Z)>r) Sincerely, Collin Merenoff Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 11-04-00 (The Mandelbrot Set [7]) (c) Date: 11 Apr 2000 02:51:47 -0400 (EDT) FOTD -- April 11, 2000 (Rating 7) Fractal visionaries and enthusiasts: The formula for today's fractal is -(Z)-3(Z^(-2))+C, and like most of my FOTD formulas, (Formulae is the spelling for the over-educated.), its apparent simplicity belies its potential for creating fractals. The parent fractal of today's scene is a lopsided circle with a skewed hyperbola with fractal edges inside -- a rather unpromising image. However I consider unpromising scenes a challenge, and I gladly accepted today's challenge. I named the picture "The Mandelbrot Set" after that most famous of all fractals, whose outline appears in glowing bronze at the center of today's picture. I devoted a little extra time to coloring today's image, finally working out a palette that I feel rates an honest 7. To see the above-average picture, either run the parameter file and wait 9 minutes, or download the completed image and wait one minute. That download may be found at: and at: The fractal weather today was sunny and 63F (17C), barely warm enough for the fractal cats to sneak outside. Until next time, which will really come in 22 hours, take care. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ The_Mandelbrot_Set { ; time=0:08:54.00, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=3.57871498151/1.535460434974/281530.3/1/55 params=-1/1/-3/-2/0/0 float=y maxiter=1200 bailout=25 inside=0 logmap=80 symmetry=xaxis periodicity=10 colors=000mcKphmrUZzenwjznsonkomlzmlp<11>hsugsugtv<3\ >evwKzzdwxzsUcxycyydzz<59>8Fl7El7Dl6Cl<73>328328327<\ 2>326325114<24>S6BU6BV6C<3>Z7D_BD<4>dAEeAEfAEgAEhAE<\ 7>pHEqIErJE<3>vNFwOGxPGyQG<2>zTHzUHzUKzUI<13>zUN } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: (fractint) Branch Cuts Date: 11 Apr 2000 09:16:12 GMT Thankyou people!!! I now have two working formulas: ---BEGIN MandelbrotBC = { ; Z = Z^E + C e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<4 } JuliaBC = { ; Z = Z^E + C e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q C=p3 Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<4 } ---END Plug these into the evolver, with real(p1) changing from 2 to 3 along the X axis and real(p2) changine from -6 to +6 along the Y axis and you have a real treat of an image (depending on the other parameters; I used p3=-1). Now, if I can just remember how to do that IsMand() stuff... ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 12-04-00 (Edge-on Galaxy [7]) (c) Date: 12 Apr 2000 00:22:20 -0400 (EDT) FOTD -- April 12, 2000 (Rating 7) Fractal visionaries and enthusiasts: Today's FOTD image, which was once again created by the omni- present MandelbrotMix4 formula, reminds me of a telescopic view of two overlapping galaxies, one face-on, the other edge-on. I named the picture "Edge-on Galaxy" because it is the edge-on effect that makes the picture. The iterated formula is (1/Z)+(Z^(-1.1))+(1/C), an expression that I chose purely on a whim, having nothing particular in mind. Most of the scene consists of bof61 inside fill, and the maxiter is 6000, a combination that means a slow parameter file. The most patient fractalists will run the parameter file and wait 1/2 hour to see the GIF image, which in this case is more brilliant than the JPEG image posted to: and to: Before getting to the all-unimportant weather report, I must comment on the "branch cut" formulas worked out by Andrew Coppin with help from several other list members. The formulas very efficiently do what they are designed for, and open an entire new door for exploration. When I have done a little experimen- ting with the formulas, I'll likely have a few FOTD's created by them. Now on to what you've all been waiting for -- the weather. It was cloudy and cool all day, with a temperature of 55F (13C), which was too chilly for the cats to venture out of doors. In the evening a light rain began. Now isn't that report thrilling? The latest burst of philosophy has just about exhausted itself, so there will be a short break before I return with more words of wisdom. But wise or not, I'll return tomorrow with another wonderful fractal and some notable words. Until that time comes, take care, and without fractals the world just wouldn't be the same. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Edge-on_Galaxy { ; time=0:32:02.82, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=-3.08437/8.85332/2.418791/1/80 params=1/-1/1/-1.1/0/0 float=y maxiter=6000 bailout=25 inside=bof61 logmap=87 periodicity=10 colors=0000z0<9>0z0<4>0z00z20z40z7<2>0zC0zG<3>0yO0yP\ 0yR0yT0yX0yY0y`<3>0yg0yi0ym<3>0yt0yv0yw0zr0yy0Vz00z0\ Az0It0Pk0Xd0dV0kO0rE0y70z0<11>0z0<4>0z0000<40>000<4>\ 00000200200400700700200400700700800800A00A00C00C00E0\ 0E00G00G00I00I<2>00O40M70MA0KC0KG0II0IM0GO0GP0GT0EV0\ EY0C`0Cd0Ae0Ai08k08n07p07r27v74wA4zE2zI2zM0<2>zX0<2>\ zw0zz0zz0zz0zz2zz2zz4zz7IEkIGmIGmKGmKGmMImMImMImOImO\ KmOKnPKnPMnPMnRMnRMnROnTOnTOnVMpTOn<2>TPmTPmTRkTRkTT\ iTTiTTiTVgRVgRXe<3>RYdRYdR`bR`bRb`Rb`Pb`PdY<2>PeXPeX\ PgVPgVPiTPiTPiTOkROkROkROmP<2>OnOOnOOpMOpMOyCKy8Iy7E\ y4Cy28y07z02z0 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: (fractint) Branch Cuts Date: 12 Apr 2000 09:14:55 GMT I know that Log is multivalued with complex numbers, and therefore X^Y can be multivalued... but are there any other formulas that are? I think Sin, Cos, etc are all true function even in complex space, aren't they? PS. I tell you what would be usefull in the formula parser... We have a real() function, an imag() function, but it would be nice to have mag() and arg() functions too. And if the GUI could be changed to allow the input of complex numbers in polar form... But I guess if I want that I'll have to code it myself (shiver!) ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) Branch Cuts Date: 13 Apr 2000 13:11:39 +1200 At 09:14 12/04/2000 GMT, you wrote: >I know that Log is multivalued with complex numbers, and therefore X^Y can >be multivalued... but are there any other formulas that are? I think Sin, >Cos, etc are all true function even in complex space, aren't they? > sqrt is multivalued... sqrt(x^2) = +/-x ... but of course that's x^(1/2). x^(1/3) is triple-valued (and Fractint's Newton type will help you locate them), x^(1/4) is quadruple-valued, .... Since the sine, cosine, hyperbolic sine, ... functions are periodic (the hyperbolic ones with imaginary period), their inverses are multiple-valued. Eg, sin(y)=x, Arcsin(x)=y+2n*pi but again, one can expand arcsin in terms of logs and noninteger exponents, so that's not so surprising. sin itself can be expanded without such beasties, as a series using only divisions, multiplications, and natural-number exponents. Since all of these are single-valued, a sum of such (in of course those cases where the sum exists) is also single-valued. In short, it's nonintegral exponents that give you your multiple values. If the exponent is a rational number, then its denominator (when the fraction is written in lowest terms) specifies the number of possible values. If the function has a number of such exponentiations, the multiplicity of the function is determined by the lowest common multiple of these denominators. And of course, if there are an infinite number of distinct exponents in the expansion of a function (such as those for Log, Arcsin, etc.) then there are an infinite number of "sheets in the Riemann surface" to lapse into technical argot at the end. Well, maybe not that short. Shorter: z is a complex number, n and m are nonnegative integers with no common factor, v is an irrational number z^n => single-valued z^n/m => m-valued z^v => infinitely-valued When the exponent is itself complex, consider z^(x+iy) = z^x*z^(iy) - the i rotates the graph of the function 90 degrees in the complex plane, so doesn't alter its multiplicity. Morgan L. Owens "But what's a good way of drawing a Riemann surface?" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Tim Wegner Subject: Re: (fractint) Branch Cuts Date: 12 Apr 2000 21:26:07 -0600 Andrew wrote: > PS. I tell you what would be usefull in the formula parser... We have a > real() function, an imag() function, but it would be nice to have mag() and > arg() functions too. That's not too hard, though I'd want to make sure it would really be useful. >And if the GUI could be changed to allow the input of > complex numbers in polar form That would take more work, not hard, but work. Tim Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 13-04-00 (Utter Chaos [5]) (c) Date: 13 Apr 2000 01:45:05 -0400 (EDT) FOTD -- April 13, 2000 (Rating 5) Fractal visionaries and enthusiasts: Finding some spare time this afternoon, I brought up Andrew's Branch-Cut formula to see what it can do. The first thing I noticed is that the images the formula creates extend far beyond the bailout of 4, but raising the bailout to 100 (a minor adjustment) solved this problem. Then I noticed something strangely familiar with the images the formula creates when e=2.5. I had seen these shapes somewhere before. A moment later, I recalled the default Z^2.5+C fractal, which is filled with midgets of the most extraordinary shapes. The shapes created by the new formula are identical to the various shapes of the midgets in the default Z^2.5 fractal. And not surprisingly, its close relative, the symmetrical (-Z)^2.5+C fractal, is one of these shapes. I also noticed that exponents which produce boring images with the default complex-log value become very interesting as one examines farther out the corkscrew. The formula for today's fractal is Z^1.005+C, which draws a tiny bean-shaped hole at the center of a series of concentric circles when the default log is calculated. As today's image shows, some of the other log- slices of this formula are far more interesting. This is the most unusual chaotic fractal image I have yet encountered. It is "Utter Chaos" yet with enough traces of order to produce a curiously surrealistic effect. I was a bit hasty on the coloring, so I doubt that the present palette would be difficult to improve upon. The parameter file runs unusually slowly. Only the most steadfast will fail to download the completed JPEG image from: or from: The fractal weather today was sunny but quite chilly, and tonight will see a late season frost. The temperature of 54F (12C) was too cold for the cats. With such an interesting new formula to play with, I did no pondering today. And since I'll likely be playing with the formula again tomorrow, I'll do no pondering then either. But in a few days the urge to philosophize will once again arise, and then watch out world. Until tomorrow, take care, and I wonder how many dimensions the hypercomplex-log figure exists in. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Utter_Chaos { ; time=1:21:04.48, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-0.0437149579/0.1523876687/605.378/1/4.999 params=1.005/0/15.9/0 float=y maxiter=50000 bailout=25 inside=0 logmap=1063 periodicity=10 colors=000zZKscd<13>vgivgiwgi<2>whjwhjuii<10>gmbfnad\ n`co`bo_bp`<49>TMPTLPTLP<31>FCFECFEBE<4>CCFCCFCDFCDF\ BDFBEF<7>AGF9HF9HF<3>8IFKJF<3>KKFKKFMLFOLFQLF<4>QNGQ\ NGQNG<2>QOGQPGQPIPPK<2>AQQ8RS3RU<3>2Ra2Rc2Re2Rg<2>1R\ k0Rl1Rm1Rn1Ro<3>CRsFRtIRuKRv<3>IRz7Rz<3>8Rz8Rz8Rz8Rz\ 8Rz<16>TTzUTzVTz<3>ZTz<4>MTzKTzIUz<2>AUz8Uz4Uz<6>CUz\ AUzAUzAUz } frm:MandelbrotBC {; Z=Z^E+C (formula by Andrew Coppin) e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Damien M. Jones" Subject: Re: (fractint) Branch Cuts Date: 13 Apr 2000 09:24:30 -0400 Tim, Andrew, - > PS. I tell you what would be usefull in the formula parser... We - > have a real() function, an imag() function, but it would be nice - > to have mag() and arg() functions too. You already have mag()--use cabs(). atan() is less convenient as arg() because you have to check for quadrant. Perhaps implementing atan2() like C? Or just calling it arg()? This *would* be useful, IMO. I vote for calling it atan2(), but that's the programmer in me... Damien M. Jones \\ dmj@fractalus.com \\ Fractalus Galleries & Info: \\ http://www.fractalus.com/ Please do not post my e-mail address on a web site or in a newsgroup. Thank you. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Karl Scherer" Subject: (fractint) fractals for art competitions Date: 14 Apr 2000 10:36:57 +1200 This is a multi-part message in MIME format. ------=_NextPart_000_0005_01BFA5FD.5BB71FA0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Hi Fractal friends, I have two questions today: 1. Can somebody tell me some art competitions on the net=20 - where I can send fractals (as gif files or otherwise) and - where I do not have to disclose the formula and/or give away my copyright?=20 Thanks for any help on this. 2. Does any of you guys do exhibitions with framed art work? =20 I just had two exhibitions with 100 framed fractals with lots of good = feedback=20 and quite good sales. (framed, size A2 go for US$100, size A3 for US$50) Furthermore, I now have permanent exhibitions at the Articus Cafe, Upper = Symonds Str, Auckland, NZ and at the Chess Parlour, Verrans Corner, Northshore. I would like to hear from your experiences with selling fractal art. I am trying to find a producer for a calendar as well. Any feedback is appreciated. Thank you! Karl Scherer 11 Utting Str, Auckland, New Zealand karl@kiwi.gen.nz Seen my homepage lately? http://www.kiwi.gen.nz/~karl ------=_NextPart_000_0005_01BFA5FD.5BB71FA0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
Hi Fractal friends,
 
I have two questions = today:
 
1.    Can somebody tell me some art competitions
on the net
   - where I can=20 send fractals (as gif files or otherwise) and
   - where I do not have = to disclose=20 the formula
     and/or give = away my=20 copyright? 
 
Thanks for any help on = this.
 
 
2.   Does any of=20 you guys do exhibitions with framed art work?
 
I just had two exhibitions with 100 = framed fractals=20 with lots of good feedback
and quite good sales. (framed, = size=20 A2 go for US$100, size A3 for US$50)
 
Furthermore, I now have permanent exhibitions at the Articus Cafe, = Upper Symonds Str, Auckland, = NZ
and at the Chess Parlour, Verrans = Corner,=20 Northshore.
 
I would like to hear from=20 your experiences with selling fractal art.
I am trying to find a producer for = a calendar=20 as well.
Any feedback is = appreciated.
Thank you!
 
Karl Scherer
11 Utting Str, = Auckland, New=20 Zealand
karl@kiwi.gen.nz
Seen my=20 homepage lately?
http://www.kiwi.gen.nz/~karl
------=_NextPart_000_0005_01BFA5FD.5BB71FA0-- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: John R Goering Subject: (fractint) Prime numbers and the M-set Date: 13 Apr 2000 21:23:48 -0400 Hi to all, I recently received a question concerning prime numbers and the Mandelbrot set. So, does anyone know if there is a meaningful relationship between the M-set and the prime numbers? I appreciate your help, John Ralph Visit my homepage at http://homestead.juno.com/johnrhg John Ralph H. Goering johnrhg@juno.com Jesus says, "Behold, I am coming soon!" (Revelation 22:12, NIV) ________________________________________________________________ YOU'RE PAYING TOO MUCH FOR THE INTERNET! Juno now offers FREE Internet Access! Try it today - there's no risk! For your FREE software, visit: http://dl.www.juno.com/get/tagj. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: LeeFbx@aol.com Subject: (fractint) Zoom limit? Date: 14 Apr 2000 00:00:06 EDT Hi, While using Fractint v20.0, after I zoom in about ten times or so, I seem to reach a level where the image is no longer sharply defined but just colored squares about a quarter inch or so in size. I must be overlooking something. What should I do in order to zoom to deeper levels? Thank you, Lee Fairbanks Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 14-04-00 (Silver Pilgrimage [7]) (c) Date: 14 Apr 2000 00:02:26 -0400 (EDT) FOTD -- April 14, 2000 (Rating 7) Fractal enthusiasts and visionaries: Today's fractal is another one created with the Mandel BranchCut formula, which I spent some time with today, as I expected I might do. The formula is Z^1.33+C, an extremely simple expression that works wonders when some of its more remote parts are calculated. The bud in the image is of order 1.33, which means it should have 1/3 lobe. Actually, the bud is the most perfect 1/3-lobed bud I have yet found. And those radiating branch cuts add just the touch to rate today's FOTD a stately 7. The bud in the picture is on the southeast shore of the main fractal, a lopsided bay with chaotic debris extending far into the northwest suburbs. Many smaller buds dot the shore in the vicinity. I'll investigate these smaller buds tomorrow, and if I find anything of interest that makes a presentable picture, I'll declare it FOTD for 15-04-00. I named the picture "Silver Pilgrimage" for poetic reasons rather than as a description. The slight silvery effect around the edges was all the excuse I needed. At 4-1/2 minutes, the parameter file is a welcome relief from yesterday's marathon file. And of course the JPEG'd image has been posted as always to: and to: The fractal weather, for anyone who for some reason is interested, was partly cloudy and 49F (9.5C), ideal for strenuous outside work, not so good for fractal cats, who complained as they turned back indoors. As forecast, the philosophy went nowhere today. It's simmering just under the surface however, and could erupt into a paroxysm of wisdom any day now. To see whether that day could be tomorrow, check back then, when I'll return with a new fractal and some old words. Until next time, take care, and I've never seen a real fractal -- I've seen only pictures of fractals. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Silver_Pilgramage { ; time=0:04:32.92, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=t center-mag=0.784669/-0.335969/3.197277/1/117.5 params=1.33/0/-3/0 float=y maxiter=25000 inside=0 logmap=9 periodicity=10 colors=00075B93CC7FFAHHDJ<6>MYXM`ZNc`<2>PlfPohOmg<14\ >DWfDVfCUf<2>AQf9Pf7Pe<16>YDq_Dr`Cs<3>fAu<19>mdXmfWm\ gU<3>nmQonQpoQ<3>stQtuQuvQvwQvxQ<2>hlY<3>RmfNmhImkEm\ m7mw<3>HmSKmKIm5<3>XmV_m`YmRXnHVt5Wx7<19>`QV`OW`MY<3\ >aGa<3>THeRHfOIg<3>GIj<17>cOpePqfPq<2>jQrkQrmPt<24>S\ eJReIQfG<3>NhBVfFbdIpdL<3>SXLMVLOXN<9>Zfa`gbahd<2>dk\ hfmjeli<3>aih`ih`hgaihbjickjblkaml } frm:MandelbrotBC {; Z=Z^E+C (formula by Andrew Coppin) e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Tim Wegner Subject: Re: (fractint) Zoom limit? Date: 14 Apr 2000 00:32:21 -0600 > While using Fractint v20.0, after I zoom in about ten times or so, > I seem to reach a level where the image is no longer sharply defined > but just colored squares about a quarter inch or so in size. > I must be overlooking something. What should I do in order to > zoom to deeper levels? First of all, Fractint is designed to stop you when the zoom limit is reached, but the zoom limit detection doesn't always work right, especially if the zoom box is rotated or skewed. Arbitrary precision will kick in for the Mandelbrot and a few other types and let you zoom all the way to 10^1500 or so. But for most fractal types, ten or so zooms is about the limit of double precision. Tim Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Sylvie Gallet Subject: (fractint) Pars: Nacht und Nebel... Date: 14 Apr 2000 17:38:00 -0400 Hi All, Here's some Mandelbrotmix4's. Some of them use the same parameters as Jim's "Jungle of Fractals" (Feb 25). 6041302.GIF { ; Nacht und Nebel t=3D 0:39:57= .97 ; Copyright Sylvie Gallet, Apr 14, 2000 ; ; t=3Dcalc time using a PII 300 at 1600 x 1200 reset=3D2000 type=3Dformula formulafile=3Dfractint.frm formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1 center-mag=3D-3.05548/9.30136/3.942029/1/-109.999 params=3D-1/1/2/-1.5/0/0 float=3Dy maxiter=3D2000 bailout=3D25 inside=3D= 0 symmetry=3Dnone periodicity=3D0 sound=3Doff colors=3DRRRTTT<41>FFFFFFFFF<3>DDDCCCCCC<3>888777666<3>555555555<2>555\= 555666777<18>HHHIIIIII<4>MMMMMMNNN<41>_________<4>bbbbbbccc<5>dddeee\ eeeffffff<19>llllllmmm<2>nnnnnnmmm<69>TTT } 60311002.GIF { ; . t=3D 0:47:42= .59 ; Copyright Sylvie Gallet, Apr 11, 2000 ; ; t=3Dcalc time using a PII 300 at 1600 x 1200 reset=3D2000 type=3Dformula formulafile=3Dfractint.frm formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1 center-mag=3D+2.88673055761374900/-3.59466658910688800/2.528976e+011 params=3D1/-1.5/-3/0.5/0/0 float=3Dy maxiter=3D1600 bailout=3D25 inside=3D0 logmap=3D104 symmetry=3Dnone periodicity=3D10 sound=3Doff colors=3D0A54F6<9>FU8GW9HX9<2>KaALbAOcA<4>elEhnFlpG<3>zwJ<8>zeFzcEzaE<\= 3>zUB<7>zi5zk4zm4<2>zs1zu0zu1<24>zynzypzyr<2>zyxzzzzzz<163>3E5 } 60401A03.GIF { ; . t=3D 0:24:32= .45 ; Copyright Sylvie Gallet, Apr 11, 2000 ; ; t=3Dcalc time using a PII 300 at 1600 x 1200 reset=3D2000 type=3Dformula formulafile=3Dfractint.frm formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1 center-mag=3D+72.39005639767717000/+0.00000005358312205/18109.86 params=3D1/100/-2/0.01/35/0 float=3Dy maxiter=3D1800 bailout=3D25 inside=3D0 logmap=3D47 symmetry=3Dnone periodicity=3D10 sound=3Doff colors=3D000zzz046<8>0MX<3>0Uh1Xk1Wi<8>7FM7EK8CH<2>A69B46D46<18>nAJpAK\= rAL<2>xBNzCOzDO<17>zjOzlOznO<3>zvO<22>zKPzIPzHP<3>z9Qz7Qz6Rz4Rz2Rz0S\ <25>C3AA39838<2>236045046<17>0DK0EK0EL0FL0FM<21>2Q`2Ra2Rb2Sb2Sc2Td<7\ >AYfBZfCZf<23>_kd`ldald<3>end<15>07B } 60401A08.GIF { ; . t=3D 1:01:32= .91 ; Copyright Sylvie Gallet, Apr 11, 2000 ; ; t=3Dcalc time using a PII 300 at 1600 x 1200 reset=3D2000 type=3Dformula formulafile=3Dfractint.frm formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1 center-mag=3D+72.39004428961769000/-0.00001110987082908/1.185761e+011/\= 1.0003 params=3D1/100/-2/0.01/35/0 float=3Dy maxiter=3D1800 bailout=3D2= 5 inside=3D0 logmap=3D144 symmetry=3Dnone periodicity=3D10 sound=3Doff colors=3D000<9>0KU0MX0O_<3>1Xk<5>4MX5LU5JS<3>8CH9AF98CA69B46<5>N5BP6CR\= 6D<10>m9Ko9Lq9M<2>wAOzBPzCP<16>zfUzhVzjVzlWznW<2>ztXzvYzv_<4>zwizxkz\ xm<3>zzv<9>zVbzS`zOZ<2>zFTzBRz9Q<3>z2Rz0Sx0R<24>C3AA39838<2>23604504\ 6<15>0CI0DJ0DK0EK0EL0FL<22>2Q`2Ra2Rb2Sb2Sc<2>4Ue5Ve6We7We8Xf<27>_kd`\ ldald<3>end<15>07B } 60401B04.GIF { ; . t=3D 2:29:42= .95 ; Copyright Sylvie Gallet, Apr 11, 2000 ; ; t=3Dcalc time using a PII 300 at 1600 x 1200 reset=3D2000 type=3Dformula formulafile=3Dfractint.frm formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1 center-mag=3D+72.47170030731296000/-0.04740244275976058/1503.494/1/-90 params=3D1/100/-2/0.01/35/0 float=3Dy maxiter=3D1800 bailout=3D25 inside=3D0 logmap=3D75 symmetry=3Dnone periodicity=3D10 sound=3Doff colors=3D000zzz0Sb<23>0CI0BH0BG<2>09E08D08D08D<9>059058058<2>047047058\= <15>0DK0EK0EL0FL0FM<21>2Q`2Ra2Rb2Sb2Sc2Td<9>CZfD_fE_f<13>SflTflUgmVh\ m<3>Zjo_jp`kpakqblrcmrcmr<26>HTbGSbFRa<2>CO_CNZCMX<7>BDKBBJBAH<2>B7C\ A5AB46<3>J59L5AN5B<3>T5DV5EX5E<4>d7Hf7Ih7J<3>o8Lq8Ls9M<2>x9OzAPzCP<1\ 4>zhZzjZzm_<3>zvb<2>zqazpazpb<12>www } 60401B07.GIF { ; . t=3D 2:18:43= .14 ; Copyright Sylvie Gallet, Apr 11, 2000 ; ; t=3Dcalc time using a PII 300 at 1600 x 1200 reset=3D2000 type=3Dformula formulafile=3Dfractint.frm formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1 center-mag=3D+72.47183790716201000/-0.04891345439138522/75333.13/1/119\= .999 params=3D1/100/-2/0.01/35/0 float=3Dy maxiter=3D1800 bailout=3D25 inside=3D0 logmap=3D140 symmetry=3Dnone periodicity=3D10 sound=3Doff colors=3D000000025<86>1P_1P`1P`1Q`1Qa<3>2Sc3Tc4Td<3>6Ud7Ve8Ve<26>Zlt_m\= t`nu<2>cpwcpwbov<17>NZgMYfLXe<3>IUcHTbGSb<3>CO_CNZCMX<7>BDKBBJBAH<2>\ B7CA5AB46<3>J59L5AN5B<3>T5DV5EX5E<4>d7Hf7Ih7J<3>o8Lq8Ls9M<2>x9OzAPzC\ P<14>zhZzjZzm_<3>zvb<2>zqazpazpb<12>www } 6041301.GIF { ; . t=3D 2:54:43= .98 ; Copyright Sylvie Gallet, Apr 14, 2000 ; ; t=3Dcalc time using a PII 300 at 1600 x 1200 reset=3D2000 type=3Dformula formulafile=3Dfractint.frm formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1 center-mag=3D+1.16611516126891800/+0.26169401064720740/3.96582e+007 params=3D1/1.8/-1/-0.5/0/0 float=3Dy maxiter=3D4000 bailout=3D25 inside=3D0 logmap=3D378 periodicity=3D0 sound=3Doff colors=3D000zzz05F<29>8IR8IR9JS<29>IR_JS`JS`KSaKSa<2>LTbLUbNWd<3>VclYe\= n_gp<3>hpy<4>UajQYg<32>_fp`gq`gq`hqahq<2>birbirdks<3>lsxnuzksx<3>_gp\ WdmUbl<9>COYANX8LV<2>2HR0FP0GQ<3>8NXAPZCR`<3>KZh<3>CTbASa8Q_<3>0KU<2\ >L0B<11>kCNmDOpEPrFQtGRwHS<25>xnXxoXxpYxrYxsYxtYyvZzx_<21>www } 6041307.GIF { ; . t=3D 1:07:14= .20 ; Copyright Sylvie Gallet, Apr 14, 2000 ; ; t=3Dcalc time using a PII 300 at 1600 x 1200 reset=3D2000 type=3Dformula formulafile=3Dfractint.frm formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1 center-mag=3D-1.02154424034962000/+3.34908648639290700/1.443724e+008 params=3D-1/1/2/-1.5/0/0 float=3Dy maxiter=3D2000 bailout=3D25 inside=3D= 0 symmetry=3Dnone periodicity=3D0 sound=3Doff colors=3D00PTgv<3>WiwXjwYjx<23>nwynwyoxy<3>qyyryxryxsywsyw<3>uzuuzuvzt\= <3>wztwzsxzs<4>xypxyoxynxxnxxmxxl<13>xsbxrbxraxraxr`<3>wpYwpYwoX<5>t\ lStkRsjQsiPshO<2>rgNqfMqeLpdKpcJ<4>n_HmZGlYFkYEjXD<3>hUBgTAfS9<8>_L5\ ZK4ZK4<4>UG2UG2TF1<2>QC1PC1PB1OB1NA1<8>H60G50F40<2>E41D31D32C22C22<2\ >A12913913814814<3>606506507<2>307308208209209<7>12D12E02E<3>03H03I0\ 3J<3>05L06M06N<3>28R29R29S<2>2BU3CV3DX<7>7Jb8Kc8Ld<3>ANfBNgBOg<6>GTm\ HUnHVn<3>LZqM_rM`r<3>PctPcuQduQdvRevSfv } 6041403.GIF { ; . t=3D 0:57:25= .08 ; Copyright Sylvie Gallet, Apr 14, 2000 ; ; t=3Dcalc time using a PII 300 at 1600 x 1200 reset=3D2000 type=3Dformula formulafile=3Dfractint.frm formulaname=3Dmandelbrotmix4 function=3Dident passes=3D1 center-mag=3D+2.53408422974110600/-5.58614796935317300/786.2559/1/105 params=3D1/0.55/-1/0.65/8/0 float=3Dy maxiter=3D5000 inside=3D0 logmap=3D74 symmetry=3Dnone periodicity=3D0 sound=3Doff colors=3D000`NC<22>rgOshOsiP<3>wmRxnRxoSypSzqT<3>xoPxnOwlN<4>qeIodHnbG\= <2>jZDiXCjYE<23>vtpwuqwvs<2>yyxzzzyxx<14>bSNaQL_NI<2>WHBUE8UF8<4>ZLC\ _ND`OE<3>cTHcUIdVJ<11>oidpkeqlgrnisoj<2>vspwurvsp<2>pkinhfmfclda<8>W\ KFUHDSFA<2>M83K50K50<8>RA9SAASBB<5>XEHYFIZGJ_HK_HK<4>cLPdMQdNR<2>fQT\ gQUgRUgRV<59>zzw } frm:MandelbrotMix4 {; Jim Muth a=3Dreal(p1), b=3Dimag(p1), d=3Dreal(p2), f=3Dimag(p2), g=3D1/f, h=3D1/d, j=3D1/(f-b), z=3D(-a*b*g*h)^j, k=3Dreal(p3)+1, l=3Dimag(p3)+100, c=3Dfn1(pixel): z=3Dk*((a*(z^b))+(d*(z^f)))+c, |z| < l } Cheers, - Sylvie Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 15-04-00 (Midget Madness [4]) (c) Date: 15 Apr 2000 01:49:00 -0400 (EDT) FOTD -- April 15, 2000 (Rating 4) Fractal visionaries and enthusiasts: Today's picture shows what happens when a midget goes totally mad. To begin, no midgets should exist in the Mandeloid of order 1.15. This holds true however only in the default section of the entire spiral figure. As we examine ever farther out the spiral, the little default jelly-bean blossoms into figures of the most extraordinary shape. And it is in these far-out slices that the unexpected midgets lurk. Most of today's picture consists of branch cuts radiating from the midget, which actually rather resembles a Julia midget. In fact, in some areas of the parent fractal the cuts become so numerous that they determine the actual image more than the iteration bands. Since discontinuities are not all that interesting, I could rate the image no higher than a 4. I named the picture "Midget Madness" when I was struck by the disorganization of the scene. And yes, smaller midgets do exist in some of the fragments scattered around the area. I might show one of these smaller midgets tomorrow, but more likely I'll return to the MandelbrotMix4 formula for some more good old quadratic midgets. At 8 minutes, the parameter file of today's image is a bit slow. Things can be speeded up quite a bit by downloading the JPEG'd image file from: or from: And now, on to what you've all been waiting for -- the fractal weather report. Mostly cloudy and 60F (15.5C) describes the day fairly accurately. The temperature was a bit chilly for the fractal cats, but they did manage to have a 15-minute romp on the porch. As I feared it might, the philosophy went nowhere today, so I'll try again tomorrow. Until then, take care, and take it easy. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Midget_Madness { ; time=0:06:08.60, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-1.5935665488/-3.77571428/160509.4/1/-80 params=1.15/0/23.74/0 float=y maxiter=12000 bailout=25 inside=0 logmap=120 periodicity=10 colors=000afzbfz<2>igzkgznizoizrizzszsiziawfZueYrcVq\ bUn_RkZQjYNgXMeVJcSIaRFZQEYOBVMASK7RJ6OI3MD0HH2K<2>O\ KURQXUXZYbb_gebngeskgznizsjzqjzn<3>jkcjgajeZ<3>kQOkM\ MkIJkEHzDIkBFYBEIBD07E3BB4E86H67J3AM0BO0DR0BV0<3>MQ0\ OO0RO2UN4XM6ZK7aJAcJB<3>nEIqDKsDMvBNyAQz8Rz7SVE8z7Uz\ ASzBRzDRzEQzFOzIOzJNzKNzMMzNKzOKzRJ<2>zVHzXHzZF<2>zb\ DzcDzeBzgBziAzj8<2>zn7ykYuivqfumcsiaseZraYqYXqUVoQUo\ MSnIcmEomAmk8ij8fj8bi8ag8Zg8Xf8Ve8Ue8Uc8UcBXbEYbH_aI\ aaKcaNe_Qg_RiZUkZXmZZoY_qYbsXeuXeyYfvXfsVfrU<3>fiOgg\ NgfMgfM<2>gfIgfHifFifEifDifBifB<3>jf6jf4jf3jf2jf0mf0\ kf0jf0jf2if4gf7gf8ffBefEefFcfIbfKbfMafO_eR_cSZbVYaYY\ _ZXZaV_cVbeUcgSfjSgkRjnQkqQnrOouOqvNruMsuKsu<3>IsuHs\ uFsuFssEssDssDssBssAssAss8ss7ss2su4ss<3>Fsq6sz<3>Fsz\ IszJsz<6>Zsz } frm:MandelbrotBC {; Z=Z^E+C (formula by Andrew Coppin) e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Damien M. Jones" Subject: Re: (fractint) fractals for art competitions Date: 15 Apr 2000 23:07:51 -0400 Karl, - 1. Can somebody tell me some art competitions on the net - where I can send fractals (as gif files or otherwise) and - where I do not have to disclose the formula - and/or give away my copyright? Well, there's always the "big" fractal contest, held in late summer/early fall. The web site for this year's contest will be www.contest2k.com, and I expect more details of the contest will be posted there within six weeks. - 2. Does any of you guys do exhibitions with framed art work? There are several fractal artists who do exhibitions, yes. I dare not name names because I'm sure I'll leave someone out who'll be disappointed that I forgot. (Working a few sixty-hour weeks has played havoc with my memory. I'll be OK after some time off, though.) - I just had two exhibitions with 100 framed fractals with lots of - good feedback and quite good sales. Wow, that's great! I always like to hear of people selling fractal artwork. Damien M. Jones \\ dmj@fractalus.com \\ Fractalus Galleries & Info: \\ http://www.fractalus.com/ Please do not post my e-mail address on a web site or in a newsgroup. Thank you. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 16-04-00 (Square-Root of Two [5]) (c) Date: 16 Apr 2000 01:04:17 -0400 (EDT) FOTD -- April 16, 2000 (Rating 5) Fractal enthusiasts and visionaries: With today's FOTD we come to the end of my current obsession with the BranchCut formula and the weird images it draws. Tomorrow we'll return to my obsession with the MandelbrotMix4 formula and the weird midgets it draws. I named today's picture "Square-Root of Two" because the formula behind the image is Z^(sqrt(2))+C. The parent of today's midget is a distorted Mandeloid with a prominent negative tail trailing off in a northerly direction, and a prominent triangular bud set off by a well-defined Seahorse-type Valley. Today's scene lies in the west branch of this valley. Once again, the image is composed of many discontinuities radiating from the tiny central, almost-formless midget, though in today's picture the fragmented features in the discontinu- ities are far better defined. The parameter file takes over 6 minutes, making the download the better choice. That download may be found at: and at: The weather today was boring -- cloudy with occasional light rain -- totally unworthy of being mentioned in a FOTD discussion. And I have no idea why I continue mentioning it. The temperature of 60F (15.5C) was unworthy of a day in April. The fractal cats, being noble creatures, refused to go out into the unworthy conditions, spending the day lying on their backs on the carpet with all eight feet in the air. Once again today I failed to philosophize, but tomorrow will be another day, (it always is), and I'll have another chance to show my philosophical insight, (if I have any). So check in then. If you find no philosophy, you'll at least find a nice one-layer fractal. Until then, take care, and how can there be a picture of a fractal that isn't there? Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Square-Root_of_Two { ; time=0:06:18.94, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=t center-mag=-0.029545181/0.771836852/227204.5/1/34.999 params=1.4142/0/0/0 float=y maxiter=2000 bailout=25 inside=0 logmap=139 symmetry=none periodicity=10 sound=off colors=000JCSJCS<3>NK_OMaPOc<2>SUiTWjTYjR_jPakNbkKbm\ <7>LXcLWaLV`<3>MRWMPVMOUMMVMKS<3>MCNMALM9KM7JM4IN1GN\ 0FN4ENDD<3>NA8N97N85<2>N52K40N51<3>W9BYAD`BGcCIfDKhE\ NlFP<3>uJZwKayLczLdzLezMdzNd<3>wPdvQduRd<8>pXcoXcoYc\ oZc<19>fkbelbelb<3>cobeqa<16>HKmGInEGo<3>99q<13>TCSU\ CQWCO<2>_CI`CH_BG<35>ij_ik_il`im`jnajoajobjobkoa<33>\ lo5lo4lo3lo2lo1<2>lo0loRloUloY } frm:MandelbrotBC {; Z=Z^E+C (formula by Andrew Coppin) e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Barry N Merenoff <110144.2274@compuserve.com> Subject: (fractint) Zoom limit? Date: 16 Apr 2000 18:38:58 -0400 Try forcing arbitrary precision. This is explained under command- line parameters. Sincerely, Collin Merenoff Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 17-04-00 (Stormy Minibrot [8]) (c) Date: 17 Apr 2000 00:55:51 -0400 (EDT) FOTD -- April 17, 2000 (Rating 8) Fractal visionaries and enthusiasts: With today's lurid scene, we return to the MandelbrotMix4 formula and the endless variety of midgets it creates. The mathematical expression that draws today's image is (Z^1.1)-(Z^(-1.11))+C -- another whimsical invention of mine that does more than one might suspect. Yes, when I enter parameters into the M-Mix4 formula, I often turn off my mind (an easy task) and let my fingers strike whatever number keys they will. I find this method to be about as effective and far faster than thinking about possible parameters before striking the keys. Today's parameters were found this way. I named the picture "Stormy Minibrot" when I noticed that the dark areas around the edges looked rather like storm clouds, which are nearby this evening. A bit of color tweaking and a trip through a graphic program completed the effect. I consider the picture to be the best in several weeks -- well worth the superior rating of 8. At just under 7 minutes, the parameter file is a bit on the slow side, making the relief of a download worth considering. That download may be found at: and at: The fractal weather was perfect today. After a brief morning shower, it turned sunny and warm for the rest of the day, with an afternoon temperature of 82F (28C), which brought the cats out doors. Tonight we have lightning in the north and an occasional rumble of thunder, but it's still calm and warm here at Fractal Central. Well, I see the lightning has now spread to the west as well. I guess that's a sign to shut down the fractal factory and call it a night. Until tomorrow, take care, but don't take so much care that life stops being fun. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Stormy_Minibrot { ; time=0:06:54.20, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=-0.40374468230415920/+2.08435374453009100\ /2.657595e+010/1/-132.5 params=1/1.1/-1/-1.11/0/0 float=y maxiter=1200 bailout=25 inside=0 logmap=142 symmetry=none periodicity=10 colors=000701902A13023134444766A76C87G97IA8MB9OC9SEA\ UFAYGBZGB`HCaHCcHEeIEgIFhKGjKGkLHnLHoLIqMIsMKuNKvNLw\ NMwOLwQKwTIwWHw_GwaFweEwhCwjB<2>wt8ww7xz4<3>ut9tsAsp\ BsnCqmEpjF<2>neImcKmaKk`LjZMjWNiVOhTPgSQgPSfNTeMUeKV\ cIWbGYbFY`GW<3>SHTPHTOHSMIQKIQHIPFKOCKOAKN9KN<2>BMLC\ NLENKEOKFOKGPIGQIHQHISHISGKTG<3>MVENWEOWCOYCPYCQZBQ_\ BS_A<3>Ua9_McZOaZP_j_ajbYjeUjhPjjMhhKgfIfeGebFfcFcaE\ a`E`ZCZYCWVBVUBTTASQAPP9NN9MM8KL8HI8GH7EF7CE6AB68A47\ 94473263132022000012034<3>3EF4GI6KL7MN9OQAQTBUVCWZEZ\ `F`bGcf<2>KjmG33F88ECBCHFBMKAQN9VQ8_V7cZ6ha4mf3qi0yk\ 3vm<2>AmmCimGgnIcnLanNanPanTbo<2>_coacoecqceobenbema\ fj<2>`gf_ge_hcZhaZi`Yi_YjYWjWWkVVkTVmSUmQ<2>ToMhoWxo\ f<2>0qM0qN0sO<2>1tQ1uQ2uS<3>3wV4xV4xW6yY<3>8z_8z`6z_\ <2>Az`Vz0Sz0Nz0Iz0Fz0Az1 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jean-Pierre Louvet" Subject: (fractint) Fractal Art FAQ Date: 17 Apr 2000 14:30:07 +0200 Version 0.3 of the draft is now on the server (a few changes in the text, and a better layout: needs font Trebuchet and CSS). http://www-hs.iuta.u-bordeaux.fr/f-art-faq/ Your collaboration is always expected. J.P. Louvet | Phone : (33)05-56-84-58-35 IUT Universite Bordeaux 1 | 33405 Talence CEDEX France | email : louvet@hse.iuta.u-bordeaux.fr Fractales sur serveur Web Universite Bordeaux I : http://www.cribx1.u-bordeaux.fr/fractals/ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jean-Pierre Louvet" Subject: Re: (fractint) Fractal Art FAQ Date: 17 Apr 2000 18:15:04 +0200 I apologize. The default page of the faq was corrupted. Now it's good. http://www-hs.iuta.u-bordeaux.fr/f-art-faq/ J.P. Louvet | Phone : (33)05-56-84-58-35 IUT Universite Bordeaux 1 | 33405 Talence CEDEX France | email : louvet@hse.iuta.u-bordeaux.fr Fractales sur serveur Web Universite Bordeaux I : http://www.cribx1.u-bordeaux.fr/fractals/ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 18-04-00 (Jaws [5]) (c) Date: 18 Apr 2000 00:30:27 -0400 (EDT) FOTD -- April 18, 2000 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal has bite to it. The red triangular features remind me of shark's teeth, making the name "Jaws" a natural. The formula behind the image is -4*(sqrt(Z))-4*(1/sqrt(Z))+1/C -- another of those surprisingly simple expressions I so enjoy investigating. Actually, I had one of my better fractal days today, finding several images worthy of the lofty status of FOTD. I also had some success combining elements of the Branch-cut formula with the M-Mix4 formula, but the combination needs further work before it becomes usable. Fractint also needs about three more variable parameter entries for type=formula, but that's another problem. The parameter file of today's image runs in under 5 minutes. If that is still too slow, the image has been posted to: and to: from where it may be downloaded with a minimum of effort. The weather was cloudy, cool, dreary and rainy today. The wetness and temperature in the mid 40's (around 7C) kept the cats sung inside. Since all my spare time was devoted to fractal work, I have no philosophical wisdom to impart at this time. I'll try again tomorrow. Until then, take care, and be courageous when your fractal disappoints. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Jaws { ; time=0:04:56.06, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=+0.11569020706787590/+0.04430017102855769\ /1.427953e+009/1/72.499 params=1/0.5/1/-0.5/-5/0 float=y maxiter=1200 bailout=25 inside=0 logmap=88 symmetry=none periodicity=10 colors=000X04X04k04x04z04z05z05<3>d06Z06S08M08G08A0A\ 40B00J00Q00X82dH2kP4qW4xQ2wM2sH0oD0k80f40d25b2Bb2Gb2\ Mb2Qb2Wb2_a2ea2la2ta2za2za2za5zX6zU8wSAqPBkMEfJGbGHZ\ DJUAJQ6JM4JJ8JHDJKHX_K_bPbdTefWhh_kkdmlhpokspovssxtv\ wsmvsfts_sqTqqMpqEoq6koAfmDdlG_iJXhMTfPQeQUdWZb_baef\ _iiZomXsqWxvUzzTzzSz<2>zXzzZvz_qzamzbkzef<3>zkQzlMzm\ JzkJziJxfJteJpbJkaJfZJaXJXUJTTJNQJJPJENJJSNMUQPZT<3>\ alddofhsikvlmzo<3>zzzzzzzzwzzqzzlzzfzzb<2>zzMzzGxzBx\ z5xz0xz0xz0vp2tXGsDTq0dt0av8_wGXxNWzUTz_SzfPzmNztKzz\ JzzHzzEzvDtqBplAkf6fb5aX4XT2SN0NH0HD0D60820E80JE0PK4\ TQ6ZWAbaEhfH<2>vwQzzT_mA8_0SWAiSSzPh<2>mvBltGlsJlsMl\ qPlqSlpUloXloalmd<2>lkllkoliqlitbewTaxJZz8Uz0Sz0Uz0X\ z2_w4av5ds5fq<2>AmkBpiBqhGpf<3>UkeXieahe<2>kddobdqbd\ ddkSdqEex0ez2dz4bv4ap5_l5_f6Zb6XX8WX8WX4XX4XX4XX } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Andrew Coppin" Subject: (fractint) Branch Cuts (what else?!?!) Date: 18 Apr 2000 13:03:47 GMT A big thankyou to all those who helped me with the multivalued-log formula. And thanks Jim for a few rather nice FotDs with it. I would be very interested to see it combined with your Max4 formula (I really haven't got a clue how that thing works, but it's very cool) I suspected that you might find interesting things by moving the function domain... ...But the *real* reason for my wanting to create this formula was for amination... I'd like to animate the branch cuts. If I come up with anything good I'll post it to my web site (if I can get it here on disk!) I'm also going to look at the multivalue properies of the inverse trig and hyperbolic functions... Thankyou Morgan for pointing that out (I should have realised myself, but I'm thick) PS. Everyone says that FractInt should have more formula parameters; it's perhaps the most requested feature aside from true colour... And yet it doesn't happen. Is this just lack of time or is there some fundemental barrier here? ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jean-Pierre Louvet" Subject: (fractint) New: Fractal art FAQ 0.3a Date: 18 Apr 2000 16:03:17 +0200 Version 0.3a is on the server. Some text is added or modified. I have made changes in the layout because I have discovered yesterday that Netscape and IE don't handle tables in the same way. If you use Netscape you will see the change if you compare with version 0.3 (I hope that the corrupted default page which was on the server yesterday for several hours is not hidden in some cache). Some changes also in the style sheet to override some problem with Netscape (however a little problem remains in the legend of one figure). If you experience difficulties you can avoid the default page by going directly to contents.html. http://www-hs.iuta.u-bordeaux.fr/f-art-faq/ J.P. Louvet | Phone : (33)05-56-84-58-35 IUT Universite Bordeaux 1 | 33405 Talence CEDEX France | email : louvet@hse.iuta.u-bordeaux.fr Fractales sur serveur Web Universite Bordeaux I : http://www.cribx1.u-bordeaux.fr/fractals/ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) Branch Cuts (what else?!?!) Date: 19 Apr 2000 02:50:50 +1200 At 13:03 18/04/2000 GMT, Andrew Coppin wrote: > >...But the *real* reason for my wanting to create this formula was for >amination... I'd like to animate the branch cuts. If I come up with anything >good I'll post it to my web site (if I can get it here on disk!) > I've already dickered a little with that idea myself - nothing pretty: just somethign to get an intuitive idea of what's going on. Changing the argument is equivalent to a rotation of the cut about the origin; going from 0 to 2pi sees the cut sweeping around, with the fractal winding up (!) upside down from where it started. Another full rotation gets it back to where it started. Needless to say, of course, that we're talking fractals here, so the visible behaviour is a bit more complicated than this. >I'm also going to look at the multivalue properies of the inverse trig and >hyperbolic functions... Thankyou Morgan for pointing that out (I should have >realised myself, but I'm thick) > Only a victim of coincidence - I just happened to be mucking around with them and their Reimann sheets for another reason at the time. This thread has helped me with a few more ideas in return. >PS. Everyone says that FractInt should have more formula parameters; it's >perhaps the most requested feature aside from true colour... And yet it >doesn't happen. Is this just lack of time or is there some fundemental >barrier here? > There is indeed a fundamental barrier. No matter how many knobs and buttons are added to Fractint, there'll always be something else that someone wants to twiddle. And the more knobs and buttons there are, the more ideas for twiddly bits there seems to be! Morgan L. Owens "'A _bit_ more complicated'? Oooh...." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Tim Wegner Subject: Re: (fractint) Branch Cuts (what else?!?!) Date: 18 Apr 2000 17:57:51 -0600 Morgan wrote: > There is indeed a fundamental barrier. No matter how many knobs and buttons > are added to Fractint, there'll always be something else that someone wants > to twiddle. And the more knobs and buttons there are, the more ideas for > twiddly bits there seems to be! Actually we are more than happy to respond to specific requests for new features. We do have limited time, but if something makes sense to us, and the proposal is well thought out, and it looks feasible, we'll do it, sometimes suprisingly quickly. I haven't been reading the messages closely. We were discussing mag and arg parameters, and also atan2. I didn't get a clear consensus from that discussion. If someone would care to state a proposal, or upload it to the wishlist, or both we could have a look. Tim Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JWeaver285@aol.com Subject: (fractint) 3D Star Par Date: 18 Apr 2000 22:21:51 EDT Hi all, I hope this works correct. If so enjoy the cycle,,,,,only slow it down a lot! :) Take care~ Jim Weaver _____________________________ StarBK3D.gif { ; generate and save this image first.... ; image(c)2000 Jim Weaver reset=1960 type=mandelcloud passes=t center-mag=-0.33415666398458920/-0.11654631378666610/0.9733577/1.5407/67\ .148/-14.814 params=75 float=y maxiter=20000 colors=000pX4<9>xn7yp8yqAyqCyqD<13>sqknsqprq<8>CCs<4>88b88Z77U<3>2260000\ 00<8>10`20e000kkkD7g<3>xbz<9>51U<5>64565885B<37>wowxsx<13>A00<15>m00o00o\ 03<14>z0z<2>z0oz0kz2i<3>wDa<16>ZDm<4>IBs03w<8>0Bb1B`3BZ<12>O53Q40R50<18>\ mQ3nR3nS3oU3pW3 } Star3D.gif { ; this should turn StarBK3D into somethin' cool(CYCLE IT) ; image(c)2000 Jim Weaver 3d=yes filename=starbk3d.gif scalexyz=100/100 roughness=150 waterline=0 transparent=0/1 ambient=20 rotation=70/45/0 perspective=100 xyshift=0/0 colors=@jc216.map } Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JWeaver285@aol.com Subject: (fractint) 3D Star Par Date: 18 Apr 2000 22:21:51 EDT Hi all, I hope this works correct. If so enjoy the cycle,,,,,only slow it down a lot! :) Take care~ Jim Weaver _____________________________ StarBK3D.gif { ; generate and save this image first.... ; image(c)2000 Jim Weaver reset=1960 type=mandelcloud passes=t center-mag=-0.33415666398458920/-0.11654631378666610/0.9733577/1.5407/67\ .148/-14.814 params=75 float=y maxiter=20000 colors=000pX4<9>xn7yp8yqAyqCyqD<13>sqknsqprq<8>CCs<4>88b88Z77U<3>2260000\ 00<8>10`20e000kkkD7g<3>xbz<9>51U<5>64565885B<37>wowxsx<13>A00<15>m00o00o\ 03<14>z0z<2>z0oz0kz2i<3>wDa<16>ZDm<4>IBs03w<8>0Bb1B`3BZ<12>O53Q40R50<18>\ mQ3nR3nS3oU3pW3 } Star3D.gif { ; this should turn StarBK3D into somethin' cool(CYCLE IT) ; image(c)2000 Jim Weaver 3d=yes filename=starbk3d.gif scalexyz=100/100 roughness=150 waterline=0 transparent=0/1 ambient=20 rotation=70/45/0 perspective=100 xyshift=0/0 colors=@jc216.map } Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 19-04-00 (Four of Clubs [6]) (c) Date: 19 Apr 2000 00:32:38 -0400 (EDT) FOTD -- April 19, 2000 (Rating 6) Fractal visionaries and enthusiasts: When I saw today's picture I immediately noticed the four black club-like appendages overlaid by almost painfully brilliant red. I immediately named the picture "Four of Clubs". The formula behind this scene is once again Andrew's MandelbrotBC, analyzing the remote parts of the parent Z^2.003+C figure. This parent image appears as a normal Mandelbrot set rotated 135 degrees CW. The discontinuity at first escapes notice, but it is there, coming in from the right and intersecting the period-5 bud that lies on the SE shore of the main bay. I examined the area of the intersection to find today's image. Once again I found many discontinuities in the area, and also some rather interesting midgets, one of which I captured and saved for posterity as today's FOTD. The value of 800 assigned p2 is most likely excessive. It exists because I found the image with the evolver set to a range of + or - 1000. In all likelihood, a similar image exists far closer to the default log slice. The 20-minute parameter file is too slow for casual fractaling. I strongly recommend a download of the JPEG image from: or from: For those who actually care about such things, the fractal weather today was continued cool and rainy, with a temperature of 44F (6.5C) that kept the fractal cats safely indoors. The philosophy suffered today as I continued trying to combine the Branch-cut and MandelbrotMix4 formulas without sacrificing the flexibility of either. It might not be possible without additional parameter entries for type=formula, but I'll keep at it. Who knows, I might even find a way to do it. But for now it's time to shut down the fractal machinery and shutter the fractal shoppe for a day or so. Until then, take care, and beware of get-rich-quick multi-level fractal schemes. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Four_of_Clubs { ; time=0:20:03.26, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-0.53234200327165420/-0.02047375192287425\ /1.285565e+010/1/-67.5 params=2.003/0/800/0 float=y maxiter=4500 bailout=25 inside=0 logmap=575 symmetry=none periodicity=10 colors=000LeJ<11>PWHQWHQVH<2>RSHRSHTTL<4>bX`dYcfYf<3\ >n`s<4>TanPamLal<3>4ai<3>AgaCh`DjZ<2>InTJoSKnT<9>TkX\ TkXUkY<2>XjZXjZ_kR<2>im1<18>mM5mL6mJ6mI6<3>pC7qA7r97\ s76<3>wB7xC7yD8<3>zG8zH8yI9<8>pPAoQAnRB<3>jVBlWC<20>\ HB5GA5E94D84B74A64<2>936937948958<3>9CC9EC9GD9IE<5>9\ PJ9QK9RK<2>9UN9VO7VM<15>Ybm_coacqbdrddtfevfewgew<2>i\ Rv<9>mTwmTwmUw<12>rUyrUzrUz<5>uUzvUzvUz<3>yUzzUzzUz<\ 5>zUz } frm:MandelbrotBC {; Z=Z^E+C (Formula by Andrew Coppin) e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Khemyst@aol.com Subject: (fractint) easter egg Date: 19 Apr 2000 00:51:19 EDT Happy Easter all. Easteregg { ; Mods to Moire Mask ; Easter Egg (C) 1999 P. Kyle reset=1960 type=formula formulafile=frac_ml.frm formulaname=ca10-08 center-mag=-7455.29/-7455.39/0.0001798271/1/44.999 params=0.1300804/0/2.71828182845905/0.01 float=y maxiter=647 inside=maxiter outside=real logmode=fly potential=255/334/0 invert=6/0/0 colors=110<46>00z<30>112110332<30>zzz<30>222000002<30>00z<30>002000110<4\ 6>zz0 } Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Fernando Henrique Bresslau" Subject: (fractint) disk rendering for tesseral Date: 19 Apr 2000 11:52:21 -0300 Hi, all! I´m happy to tell you that I´m having a little (5 images) exhibition at my university next week. I´m rendering 4000x3000 images to print them in A4 paper in 300 dpi. The only image I can´t render is a midget which uses tesseral and fill collor=0. The proble is that, above about 2048x1536, the fill color parameter is overidden. the disk/ram video modes I inserte in fractint.cfg symply copying an already existing disk/ram video mode and changin the resolution. Can anybody help me out? I have an ancient samtron 14´´ SVGA Monitor, and an onboard 4 megs AGP sis videocard in my PII300/64MB RAM. Thanks a lot, Fernando __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.yahoo.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Fernando Henrique Bresslau" Subject: (fractint) The Par file Date: 19 Apr 2000 11:58:56 -0300 I think I ought to shave sent the pars... tesseral { ; ; ; This image was generated in a PII300 64MB RAM ; Apr 19, 2000, 11:45:21 calctime 0:00:07.80. ; Paste left by Fernando Bresslau bresslau@ozdobe.org ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=fractint.frm formulaname=mandelbrotmix4 function=sin passes=t center-mag=-1.01781036168132900/+0.88593235071707930/10752.69 params=-4/-2/-3/-1/0/0 float=y maxiter=2000 fillcolor=0 inside=0 viewwindows=4.2/0.75/yes/683/512 sound=off colors=000zP0<7>aP5ZP5WP6<3>JP8FQ9CQ7<3>0P0<4>1VD1WF2YI<3>3aS3bV4dY4e`4f\ c<3>LlTPmQUnN<3>itBmv8rw6vy3zz0<4>ye1ya1yY1<3>xH2<9>N61J51F41<3>000<4>00\ 0<2>000<3>D08H0AJ09<4>Y0Q_0Tb0W<2>k0fn0io4j<3>rLosPpsUq<3>wiuxmvyrxyvyzz\ z<4>bbfYYbTTZ<2>FENA9J7AI3AH0BG<3>0DJ0EK0EL0FM<4>AAIC9HE8H<3>M4DO3CQ2CS1\ BU0A<4>LBLJDNIFQ<3>BNY9P_8Rb6Td4Vf<42>jpbkqblqb<3>ptbqubrubsvbtwb<2>xyjz\ zmzzj<7>zzLzzHzzE<2>zz4zz0zx0<5>zj1zh1zf1<5>yS3 } __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.yahoo.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) disk rendering for tesseral Date: 20 Apr 2000 10:01:01 +1200 At 11:52 19/04/2000 -0300, you wrote: >Hi, all! >I=B4m happy to tell you that I=B4m having a little (5 images) exhibition at= my >university next week. I=B4m rendering 4000x3000 images to print them in A4 >paper in 300 dpi. The only image I can=B4t render is a midget which uses >tesseral and fill collor=3D0. The proble is that, above about 2048x1536,= the >fill color parameter is overidden. the disk/ram video modes I inserte in >fractint.cfg symply copying an already existing disk/ram video mode and >changin the resolution. Can anybody help me out? I have an ancient samtron >14=B4=B4 SVGA Monitor, and an onboard 4 megs AGP sis videocard in my= PII300/64MB >RAM. >Thanks a lot, >Fernando > It may be that the disk/ram "video" mode is rendering your image in one-pass mode, because this would cause the least wear and tear on a hard disk. (I don't know how all those numbers work, either, but would like to 'cos I find this a drawback as well.) One suggestion for a workaround is that you use Fractint's ability to render an image in chunks and then reassemble them. (2000x1500 just fits within the limits you give). Hitting F1 from the Save Parameters screen and scrolling down will describe how to save an image as multiple parameter entries. Beware that the centre lines of the reassembled image will be _two_ pixels wide instead of one. That's because these are the boundaries of the chunks. Fortunately, the lines would have been there anyway if the whole 4000x3000 image had been rendered in one go, just thinner. At 300dpi, though, I don't think many people would notice if you touched it up slightly and deleted the excess by hand prior to printing. Morgan L. Owens "No - it's not a disk. I'm using RAM. Can't you tell?" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: Re: (fractint) disk rendering for tesseral Date: 19 Apr 2000 19:34:02 -0500 Morgan wrote: > It may be that the disk/ram "video" mode is rendering your image in > one-pass mode, because this would cause the least wear and tear on a hard > disk. (I don't know how all those numbers work, either, but would like to > 'cos I find this a drawback as well.) If the video mode goes above 2048 in either the X or Y direction, one-pass mode is forced. This is due to a buffer size problem with the solid-guessing logic. I'll have to check if tesseral and boundary trace have a similar problem. Jonathan Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Jonathan Osuch" Subject: Re: (fractint) disk rendering for tesseral Date: 19 Apr 2000 20:57:26 -0500 > I'll have to check if tesseral and boundary trace have a similar problem. Yes, tesseral has the same buffer size problem that solid-guessing has. The boundary trace method doesn't, however. So we should be able to make it work with a resolution greater than 2048. BTW, the buffer size problem is not insurmountable. But, it will end up going away when we port to a 32-bit environment. Jonathan Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Fernando Henrique Bresslau" Subject: Re: (fractint) disk rendering for tesseral Date: 19 Apr 2000 23:02:14 -0300 thanks to you all, I got it solved the problem with less resolution. It still looks very nice! But the answers will help me a lot in the future. Fernando Bresslau __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.yahoo.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 20-04-00 (A Blown-up Midget [6]) (c) Date: 20 Apr 2000 00:42:53 -0400 (EDT) FOTD -- April 20, 2000 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal is a true blast from the past. It's a blast because it shows a midget caught in the act of exploding, and it's from the past because it first appeared on the Fractal-art list way back on May 9, 1997, in the very early days of the FOTD. I notice from the reset=1821 in the parameter file that the image was calculated by the version of Fractint that came packaged with the second edition of "Fractal Creations", a fine book on fractals, authored by our own Tim Wegner, supreme moderator of the Fractint list. As one might suspect, I spent a bit of time this afternoon browsing through those old FTOD's. I was surprised at how fresh some of the oldies still look. I'll repost the best of them occasionally. I named today's picture "A Blown-up Midget" because that name quite accurately describes the scene. Not only is the midget blown-up by a magnitude of many millions, it also appears to be caught in the act of exploding. The expression behind the explosion is a very simple Z^1.6+C, which has been calculated by the built-in manzpower formula. The blast takes 18 minutes, so I'd recommend downloading the JPEG image from: or from: unless you want to risk blowing your top while you wait for the parameter file to run. The fractal weather was cloudy and chilly in the morning followed by sunny and mild in the afternoon. The temperature of 66F (19C) was just warm enough to lure the fractal cats onto the porch, where they perused the area for over an hour. The day was somewhat busy, leaving me little chance to ponder the deep mysteries of existence. But another wave of wisdom is building, and when it arrives the world will be that much the better. Until next time, take care, and a fractal a day keeps the blues at bay. Jim Muth jamth@mindspring.com START 20.0 PARAMETER FILE================================== A_Blown-up_Midget { ; time=0:18:52.12, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=1821 type=manzpower center-mag=-0.14024593128696220/+0.75429553466197400\ /2.374374e+007 params=0/0/1.6/0 float=y maxiter=4800 inside=0 logmap=yes colors=000AmL<10>7WT7VT7TU<2>6PW6NX4LY<6>IRWKSVMTV<2\ >SVUUWUXUS<12>HkkGlmEmn<3>Art<5>9gv8ev8dv<3>8Yw<3>Sh\ mXkjamhfpekrc<3>pnp<3>TZeZjp<2>03E<3>AGACK9FN8HQ7JT7\ C94<3>IAUJA_F6hKAePBd<2>MHa9UW<3>7cR6eQ5gP3jN<12>OeQ\ QeQRdQ<2>WcRYcRaeP<10>FMfDKhBJi<3>3Co<7>NOZQPXSQV<2>\ _VPaWNfZK<10>IKUGJVEIW<2>7EZ5D_2Da<3>5AU5AT69R78A788\ 877878963A06A50B40B49C37B38F47<8>_B5aC5cC5<2>jF4lF4m\ H5<16>ulIunJvpJ<3>wwM<5>_vJWuJSuI<3>CuH<3>AnK } END 20.0 PARAMETER FILE==================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) Not Branch Cuts (at all) Date: 20 Apr 2000 21:18:35 +1200 At 17:57 18/04/2000 -0600, Tim Wegner wrote: >Morgan wrote: > >> There is indeed a fundamental barrier. No matter how many knobs and buttons >> are added to Fractint, there'll always be something else that someone wants >> to twiddle. And the more knobs and buttons there are, the more ideas for >> twiddly bits there seems to be! > >Actually we are more than happy to respond to specific requests >for new features. We do have limited time, but if something makes >sense to us, and the proposal is well thought out, and it looks >feasible, we'll do it, sometimes suprisingly quickly. > Oh, I know; I was just saying that, whatever Fractint _can_ do, there will always be someone who can look at it, think for a bit and then say "Hey, what about....". After all, isn't that pretty much what's happened? Okay then, I do have a specific request, and the code is virtually all there already. Basically, as well as being able to run user formulas as standard escape-time fractals, add a new type for running them as dynamical orbits. To draw a parallel: popcornjul <-> popcorn mandel <-> mandelcloud formula <-> *dynaform* (or some such name). The parameter entry screen would have the "#0 of intervals..." field added after all the usual user parameter fields, and the bailout of the formula would be ignored. Many of the formulae I've collected look better rendered this way, and I've only added simple bailouts so that they work as escape-time fractals (though usually boring ones). I've hung on to them in anticipation that this type would eventually be implemented. Does this sort of thing make sense? This is really wishlist material I suppose, but I was just wondering if anyone else plays with these types enough to make it worthwhile. Morgan L. Owens "And then someone will look at it and say 'how about...' and the process starts all over again." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 21-04-00 (A Ghostly Specter [4]) (c) Date: 21 Apr 2000 00:23:20 -0400 (EDT) FOTD -- April 21, 2000 (Rating 4) Fractal visionaries and enthusiasts: All my FOTD fractals are single layer. This is a self-imposed limitation, not a limitation Fractint, which can create quite effective 2-layer images for those who prefer more than one layer. I mention the layers because a quick glance at today's fractal image gives the impression of more than one layer. This impression is an illusion. The brilliantly blue midget near the center is obvious enough, but behind the midget, lurking like a ghost in the shadows, lies a far greater Mandeloid. The curved shoreline and one bud of the ghost-brot are vaguely outlined by the blue areas of the background. The overall scene is filled with floating ectoplasm-like fragments of fractal material. Such fragments are typical of fractional exponent fractals of an order between zero and 2. The formula that found the ghost is once again the MandelbrotMix4, this time calculating Z^1.9+Z^0.3+C. The parameter file is a slow one, making a download of the image almost a necessity. If Mindspring gets its news server back online, that image will soon be posted to: and to: Otherwise it will not be posted until tomorrow. The fractal weather today was partly cloudy and mild, with a temperature of 65F (18C), which made the cats happy. The philosophy floundered today. I'll try again tomorrow. Until then, take care, and the best fractals are yet to come. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Ghostly_Specter { ; time=0:37:06.80, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.83681566175273090/-0.58535383767370750\ /3014.882/1/90 params=1/1.9/1/0.3/0/0 float=y maxiter=18000 logmap=75 symmetry=none periodicity=10 colors=000ZAzB53cG3ZF3UE3R43O43L43K32J43U43Q43M43K53\ K53C53<164>ecFecFfcF<2>fdFfdFecE<57>viLviLwiLwiLwiLv\ jMwiLwiLB53B53 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "caren park" Subject: (fractint) anyone remember an old lady that looked like me? Date: 21 Apr 2000 11:37:18 -0700 i'm not exactly back yet, but i'm still around occasionally... retirement just isn't close enough for me... yet... :) 00 caren park (an old Stone Soup artist from Way Back When we had to march through miles of mile-high snow in august to make a good fractal... :) __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.yahoo.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Khemyst@aol.com Subject: (fractint) sstools.ini Date: 21 Apr 2000 23:13:15 EDT I'm trying to organize the directory and subdirectory.... is this the proper format for sstools.ini or should I leave off the file entirely, just pointing to a subdirectory? I tried searching the archives but did not do too well there. Thanks. [fractint] map=D:\fractals\frain97\map\*.map parmfile=D:\fractals\frain97\parmfile\*.par formulafile=D:\fractals\frain97\form\*.frm lfile=D:\fractals\frain97\lfile\*.l ifsfile=D:\fractals\frain97\ifs\*.ifs or: [fractint] map=D:\fractals\frain97\map\ parmfile=D:\fractals\frain97\parmfile\ formulafile=D:\fractals\frain97\form\ lfile=D:\fractals\frain97\lfile\ ifsfile=D:\fractals\frain97\ifs\ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Gerald K. Dobiasovsky" Subject: Re: (fractint) sstools.ini Date: 22 Apr 2000 06:56:44 +0200 > I'm trying to organize the directory and subdirectory.... > > is this the proper format for sstools.ini or should I leave off the file > entirely, just pointing to a subdirectory? I tried searching the archives > but did not do too well there. > > Thanks. > > [fractint] > map=D:\fractals\frain97\map\*.map > parmfile=D:\fractals\frain97\parmfile\*.par > formulafile=D:\fractals\frain97\form\*.frm > lfile=D:\fractals\frain97\lfile\*.l > ifsfile=D:\fractals\frain97\ifs\*.ifs > > or: > [fractint] > map=D:\fractals\frain97\map\ > parmfile=D:\fractals\frain97\parmfile\ > formulafile=D:\fractals\frain97\form\ > lfile=D:\fractals\frain97\lfile\ > ifsfile=D:\fractals\frain97\ifs\ Hi, unless you want to point to a particular file (no wildcards) just point to the subdir names - but without the backslashes at the end. Gerald Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: JimMuth@aol.com Subject: (fractint) FOTD, 22-04-00 (Spiralling Inward [2]) Date: 22 Apr 2000 02:00:52 EDT FOTD -- April 22, 2000 (Rating 2) Fractal visionaries and enthusiasts: Today's fractal non-wonder rates a much-below-average two on my 0-10 scale of fractal worthiness. I gave it so little effort because I'm annoyed. The mighty Mindspring-Earthlink conglomer- ate, which claims to be threatening to take over AOL's position as number one, is once again down for the count, and unless I place a long-distance call I cannot access their news server to post the image. The M.S. Tech support says to be patient, that it's not their fault. I say of course it's not their fault -- it never is -- it just happened. But whether they're to blame or not, the result is the same. The situation is humorous because I can still access the Mindspring mail server by using the network of their arch-rival AOL. Too bad this doesn't work with the news server, which replies, "access denied". The FOTD image is a routine spiral in the fractal created by the formula Z^2.4142+Z^0.4142+C. 0.4142 is the reciprocal of 2.4142, though I doubt if this plays any part in the image. I named the picture "Spiralling Inward" for descriptive reasons. The parameter file takes just under 10 minutes on a modest Pentium. And running the parameter file is the only way to view the image, unless a miracle happens and Mindspring gets its act together. If it does get its act together, the image will be posted to: and also be available at: If not, rev up the old Fractint engine. The weather today was as exciting as today's fractal is dull, with occasional heavy rain showers and one of the noisiest thunder-and-hail-storms I have ever observed. The explosive thunder and crashing hail frightened Thomas, the fractal cat, who ran and hid under the fuel tank in the basement, and came out 1/2 hour later covered with grimy soot. Tippy braved the tempest under the bed. The temperature of 63F (17C) was comfortable enough, but the wetness kept the cats indoors. The philosophy is brewing quite nicely, in fact, it might appear as soon as tomorrow. Until then, take care, keep wishing and be patient. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Spiralling_Inward { ; time=0:09:41.62, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.28546319122988230/-0.12597513404242810\ /8.721691e+011/1/-39.999 params=1/2.4242/1/0.4142/0/0 float=y maxiter=3600 bailout=25 inside=0 logmap=159 symmetry=none periodicity=10 colors=000zcB<4>zUB<4>zKB<3>pHMnHPkGR<2>dFZbEa`Ce<16\ >`cH`eG`fF<2>`kA`m9Zm3<3>doLepPfpThqYiqajrentj<8>Oha\ Lg`If_<3>7aW<9>RKfTIgVGh<3>b9l_1l<3>nQprWqxcp<4>lVsj\ TtgRu<3>ZKwUMz<3>dBng8kj6hm3eo0`<4>o5jo6lo7n<3>oBuX7\ uE3u<3>ECmEElEGj<2>EMdEOcGNb<8>SJ_UIZVIZ<3>_GY<17>9R\ U7SU6ST<3>0UT<3>KUOPUNUUMZULbUK<3>KaQFcRAeS3hS<2>AbT\ <6>RoVTqVVsW<2>axWczXfzX<3>ozYqzYszYSzK<4>NzZMzaMzd<\ 3>VzQXzMZzIbzC<10>Iz_HzbFzd<2>9zj8zl8zm<6>8zn } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: Re: (fractint) sstools.ini Date: 22 Apr 2000 01:35:08 -0500 Gerald K. Dobiasovsky wrote: > > Khemyst@aol.com wrote: > > > > or: > > > > [fractint] > > map=D:\fractals\frain97\map\ > > parmfile=D:\fractals\frain97\parmfile\ > > formulafile=D:\fractals\frain97\form\ > > lfile=D:\fractals\frain97\lfile\ > > ifsfile=D:\fractals\frain97\ifs\ > > unless you want to point to a particular file > (no wildcards) just point to the subdir names > - but without the backslashes at the end. > Yes, that is correct, but it really doesn't matter whether it ends with a slash or not, it will work either way. Sincerely, P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Xylen Subject: (fractint) Real life fractals Date: 22 Apr 2000 03:20:47 -0600 Fractals are more than just pretty pictures, so I am always thrilled to see where they pop up.=20 "Weather, battery life and even the way your lawn grows are all linked by four mathematical laws, according to a paper published in the April 3rd Physical Review Letters. Yonathan Shapir and Jacob Jorn=E9 of the University of Rochester have shown how natural cyclical events, such as seasonal weather, generate very specific patterns-the same patterns that govern the geometric images called fractals." Check out the entire article at http://www.rochester.edu/pr/News/NewsReleases/latest/FRACTAL.TXT.html Xylen --=20 __^__ __^__=20 ( ___ )---------------------------------( ___ )=20 | / | Irony: Bill Gates claims to be | \ |=20 | / | making a stable Operating System, | \ |=20 | / | and Linus Torvalds claims to be | \ |=20 |___| taking over the world. |___| (_____)---------------------------------(_____) Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Khemyst@aol.com Subject: Re: (fractint) sstools.ini and fml_frm.zip Date: 22 Apr 2000 05:41:52 EDT Thanks. I was surprised to see there was no sstools.ini file anywhere to be found... so I wanted to create one to get the directories more organized. Does anyone know of the location of a most up-to-date fml_frm.zip? seems like the one I have is oct 99. Thanks In a message dated 04/21/2000 11:36:58 PM Pacific Daylight Time, Paul.N.Lee@Worldnet.att.net writes: << > Khemyst@aol.com wrote: > > > > or: > > > > [fractint] > > map=D:\fractals\frain97\map\ > > parmfile=D:\fractals\frain97\parmfile\ > > formulafile=D:\fractals\frain97\form\ > > lfile=D:\fractals\frain97\lfile\ > > ifsfile=D:\fractals\frain97\ifs\ > > unless you want to point to a particular file > (no wildcards) just point to the subdir names > - but without the backslashes at the end. > Yes, that is correct, but it really doesn't matter whether it ends with a slash or not, it will work either way. >> Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Gerald K. Dobiasovsky" Subject: Re: (fractint) sstools.ini Date: 23 Apr 2000 03:18:44 +0200 Paul N. Lee wrote: > Gerald K. Dobiasovsky wrote: > > > > Khemyst@aol.com wrote: > > > > > > ifsfile=D:\fractals\frain97\ifs\ > > > > unless you want to point to a particular file > > (no wildcards) just point to the subdir names > > - but without the backslashes at the end. > > > > Yes, that is correct, but it really doesn't matter whether it ends with > a slash or not, it will work either way. Mmh, in my case (DOS/Win) this only works if the backslash is not the last character before CR/LF, because then Fractint wraps around to the next line, concatenates this string to the first and complains... Regards, Gerald Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Lee Skinner Subject: (fractint) Pretty mandel Date: 22 Apr 2000 22:47:45 -0400 Here's a pretty mandelbrot that I don't expect anyone else here to genera= te. 6m019141 { ; t=3D4704:58:= 34.18 ; on a P300 at 1600x1200 Apr 22, 2000 20:43:02 ; Image Copyright 2000 by Lee H. Skinner ver=3D2000 ; Version 2000 Patchlevel 8 reset=3D2000 type=3Dmandel passes=3D1 center-mag=3D-0.743643835164816022194831/0.13182593159912230048051/1.41= 289\ 4e+019 params=3D0/0 float=3Dy maxiter=3D1048575 fillcolor=3D0 inside=3D= 0 logmap=3D522700 colors=3D000<157>kKWlKXlKX<2>mLXmLYmLW<6>tMFuMDvMA<3>zN0<3>OB6E78H68<3>= T08\ <3>dD8gG8jK8mN8pR7<3>udCwgDwkA<2>zy0<4>zyZ<3>zzz<3>dss_qqUpo<3>8hg<3>8R= T\ 8MQ8IM8DI88E85B<21>Jz0 } Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Paul N. Lee" Subject: Re: (fractint) sstools.ini Date: 22 Apr 2000 23:17:41 -0500 Gerald K. Dobiasovsky wrote: > > in my case (DOS/Win) this only works if the > backslash is not the last character before > CR/LF, because then Fractint wraps around to > the next line, concatenates this string to the > first and complains... > Interesting, I've had the backslash on mine for several releases of Windows/DOS and FractInt. I currently have it running on four of my machines in this manner: 486-DX Windows 3.11 (workgoup) FractInt 18.2 thru 19.6 P-90 Windows 95 (original) FractInt 19.6 P-200-MMX Windows 98 (original) FractInt 19.6 PIII-750 Windows 98 (rel. 2) FractInt 19.6 thru 20.0.11 I've always used Notepad to edit the text file on all of these machines. Here are just some of the lines from the last one on the list: [fractint] ; TEMPDIR=C:\Temp\ WORKDIR=F:\Fracta~1\FractInt\Work\ ; BATCH=yes ; AUTOKEY=play|record AUTOKEYNAME=F:\Fracta~1\FractInt\KEY_s\auto.key ; MAKEDOC=Fractint.doc MAXHISTORY=20 MAP=F:\Fracta~1\FractInt\MAP_s\ ; COLORS=@filename|colorspecification RECORDCOLORS=comment ; auto|comment|yes SAVENAME=F:\Fracta~1\FractInt\GIF_s\fract001.gif OVERWRITE=no ; no|yes ; SAVETIME=nnn|-nnn ; GIF87a=yes ; DITHER=yes PARMFILE=F:\Fracta~1\FractInt\PAR_s\*.par FORMULAFILE=F:\Fracta~1\FractInt\FRM_s\*.frm LFILE=F:\Fracta~1\FractInt\L_s\*.l IFSFILE=F:\Fracta~1\FractInt\IFS_s\*.ifs ; FILENAME=[.suffix] ; ORBITSAVE=yes VIDEO=SF5 ;640x480 @ 256 TEXTSAFE=save ; yes|no|bios|save Sincerely, P.N.L. http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 23-04-00 (Ejecting Minibrot [6]) Date: 23 Apr 2000 01:41:04 -0400 (EDT) FOTD -- April 23, 2000 (Rating 6) Fractal visionaries and enthusiasts: At last, Mindspring has recovered from the fire in the Washing- ton, D.C. subway tunnel, and things are back to normal. So it's time for the next glorious fractal to appear. For today's glory, I turned to Andrew's branchcut formula, assigned a value of sqrt(2) to both p1 and p2, and let the fractals fall where they may. In a valley area of a midget in the main fractal I found the smaller midget that appears in today's scene. This midget is one of the more mis-shapen ones I have yet come upon. I named the picture "Ejecting Minibrot" when the midget reminded me of one of those blobs of plasma sometimes ejected from the dark cosmic clouds that are giving birth to stars. The most interesting aspect of the image however is not the midget but the surrounding features, which are of a totally different nature in the upper and lower parts of the picture. In the upper half of the image, the features are sharply angled geometric shapes; in the lower half, the features have a far more decorative feathery appearance. The parameter file takes about one hour on an obsolescent P200. The image file, which has been posted, takes about one minute to download from: or from: The fractal weather (now that we realize the weather behaves in a fractal manner, weather is on-topic) was cloudy and raw all day, with light rain in the evening and a temperature of 53F (11.5C). It was a bit too chilly for the fractal cats, who didn't even ask to go outdoors. For now, it's time to shut down the fractal shoppe and settle into my favorite chair to watch some junky old sci-fi movie. Until next time, take care, and keep asking questions. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Ejecting_Minibrot { ; time=1:04:37.38, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-0.308892219653485/+3.559757942688036/4.6\ 21996e+008/1/44.999 params=1.4142/0/1.4142/0 float=y maxiter=50000 bailout=25 inside=0 logmap=240 symmetry=none periodicity=10 colors=000OrWRqV<3>YnS_mRbkPckOeiNgnNhrNehNkrGhhFenG\ bkIqoKNiMppNOiOkmOKfPmnPKcPmnPMcPnnPMcPnoPNdPioPNdPi\ oPOdPkoPOePkpPPePkpPPePkpPRePmpPRfPmqPSfPoqPSgPoqPTh\ PnrPTkPmrPUkPhrPUmPerPToOerPUoReqRUoSeqSVoTfpTVpUfoU\ VoVgnVWnWgnWWmYgmZWmZck_Yk_hk`Yk`fkbZibgicZicehdZhdd\ ge`ge<2>_fg_fh`eh`ei`di`dk`dkbckbckbcm<3>cbncbndbn<3\ >gbmgbmf`ke_kd_icZibZh`Yg_WgZWfZVe<3>UTbTSbSS`RR_PPZ\ PPZOOYNOWMNWKMVJMUIKTGKTFJSFIREIRCGP<2>8EN7EM5CK4BI5\ CK5CM7CN7CO8CP8CR8ET9EU9EVBEWBEYBEZCE_CFbEFc<3>FFgGF\ hGGkIGk<3>JGpKGqKIsKItMIvMIwNIwNIyIFzKGzMIzNIzOJyPJw\ RKwSKvTMt<4>ZPo_PnbRmcRkdSk<4>iVekVdkWcmWbnY`<3>s_Wt\ _Vv`UwbTwbSycR<3>zeMzeKzfJzeGzfI<2>zhKziKziMzkMzkNyk\ NwmOwnOvnPtoPtpR<3>prTosUptV<3>tt_tt`ttb<7>ttk } frm:MandelbrotBC {; Z=Z^E+C (Formula by Andrew Coppin) e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Tom Conally Subject: (fractint) Articles Date: 23 Apr 2000 09:32:55 -0400 Hi all, If you haven't seen this series of articles, they are worth looking up.This one starts with the lyapunov exponent and has lots of links http://pass.maths.org.uk/issue9/features/lyapunov/index.html including one on the Mandelbrot set. http://pass.maths.org.uk/issue9/features/mandelbrot/index.html Happy fractalling Tom Conally In every boomerang there is a perfect throw. Your life, Grasshopper, is to practice till you find that throw and become one with that boomerang! __________________________________________ Boomerangs http://fly.to/boomerangs Internet Index http://www.netpath.net/~conally/ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Tony \(Anthony\) Hanmer" Subject: (fractint) Lyapunov Date: 23 Apr 2000 21:25:37 GEST The recently posted link to a Lyapunov article has reminded me of something I have wanted to request for a while now: the actual Fractint formula for the Lyapunov type. I've searched Orgform and not found it (there was something called lyapunov, but it wasn't the same as far as I could tell). I'd like to tinker with the formula. Could someone post this to the conference, please? Thanks, Tony Hanmer ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: jerome schatten Subject: (fractint) linux install.. Date: 23 Apr 2000 10:03:43 +0000 This is a multi-part message in MIME format. --------------3359D601D6D08960C5822C40 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit I'm trying to install the precompiled version of Xfractint from 'xfractint-3.11.bin.tar.gz' on a p450 running R.H.6.2. It appears that all the files get put in the right places as I get no errors during the installation. When I try and run from the xterm window however, I get the error in the attached message. Any help would be appreciated. jerome ========================================================== --------------3359D601D6D08960C5822C40 Content-Type: text/plain; charset=us-ascii; name="xferror1" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="xferror1" xfractint: error in loading shared libraries: libncurses.so.5: cannot open shared object file: No such file or directory [root@magoosky /root]# --------------3359D601D6D08960C5822C40-- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Gerald K. Dobiasovsky" Subject: Re: (fractint) sstools.ini Date: 23 Apr 2000 21:21:44 +0200 Paul N. Lee wrote: > Interesting, I've had the backslash on mine for several releases of > Windows/DOS and FractInt. I currently have it running on four of my > machines in this manner: > > 486-DX Windows 3.11 (workgoup) FractInt 18.2 thru 19.6 > P-90 Windows 95 (original) FractInt 19.6 > P-200-MMX Windows 98 (original) FractInt 19.6 > PIII-750 Windows 98 (rel. 2) FractInt 19.6 thru 20.0.11 > > I've always used Notepad to edit the text file on all of these > machines. Here are just some of the lines from the last one on the > list: > > [fractint] > ; > TEMPDIR=C:\Temp\ > WORKDIR=F:\Fracta~1\FractInt\Work\ > ; BATCH=yes > ; AUTOKEY=play|record > AUTOKEYNAME=F:\Fracta~1\FractInt\KEY_s\auto.key > ; MAKEDOC=Fractint.doc > MAXHISTORY=20 > MAP=F:\Fracta~1\FractInt\MAP_s\ > ; COLORS=@filename|colorspecification > RECORDCOLORS=comment ; auto|comment|yes > SAVENAME=F:\Fracta~1\FractInt\GIF_s\fract001.gif > OVERWRITE=no ; no|yes > ; SAVETIME=nnn|-nnn > ; GIF87a=yes > ; DITHER=yes > PARMFILE=F:\Fracta~1\FractInt\PAR_s\*.par > FORMULAFILE=F:\Fracta~1\FractInt\FRM_s\*.frm > LFILE=F:\Fracta~1\FractInt\L_s\*.l > IFSFILE=F:\Fracta~1\FractInt\IFS_s\*.ifs > ; FILENAME=[.suffix] > ; ORBITSAVE=yes > VIDEO=SF5 ;640x480 @ 256 > TEXTSAFE=save ; yes|no|bios|save > > > Sincerely, > P.N.L. > -------------------------------------------------------------- Well, in my case Fractint is run mostly from my MS-DOS 6.22 boot partition, so I'm using the DOS editor (QBASIC in disguise). I've just tried and wrote a new SSTOOLS.INI with Notepad under Win98, but got the same results. Maybe this has to do with the localized versions of the OS's (German in my case). Anyhow, as long as it works by another way, I've no complaints :) Greetings, Gerald Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Xylen Subject: Re: (fractint) linux install.. Date: 23 Apr 2000 14:19:24 -0600 jerome schatten wrote: > xfractint: error in loading shared libraries: > libncurses.so.5: cannot open shared > object file: No such file or directory > [root@magoosky /root]# It looks like you may need to update the library listings. Try: [root/root]# ldd xfractint You may find that you are missing a library, or missing a link to it. ldconfig should fix the problem. This program evaluates the file /etc/ld.so.conf. You may want to check that file to make certain that it has all of the entries it needs. I'm running Redhat 6.0, but I've gotten the same sort of error message on other programs. check out the man pages for ldd, and ldconfig on your system for infomormation. Xylen -- __^__ __^__ ( ___ )---------------------------------( ___ ) | / | Irony: Bill Gates claims to be | \ | | / | making a stable Operating System, | \ | | / | and Linus Torvalds claims to be | \ | |___| taking over the world. |___| (_____)---------------------------------(_____) Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: jerome schatten Subject: Re: (fractint) linux install.. Date: 23 Apr 2000 13:47:25 +0000 Thanks for your suggestions... Indeed 'libncurses.so.5' is missing. It isn't on the red cd with the rest of the rpm's, and it's nowhere installed on my system. Do you have any idea where I could look for this lib, and if I find it out there somewhere, where I should install it? As you can see, I'm only a relative newbe with linux. thanks again, jerome Xylen wrote: > It looks like you may need to update the library listings. Try: > > [root/root]# ldd xfractint > > You may find that you are missing a library, or missing a link to it. > ldconfig should fix the problem. This program evaluates the file > /etc/ld.so.conf. You may want to check that file to make certain that it > has all of the entries it needs. I'm running Redhat 6.0, but I've gotten > the same sort of error message on other programs. check out the man > pages for ldd, and ldconfig on your system for infomormation. > > Xylen Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 24-04-00 (A Midget Brainiac [4]) Date: 24 Apr 2000 01:39:54 -0400 (EDT) FOTD -- April 24, 2000 (Rating 4) Fractal visionaries and enthusiasts: For today's fractal I returned to yesterday's formula, refining it a bit by entering sqrt(2) to an accuracy of 12 decimal places -- not that this made much difference in the resulting fractal. When calculated normally, this fractal has no negative tail, but when more remote slices of the infinite fractal are calculated, a tail is indeed seen to exist, and quite a long tail at that. It's actually more of a filament than a tail, extending north instead of west, and crowned by a prominent minibrot. Since I enjoy examining tails (fractal tails that is) I zoomed in on the mis-shapen midget on the tail of today's fractal, paying particular attention to the tail-filament where it enters the east valley area of the midget. In the classic Mandelbrot set, sub-midgets on filaments in the east valley area of larger midgets are surrounded by a brain-like pattern, with converging elements splitting in a 2,4,8,16... sequence. In the Z^1.414 Mandeloid, the elements should split in a 1.414,2,2.828,4... sequence. And as today's picture shows, they do indeed. At first I hoped that every other split would result in a whole- number unbroken pattern, but this is not so. The element fragments at the four level for example may add up to an even four, but they are so discontinuous that it is impossible to count them. Regardless, the sub-midgets in the east valley area of larger midgets of low-order Mandeloids make interesting pictures, as today's FOTD shows. While exploring the parent fractal, I also noticed that the midgets lie far deeper than would be expected when compared to the classic Mandelbrot set. In the classic set, a midget lies about twice as deep as the point where it first becomes apparent. Thus, if the signs of a midget appear at a depth of 10^5, the midget itself will lie at a depth of 10^10. In the Z^1.414 fractal however, the midgets lie at a depth three times the depth where their location becomes apparent. If the signs of a midget appear at 10^5, the midget will lie at 10^15. This makes midget hunting far more challenging in this fractal. But even though the effort of finding them is more difficult, the lower order midgets are worth the effort, since they come in any shape imaginable. I named today's picture "A Midget Brainiac" because the scene was found in a part of the fractal world where midgets resemble super brains. At over seven minutes, the parameter file isn't unbearably slow. Still, the download, which can be found on Usenet at: and on the web at: is the faster choice. The USA weather might not be the most important topic for those living in Australia, but here in fractal-land it was cloudy and 56F (13C) -- too chilly for the fractal cats, but pretty good for philosophy. That philosophy has been festering all day, though it's not yet quite ready to come to a head. It may erupt tomorrow however, so check then on the Philofractal list to see what trouble I might get myself into. And until then, take care, and think deep thoughts. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Midget_Brainiac { ; time=0:07:22.70, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-0.48807376750966140/+3.37326494060311700\ /6.141974e+010/1/82.499 params=1.414213562373/0/1.414213562373/0 float=y maxiter=800 inside=0 logmap=204 periodicity=10 colors=000jid<3>nlnomqpnsqnu<5>cYfaVc_Ta<3>RHSODQL9N\ I5LF2J<2>QMJWQJ`_JebJjlJnrJrxJ<3>dyRayTZyV<3>PybNydL\ yfVvccraYqZJoX<3>HeNHcLGaI<3>FU9<3>EMQEKUDKZDKbDKfDK\ mDKwDKzFKzGCsH5n<3>LSmMYmMbmQbsR`pOcJ<3>OdMOdNOdNV`K\ cXH<2>cM9<3>cUOcWScYWc__<3>TgnRhqV`iZTbPJMGA6<9>NSdN\ UhOVk<3>Qay<3>mGpsBnk9i<3>I4TB3PE6O<7>`PJbRIeUH<3>pb\ F<3>YGB<6>K`TIcVGfY<3>8rf<3>h1D<3>bDY`Gb_JgYMlXPq<3>\ QMgOLeNKbLJ`KJZ<3>hoa<3>RiONgLJfI<2>6b8<6>VdRZdUaeX\ <3>oef<3>xGZzAYyDZ<5>wV`vY`v``<3>uka<3>bckYamT_p<3>B\ Sy<3>PKoSJlVHj<2>dCc<2>YMZihb } frm:MandelbrotBC {; Z=Z^E+C (Formula by Andrew Coppin) e=p1 p=real(p2)+PI q=2*PI*trunc(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<100 } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jon Noring Subject: (fractint) 4700 hours! (was Re: [fractal-art] Pretty mandelbrot) Date: 24 Apr 2000 11:56:23 -0700 (PDT) Lee Skinner wrote: >Here is pretty Mandelbrot image I discovered. Lots of really neat places for >further zooming and looks great when color cycled. Although it may first >appear to be a layered image, it is just a standard mandel. > >6m019141 { ; t=4704:58:34.18 > ; on a P233 at 1600x1200 Apr 22, 2000 20:43:02 > ; Image Copyright 2000 by Lee H. Skinner ver=2000 > ; Version 2000 Patchlevel 8 > reset=2000 type=mandel passes=1 > center-mag=-0.743643835164816022194831/0.13182593159912230048051/1.41289\ > 4e+019 params=0/0 float=y maxiter=1048575 fillcolor=0 inside=0 > logmap=522700 > colors=000<157>kKWlKXlKX<2>mLXmLYmLW<6>tMFuMDvMA<3>zN0<3>OB6E78H68<3>T08\ > <3>dD8gG8jK8mN8pR7<3>udCwgDwkA<2>zy0<4>zyZ<3>zzz<3>dss_qqUpo<3>8hg<3>8RT\ > 8MQ8IM8DI88E85B<21>Jz0 > } I'm not sure if any one noticed, but it took Lee 4700 hours to generate the 1600x1200 version of this image on a Pentium 233! Now that's what I call patience. :^) Jon Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Sylvie Gallet Subject: (fractint) Pretty mandel Date: 24 Apr 2000 15:12:45 -0400 Hi Lee, >> Here's a pretty mandelbrot that I don't expect anyone else here to >> generate. >> 6m019141 { ; = >> t=3D4704:58:34.18 = Very impressive!!! I couldn't resist tweaking the colors so, here's an alternate color palette: 6M19141B { ; Sylvie Gallet, Apr 21, 2000 t=3D4704:58:3= 4.18 ; colors=3D0J2yuU<2>yxdzzhzzh<120>vwxvwxvwxvwxvwxvwxuvy<31>ARg8Qf7Pf<3>0K= c<2\ 0>gmpinqkpqmqr<3>vwvxyvzzw<6>ioigmgeke<3>WeYUdWRbU<2>KYOHWLHUJ<3>EMBDK9= C\ I7<2>AA0<3>RF4VH5ZI6cK7<3>l`BndCphD<3>zzH<7>www } Cheers, - Sylvie Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Sylvie Gallet Subject: (fractint) MandelbrotMix4 lakes Date: 24 Apr 2000 15:12:44 -0400 Hi All, Here's a couple of MandelbrotMix4 Lake example. Both formulas are base= d on Jim Muth's MandelbrotMix4, the original parameters used in MMix4 (p1, p2, p3) are now hard-coded in the formula (renamed as p_p1,...), in order= to make p2 and p3 available for the lake effect. 6027000l.GIF { ; Blue Grotto t=3D 0:46:27.08 ; Copyright Sylvie Gallet, Apr 22, 2000 ; ; t=3Dcalc time using a PII 300 at 1600 x 1200 ; Version 2000 Patchlevel 6 reset=3D2000 type=3Dformula formulafile=3Dmmix_lak.frm formulaname=3Dmmix4-lake-0270 function=3Drecip passes=3D1 center-mag=3D-0.40374468230415920/+2.08435374453009100/2.65758\ 7e+010/1/-132.5 params=3D0/0/40/0/0.2/300 float=3Dy maxiter=3D1200 inside=3D0 logmap=3D139 symmetry=3Dnone sound=3Doff colors=3D000<3>046058068<12>0CI0DJ0DK<7>0HO1IP1IQ1JR1JR<13>2Q`\ 2Ra2Rb<3>3Td4Ue5Ve<3>9YfAYfBZf<3>G`gIahJbh<15>fqsgrtist<3>ow\ xqxyryytzz<25>CbnAan8`m<2>3Yl1Xk1Wi<8>7FM7EK8CH<2>A69B46D46<\ 17>m9No9Oq9P<2>wASzBTzCT<3>zKSzMRzNR<3>zUTzWUzYU<3>zeYzgYzhZ\ zjZ<3>zr`ztazvb<22>zKTzISzHS<3>z9Qz7Qz6Rz4Rz2Rz0S<29>437 } 6025700l.GIF { ; Fireworks Over The Seine t=3D 0:25:14.09 ; Copyright Sylvie Gallet, Apr 23, 2000 ; ; t=3Dcalc time using a PII 300 at 1600 x 1200 ; Version 2000 Patchlevel 6 reset=3D2000 type=3Dformula formulafile=3Dmmix_lak.frm formulaname=3DMMix4-lake-0257 function=3Dident passes=3D1 center-mag=3D+72.31044472088888000/+0.16149902668392410/5.4510\ 81e+009/1/15.001/-0.004 params=3D0/0/40/0/0.2/300 float=3Dy maxiter=3D2000 periodicity=3D0 sound=3Doff colors=3D000666333000<86>000<4>000A00000000000710<3>G60I70L90<\ 3>VG0YI1_K2<6>mW4oY4qZ4<3>zf6<11>SF3PC2MA2<3>A00000<4>000<2>\ 000<3>VM5bS6jX7rb8zhA<3>RK5ID3972000<3>000<3>m_4zh5kY4<2>000\ <74>999 } frm:MMix4-lake-0257 { ; 6000401 - Formula by Sylvie Gallet & Jim Muth ; MandelbrotMix4 parameters (hard-coded): ; ------------------------- p_p1 =3D (1,100) p_p2 =3D (-2,0.01) p_p3 =3D (35,0) ; Function: i ; User-selectable Lake parameters: ; ------------------------------- ; real part of p2: 0 =3D lake transform disabled ; any value between 0 and 100: water level in % of ; the screen height (0 =3D bottom, 100 =3D top) ; imag part of p2: phase ; real part of p3: amplitude of the wave (try 0.2) ; imag part of p3: frequency (try 300) ; Lake transformation (Sylvie Gallet) ; ------------------- if (real(p2) > 0 && real(p2) <=3D 100) level =3D real(p2) / 100 ; water level phase =3D imag(p2) ; phase ampl =3D real(p3) ; amplitude of the wave freq =3D imag(p3) ; frequency angle =3D real(rotskew * pi / 180) exp_irot =3D exp(-flip(angle)) h =3D 1 / real(magxmag) w =3D h / 0.75 * imag(magxmag) tanskew =3D tan(imag(rotskew * pi / 180)) u =3D 2 * w * exp_irot v =3D 2 * h * (tanskew + flip(1)) * exp_irot z3rd =3D center + (-w-h*tanskew - flip(h)) * exp_irot z =3D pixel - z3rd b =3D imag(conj(u)*z) / imag(conj(u)*v) if (b <=3D level) dy =3D level - b z =3D z + 2*dy * (1+ampl*sin(freq*dy^0.2 + phase)) * v endif pixel =3D z + z3rd endif ; Modified MandelbrotMix4 formula (Jim Muth) ; ------------------------------- a =3D real(p_p1) , b =3D imag(p_p1) , d =3D real(p_p2) , f =3D imag(p_p2)= g =3D 1/f , h =3D 1/d , j =3D 1/(f-b) , z =3D (-a*b*g*h)^j , k =3D real(p_p3) + 1 , l =3D imag(p_p3) + 100 , c =3D fn1(pixel) : z =3D k*(a*(z^b) + d*(z^f)) + c |z| < l } frm:MMix4-lake-0270 { ; 6000417 - Formula by Sylvie Gallet & Jim Muth ; MandelbrotMix4 parameters (hard-coded): ; ------------------------- p_p1 =3D (1,1.1) p_p2 =3D (-1,-1.11) p_p3 =3D (0,0) ; Function: r ; User-selectable Lake parameters: ; ------------------------------- ; real part of p2: 0 =3D lake transform disabled ; any value between 0 and 100: water level in % of ; the screen height (0 =3D bottom, 100 =3D top) ; imag part of p2: phase ; real part of p3: amplitude of the wave (try 0.2) ; imag part of p3: frequency (try 300) ; Lake transformation (Sylvie Gallet) ; ------------------- if (real(p2) > 0 && real(p2) <=3D 100) level =3D real(p2) / 100 ; water level phase =3D imag(p2) ; phase ampl =3D real(p3) ; amplitude of the wave freq =3D imag(p3) ; frequency angle =3D real(rotskew * pi / 180) exp_irot =3D exp(-flip(angle)) h =3D 1 / real(magxmag) w =3D h / 0.75 * imag(magxmag) tanskew =3D tan(imag(rotskew * pi / 180)) u =3D 2 * w * exp_irot v =3D 2 * h * (tanskew + flip(1)) * exp_irot z3rd =3D center + (-w-h*tanskew - flip(h)) * exp_irot z =3D pixel - z3rd b =3D imag(conj(u)*z) / imag(conj(u)*v) if (b <=3D level) dy =3D level - b z =3D z + 2*dy * (1+ampl*sin(freq*dy^0.2 + phase)) * v endif pixel =3D z + z3rd endif ; Modified MandelbrotMix4 formula (Jim Muth) ; ------------------------------- a =3D real(p_p1) , b =3D imag(p_p1) , d =3D real(p_p2) , f =3D imag(p_p2)= g =3D 1/f , h =3D 1/d , j =3D 1/(f-b) , z =3D (-a*b*g*h)^j , k =3D real(p_p3) + 1 , l =3D imag(p_p3) + 100 , c =3D fn1(pixel) : z =3D k*(a*(z^b) + d*(z^f)) + c |z| < l } Cheers, - Sylvie E-mail: Sylvie_Gallet@CompuServe.com Web site: http://www.fractalus.com/sylvie/homepage.htm Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Bill Jemison Subject: (fractint) anyone remember an old lady that looked like me? Date: 24 Apr 2000 20:26:16 -0400 Subject: Re: (fractint) anyone remember an old lady that looked like me? Date: 24 Apr 2000 17:28:23 -0700 busy... am trying to get back to my bookstore without flaming out completely... some weeks are better than others, but i'm still on-course... :) are you still working on fractint fractal music? i *think* that was you playing with that stuff in the Way Back When... :) ----- Original Message ----- Sent: Monday, April 24, 2000 5:26 PM Subject: Re: (fractint) anyone remember an old lady that looked like me? Date: 24 Apr 2000 18:02:26 -0700 Caren writes: >busy... am trying to get back to my bookstore without flaming out >completely... some weeks are better than others, but i'm still on-course... >:) You still hitting the local fractal bowling lanes? :-) Best regards, Guy guyh@teleport.com (Guy Hammer) http://www.teleport.com/~guyh Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "caren park" Subject: Re: (fractint) anyone remember an old lady that looked like me? Date: 24 Apr 2000 18:05:19 -0700 i haven't bowled in competition for more than a few years now... arthur-itis ( as redd foxx used to say)... nowadays, i waste my time playing chess... sometimes well, sometimes not... :) ----- Original Message ----- Sent: Monday, April 24, 2000 6:02 PM > Caren writes: > >busy... am trying to get back to my bookstore without flaming out > >completely... some weeks are better than others, but i'm still on-course... > >:) > > You still hitting the local fractal bowling lanes? :-) > > Best regards, Guy > > > guyh@teleport.com (Guy Hammer) > http://www.teleport.com/~guyh > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.yahoo.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Lee Skinner Subject: (fractint) Pretty mandel Date: 24 Apr 2000 21:35:54 -0400 >> I couldn't resist tweaking the colors so, here's an alternate color palette: << Very nice! You had time already to generate a very small thumbnail? Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Scott D. Boyd" Subject: Re: (fractint) 4700 hours! (was Re: [fractal-art] Pretty mandelbrot) Date: 24 Apr 2000 22:51:32 -0500 On Mon, 24 Apr 2000, you wrote: > > I'm not sure if any one noticed, but it took Lee 4700 hours to generate > the 1600x1200 version of this image on a Pentium 233! > > Now that's what I call patience. :^) > That's 196+ days or approx 6.5 months! Actually, I think he ran a version of Fractint on an IBM S-390 mainframe (or maybe some super-computer) and just made up a wild figure for a Pentium 233. 8-) Lee - could you maybe post that fractal on the Web somewhere so we won't have to wait 6 months plus to see what it looks like? Until later, Scott Boyd -- email: sdboyd@fastlane.net http://www.fastlane.net/~sdboyd/ "Make it idiot-proof, and someone will make a better idiot." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: (fractint) Mime-Version: 1.0 Date: 25 Apr 2000 18:58:45 +1200 Here's a little lsystem idea I thought I'd try out after looking at reptiles too long. The hardest part was squeezing it into the lsystem parser! Morgan L. Owens "I blame it on all the inbreeding." Pentominoes{ ; What's the collective noun for reptiles? ; A group of turtles is apparently called a "bale". I'll use that. ; So this is a bale of turtle graphics reptiles. ; I ought to get on and optimise it :-) Angle 4 Axiom x ; I usually call the 'r' pentomino 'f' - but since ; that latter letter is reserved, r it is. ; i=ufffffffffffffff+vfff+flffffrfffwf[+!y]ffffff+fff+ i=[g[+gg-!p]ggggg[+g|z]ggggggg+gg+n] l=vffffffffffff+pfff+fffwfifffff-xfff+fff+uffffff+ l=[g[+g!y]gggggg[+gg+n]g+g|t] n=uffxffff+vfff-ffffff+[+!l]fff+pfffwf[+!y]fffftf+fff-fff+fff+ n=[ggg+gg!r] p=uffxfffffff+nffffff+[+!l]ffffff+vfffz-fff+fff+ p=[ggggg[+g|t]g[+ggg+w]gg+ggggg|!r] r=fff+uffxf-fff+fifffff+fff+fff[!y]-ffffff+fff+vfffz-fff+ r=[gg[+ggg!n][g+gggg|t]ggg+ggggggp] t=fff+uffxfffff[|!l]ff+fff+[+!p]fff-ff[+w]ffff+vfff+fifffff-fff+ t=[gg+ggggn][+gggg+g-y] u=[+!p]fifffff+f[+!l]ff+fff-ffwf-fff+vfff+ffffff+yfffffffff+ u=[g[+gggg[-!n]gg+t]gg+gggggg+!z] v=f[+i]fff[+u]fffff+yfff+lfffftff-f[+x]rfpffff+fff+vfffffffff+ w=yfff+lfff-fff+[+!p]fff-xfff+fff+uffffff+vfff-fff+f[+i]fffff+ w=[ggg[+ggggt]g+gggggggg|n] x=vfff+fff-f[+z]ff+fff+ufff-fff+[+!n]fff+lfff-pfff+fff+fff-fff+ x=[g[+gggy]gg[+ggggt]gg+ggggw][+ggggggggg|l] y=fff+[+!p]fff-xfff+fff+ufff-ffff[|!i]ff+fff+vffffffffffff+ y=[g[+gggg[+z]ggggggg|l]g[+gggggn]g+gggw] z=fff+[+!p]ffffff+wfifffff-xfff+fff+uffffff+vffffff-fff+ z=[g[g+g-t]+ggggg+n][+gggg+ggggg-!y] f=ggg g=ggg } Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: davides Subject: Re: (fractint) anyone remember an old lady that looked like me? Date: 25 Apr 2000 07:07:00 -0400 At 06:05 PM 4/24/2000 -0700, you wrote: ... nowadays, i waste my time >playing chess... sometimes well, sometimes not... :) Tournaments? davides@pipeline.com Back up my hard drive? How do I put it in reverse? Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 25-04-00 (Spots Before the Eyes [3]) Date: 25 Apr 2000 08:35:39 -0400 (EDT) FOTD -- April 25, 2000 (Rating 3) Fractal visionaries and enthusiasts: The FOTD is a little late today. I inadvertently fell asleep while relaxing after a busy day to gather my energy for the discussion, and now it's 8am and time to begin another busy day. As a result, today's discussion will be a short one. The formula responsible for the image is Z^(-4)+Z+C. I named the picture "Spots Before The Eyes", since this name fairly accurately describes the scene. No, I do not have spots before my eyes, that is unless I look at today's fractal or my neighbor's dalmatian dog. The picture isn't much, rating only a 3 on my 0-to-10 scale. The parameter file runs fast -- in a little over 1-1/2 minutes on a modest Pentium. It's up to the viewer to decide whether to run the parameter file or download the image from: or from: The fractal weather was sunny in the morning and increasingly cloudy during the afternoon. The temperature of 68F (20C) was warm enough for the cats to spend much of the day in the wild outdoors. The philosophy never had a chance today, so check tomorrow to see if anything develops. Until then, take care, and the best is yet to come. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ SpotsBeforeTheEyes { ; time=0:01:33.28 on a P200, 640x480 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=t center-mag=-1.80978199237521300/+0.74386581244625630\ /4.313705e+011/1/95.001/-0.002 params=1/1/1/-4/0/0 float=y maxiter=300 bailout=25 inside=0 logmap=40 symmetry=none periodicity=10 colors=000ePu<3>wXz5BR48J46B<3>`GMhIOpKRxMT<3>pYSn`S\ lcSkeS<3>DIU<3>R9bV7dY5f`3h<3>txG<3>svcsvisuosuusuzv\ pWyk1td2oY2<3>W7US1`aFA<2>aMi<3>kPCmP4gOE<2>QOg<3>cC\ tf9wi7z<2>5Jp<2>9To<2>dsD<3>owMrwOtwQnwWhwaewy<3>Uw_\ RwTPwN<3>DwWAwZ7w`4wb2wd<3>HwcKwcNwW<2>Ww8<3>dwNfwRh\ wU<3>gwXgwXhwSiwNjwI<3>fwDjwFnwG<3>VwlRwtHwS8w0<3>Jw\ _MwhOwp<3>OwSOwMOwG<3>Ew6Bw49w2<3>Pwj<3>MwkMwkGwZBwM\ 6wA<3>TwoYwyXwr<3>WwUWwOWwI<2>Iw7swEcwYPwqewlvwg<2>C\ ww<3>GwlHwiIwgJwdJwb<2>1wM<3>_wWhwZqw`ywb<3>pwUnwSlw\ Q<2>ywo<3>fwDbw4YwA<3>GwWCwa8wf<3>_wTfwPmwM<3>rweswj\ twouwtvwykwt`wp_wrZwtXwnVwhXwraws } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "caren park" Subject: Re: (fractint) anyone remember an old lady that looked like me? Date: 25 Apr 2000 08:34:32 -0700 only at FICS (www.freechess.org)... don't like USCF for a variety of reasons, and am definitely not a fan of FIDE of late... ----- Original Message ----- Sent: Tuesday, April 25, 2000 4:07 AM > At 06:05 PM 4/24/2000 -0700, you wrote: > .... nowadays, i waste my time > >playing chess... sometimes well, sometimes not... :) > > Tournaments? > davides@pipeline.com > Back up my hard drive? > How do I put it in reverse? > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Sylvie Gallet Subject: (fractint) Pretty mandel Date: 25 Apr 2000 12:21:32 -0400 Hi Lee, >> Very nice! Thanks! >> You had time already to generate a very small thumbnail? Oh, no! I generated it at 1600x1200 on my PXV 30K!!! ;-) The 1600x1200 GIF along with some 800x600 JPGs are available at: Cheers, - Sylvie Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Fliguer, Miguel" Subject: RE: (fractint) Pretty mandel Date: 25 Apr 2000 14:08:03 -0300 >>>The 1600x1200 GIF along with some 800x600 JPGs are available at: >>> Hey, great picture ! And the embossing effect on the PSP-ed image is also very cool. >>> Oh, no! I generated it at 1600x1200 on my PXV 30K!!! ;-) Huh ? Technical details ? Or is this an inside joke ? I noticed Lee used passes=1. I wonder if passes=g would have made a difference on the huge elapsed time (but I usually don't do deep zooming so I don't know if passes=g works on arbitrary precision...) Excellent work ! Regards, Miguel Fliguer http://members.xoom.com/fliguer/franktal.html PS : The web page says "4700 hs. on a P300", while the posted par said it was a P233....? Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "caren park" Subject: Re: (fractint) Pretty mandel Date: 25 Apr 2000 10:14:58 -0700 was the PSP image (bottom of that web page) paint shop pro-enhanced, or was this another feature of fractint 20 (or ultra-frac)? i liked it... LOTS... ----- Original Message ----- Sent: Tuesday, April 25, 2000 9:21 AM Hi Lee, >> Very nice! Thanks! >> You had time already to generate a very small thumbnail? Oh, no! I generated it at 1600x1200 on my PXV 30K!!! ;-) The 1600x1200 GIF along with some 800x600 JPGs are available at: Cheers, - Sylvie Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.yahoo.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Rupert Millard" Subject: (fractint) minibrots / mandeloids (whatever-you-call-'ems) Date: 25 Apr 2000 17:44:01 GMT Hello all, I find it fascinating that the 'mandelbrot shape' (I really *don't* know what to call it!) occurs in so many different formulae. I have tried looking to see what mandel, magnet1m, magnet2m, mandellamba, nova etc. have in common with each other but *I* can't see anything. <:-( Can anybody help me From, Rupert website: http://www.geocities.com/kanagrupert ps. I *think* The beauty of Fractals has something about this. But I'm too thick to understand it. (I just look at the pictures!) ________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Sylvie Gallet Subject: (fractint) Mime-Version: 1.0 Date: 25 Apr 2000 14:32:01 -0400 Hi Morgan, >> Here's a little lsystem idea I thought I'd try out after looking at >> reptiles too long. >> Pentominoes{ ; What's the collective noun for reptiles? Wow!!! It's great! Cheers, - Sylvie Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Sylvie Gallet Subject: RE: (fractint) Pretty mandel Date: 25 Apr 2000 14:31:59 -0400 Hi Miguel, >> Hey, great picture ! And the embossing effect on the PSP-ed image is >> also very cool. Thank you! >> >>> Oh, no! I generated it at 1600x1200 on my PXV 30K!!! ;-) >> >> Huh ? Technical details ? Or is this an inside joke ? Did you notice the smiley? ;-) >> I noticed Lee used passes=3D1. I wonder if passes=3Dg would have made = a >> difference on the huge elapsed time (but I usually don't do deep >> zooming so I don't know if passes=3Dg works on arbitrary precision...)= Yes, passes=3Dg works on arbitrary precision, and it would probably hav= e made a big difference. Lee always uses passes=3D1. >> The web page says "4700 hs. on a P300", while the posted par said it >> was a P233....? You're right. Where did I see it was a P300? Cheers, - Sylvie E-mail: Sylvie_Gallet@CompuServe.com Web site (New galleries: 23 and 24): http://www.fractalus.com/sylvie/homepage.htm Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Sylvie Gallet Subject: Re: (fractint) Pretty mandel Date: 25 Apr 2000 15:28:56 -0400 Hi caren, >> was the PSP image (bottom of that web page) paint shop pro-enhanced, o= r >> was this another feature of fractint 20 (or ultra-frac)? It was enhanced with Paint Shop Pro 6, usint the Sculpture effect with = a background pattern I made with Ultra Fractal. The old fractal of the wee= k (for 04/11/2000) that is still available on my home page was made the sam= e way. My gallery #23 has 15 other post-processed fractals. Cheers, - Sylvie E-mail: Sylvie_Gallet@CompuServe.com Web site (New galleries: 23 and 24): http://www.fractalus.com/sylvie/homepage.htm Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Fliguer, Miguel" Subject: RE: (fractint) Pretty mandel Date: 25 Apr 2000 16:29:55 -0300 Sylvie hinted : >>> Did you notice the smiley? ;-) I thought you were beta testing a new secret Cray prototype, code-named PXV-30K..... ;-))) >>>Yes, passes=g works on arbitrary precision, and it would >>>probably have made a big difference. Lee always uses passes=1. If I understand it well, if I ever venture into the arbitrary precision realm, I better switch to passes=1, ok ? What about difussion mode ? And the hidden synchronous orbit mode ? (I tried to plot Lee's par with this method, it finished in about 40 seconds but the image was just 4 purple squares, each in 1/4 of the screen) Regards, Miguel Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Gregory McClure Subject: RE: (fractint) minibrots / mandeloids (whatever-you-call-'ems) Date: 25 Apr 2000 14:14:33 -0700 This message is in MIME format. Since your mail reader does not understand this format, some or all of this message may not be legible. ------_=_NextPart_000_01BFAEFB.FDB1B26E Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Rupert, If I am not mistaken, the reason for these mandelbrot shapes is due to some interesting constants that pop up from fractal theory. These constants produce mandelbrot shapes in many formulas because the constants apply to many (but not all) of the fractal formulas used by fractint. One is called the Feigenbaum number and is the primary constant responsible for the "nodes" on the Mandelbrot fractal. The documentation for Fractint has some interesting stuff on this... The Kwisatz Haderach, =DF Gregory J. McClure -----Original Message----- Sent: Tuesday, April 25, 2000 11:44 AM Hello all, I find it fascinating that the 'mandelbrot shape' (I really *don't* = know=20 what to call it!) occurs in so many different formulae. I have tried = looking to see what mandel, magnet1m, magnet2m, mandellamba, nova etc. have in=20 common with each other but *I* can't see anything. <:-( Can anybody help me From, Rupert website: http://www.geocities.com/kanagrupert ps. I *think* The beauty of Fractals has something about this. But I'm = too=20 thick to understand it. (I just look at the pictures!) ________________________________________________________________________= Get Your Private, Free E-mail from MSN Hotmail at = http://www.hotmail.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------_=_NextPart_000_01BFAEFB.FDB1B26E Content-Type: application/octet-stream; name="Gregory McClure.vcf" Content-Disposition: attachment; filename="Gregory McClure.vcf" BEGIN:VCARD VERSION:2.1 N:Mcclure;Gregory FN:Gregory Mcclure ORG:Quantum Corporation;16110 TITLE:Principle Software Engineer TEL;WORK;VOICE:(719) 536-5303 TEL;WORK;VOICE:(8301) 5303 TEL;PAGER;VOICE:(719) 599-2624 TEL;WORK;FAX:(719) 536-5610 ADR;WORK:;PPO;10125 Federal Drive;Colorado Springs;CO;80908-4508;United States of America LABEL;WORK;ENCODING=QUOTED-PRINTABLE:PPO=0D=0A10125 Federal Drive=0D=0AColorado Springs, CO 80908-4508=0D=0AUnite= d States of America URL: URL: EMAIL;PREF;INTERNET:Gregory.McClure@quantum.com REV:19990322T230509Z END:VCARD ------_=_NextPart_000_01BFAEFB.FDB1B26E-- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Ron Barnett Subject: RE: (fractint) Pretty mandel Date: 25 Apr 2000 19:50:50 -0400 Wow, a ghost from the past! Welcome back caren. Ron Barnett On Tuesday, April 25, 2000 13:15, caren park [SMTP:carenp@yahoo.com] wrote: > was the PSP image (bottom of that web page) paint shop pro-enhanced, or was > this another feature of fractint 20 (or ultra-frac)? > i liked it... LOTS... > > ----- Original Message ----- > From: Sylvie Gallet > To: > Sent: Tuesday, April 25, 2000 9:21 AM > Subject: (fractint) Pretty mandel > > > Hi Lee, > > >> Very nice! > > Thanks! > > >> You had time already to generate a very small thumbnail? > > Oh, no! I generated it at 1600x1200 on my PXV 30K!!! ;-) > > The 1600x1200 GIF along with some 800x600 JPGs are available at: > > > > Cheers, > > - Sylvie > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > > > __________________________________________________ > Do You Yahoo!? > Talk to your friends online with Yahoo! Messenger. > http://im.yahoo.com > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "caren park" Subject: Re: (fractint) Pretty mandel Date: 25 Apr 2000 17:06:47 -0700 talk about a ghost from the past, son! still living in oregon, or am i thinking of someone else in my senility? :) ----- Original Message ----- Sent: Tuesday, April 25, 2000 4:50 PM > Wow, > a ghost from the past! Welcome back caren. > Ron Barnett > > On Tuesday, April 25, 2000 13:15, caren park [SMTP:carenp@yahoo.com] wrote: > > was the PSP image (bottom of that web page) paint shop pro-enhanced, or was > > this another feature of fractint 20 (or ultra-frac)? > > i liked it... LOTS... > > > > ----- Original Message ----- > > From: Sylvie Gallet > > To: > > Sent: Tuesday, April 25, 2000 9:21 AM > > Subject: (fractint) Pretty mandel > > > > > > Hi Lee, > > > > >> Very nice! > > > > Thanks! > > > > >> You had time already to generate a very small thumbnail? > > > > Oh, no! I generated it at 1600x1200 on my PXV 30K!!! ;-) > > > > The 1600x1200 GIF along with some 800x600 JPGs are available at: > > > > > > > > Cheers, > > > > - Sylvie > > > > -------------------------------------------------------------- > > Thanks for using Fractint, The Fractals and Fractint Discussion List > > Post Message: fractint@lists.xmission.com > > Get Commands: majordomo@lists.xmission.com "help" > > Administrator: twegner@fractint.org > > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > > > > > > __________________________________________________ > > Do You Yahoo!? > > Talk to your friends online with Yahoo! Messenger. > > http://im.yahoo.com > > > > -------------------------------------------------------------- > > Thanks for using Fractint, The Fractals and Fractint Discussion List > > Post Message: fractint@lists.xmission.com > > Get Commands: majordomo@lists.xmission.com "help" > > Administrator: twegner@fractint.org > > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" __________________________________________________ Do You Yahoo!? Talk to your friends online with Yahoo! Messenger. http://im.yahoo.com Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Ron Barnett Subject: RE: (fractint) Pretty mandel Date: 25 Apr 2000 20:55:49 -0400 Hi caren, Actually I was living in New Joyzee during the Fractint/Fractal Frenzy II times. I am now in the mountains of very northern New York. Are you still running a book store (I think that is what you were doing back then). Check out my website if you have a chance. Ron Barnett http://www.hiddendimension.com A fractal art and music site in the Adirondacks On Tuesday, April 25, 2000 20:07, caren park [SMTP:carenp@yahoo.com] wrote: > talk about a ghost from the past, son! still living in oregon, or am i > thinking of someone else in my senility? :) > > ----- Original Message ----- > From: Ron Barnett > To: > Sent: Tuesday, April 25, 2000 4:50 PM > Subject: RE: (fractint) Pretty mandel > > > > Wow, > > a ghost from the past! Welcome back caren. > > Ron Barnett > > > > On Tuesday, April 25, 2000 13:15, caren park [SMTP:carenp@yahoo.com] > wrote: > > > was the PSP image (bottom of that web page) paint shop pro-enhanced, or > was > > > this another feature of fractint 20 (or ultra-frac)? > > > i liked it... LOTS... > > > > > > ----- Original Message ----- > > > From: Sylvie Gallet > > > To: > > > Sent: Tuesday, April 25, 2000 9:21 AM > > > Subject: (fractint) Pretty mandel > > > > > > > > > Hi Lee, > > > > > > >> Very nice! > > > > > > Thanks! > > > > > > >> You had time already to generate a very small thumbnail? > > > > > > Oh, no! I generated it at 1600x1200 on my PXV 30K!!! ;-) > > > > > > The 1600x1200 GIF along with some 800x600 JPGs are available at: > > > > > > > > > > > > Cheers, > > > > > > - Sylvie > > > > > > -------------------------------------------------------------- > > > Thanks for using Fractint, The Fractals and Fractint Discussion List > > > Post Message: fractint@lists.xmission.com > > > Get Commands: majordomo@lists.xmission.com "help" > > > Administrator: twegner@fractint.org > > > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > > > > > > > > > __________________________________________________ > > > Do You Yahoo!? > > > Talk to your friends online with Yahoo! Messenger. > > > http://im.yahoo.com > > > > > > -------------------------------------------------------------- > > > Thanks for using Fractint, The Fractals and Fractint Discussion List > > > Post Message: fractint@lists.xmission.com > > > Get Commands: majordomo@lists.xmission.com "help" > > > Administrator: twegner@fractint.org > > > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > > > > -------------------------------------------------------------- > > Thanks for using Fractint, The Fractals and Fractint Discussion List > > Post Message: fractint@lists.xmission.com > > Get Commands: majordomo@lists.xmission.com "help" > > Administrator: twegner@fractint.org > > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > > > __________________________________________________ > Do You Yahoo!? > Talk to your friends online with Yahoo! Messenger. > http://im.yahoo.com > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > > Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Guy Hammer Subject: Blast from the past; (was: (fractint) Pretty mandel) Date: 25 Apr 2000 18:13:02 -0700 Ron writes: >Actually I was living in New Joyzee during the Fractint/Fractal Frenzy II >times. I am now in the mountains of very northern New York. Caren may have been thinking of me. I was, and still am living in NW Oregon. :-) Regards, Guy PS: Anyone heard from Bob Dodson (sp?) lately? guyh@teleport.com (Guy Hammer) http://www.teleport.com/~guyh Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Lee Skinner Subject: (fractint) Pretty mandel Date: 25 Apr 2000 21:30:38 -0400 Hi Miguel, >> PS : The web page says "4700 hs. on a P300", while the posted par said= it was a P233....? << It was computed on a P300 at my office. I made the par on my home comput= er (a P233) and I forgot to correct the CPU speed in the automated comment. Lee Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Lee Skinner Subject: (fractint) Pretty mandel Date: 25 Apr 2000 21:30:38 -0400 Hi Miguel, >> PS : The web page says "4700 hs. on a P300", while the posted par said= it was a P233....? << It was computed on a P300 at my office. I made the par on my home comput= er (a P233) and I forgot to correct the CPU speed in the automated comment. Lee Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Guy Marson Subject: Re: (fractint) MandelbrotMix4 lakes Date: 26 Apr 2000 05:21:29 +0200 At 15:12 24/04/00 -0400, you wrote: >Hi All, > > Here's a couple of MandelbrotMix4 Lake example. Both formulas are based >on Jim Muth's MandelbrotMix4, the original parameters used in MMix4 (p1, >p2, p3) are now hard-coded in the formula (renamed as p_p1,...), in order >to make p2 and p3 available for the lake effect. > Oohhh.. thanks Sylvie, Jim! That's a b'ful playground for little animations (and tests)!! cheers, Guy Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 26-04-00 (Worth a Diamond [5]) Date: 26 Apr 2000 00:56:54 -0400 (EDT) FOTD -- April 26, 2000 (Rating 5) Fractal visionaries and enthusiasts: I named today's FOTD "Worth a Diamond". The rather vague diamond shape around the electric blue minibrot in the background inspired the name. The formula that drew the fractal in which I found the diamond is Z^(-1.2)-(Z^1.2)+C. This parent fractal consists of two disconnected and quite distorted Mandeloids. I can tell just by looking at these twisted figures that they are filled with interesting midgets. In fact, I might devote an entire week to investigating this particular two-part fractal. The parameter file runs in just over one minute on a modest Pentium. This is probably the most simple way to view the image. But for those who would rather see the image already rendered, it has been posted to: and to: The fractal weather was quite unpleasant today, as a steady chilly rain fell and the temperature hovered around 48F (9C). These conditions kept the cats safely ensconced indoors all day, their frustration building as the day progressed. Luckily, a good meal of their favorite food kept their frustration under control. My philosophical musings also grew as the day progressed, but they never reached the level of being worthy of being made public. As usual, I'll try again tomorrow. Until then, take care, and enjoy today's fractal. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Worth_a_Diamond { ; time=0:01:06.19, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident center-mag=+0.14392839195860990/+2.73449807098121600\ /16024.72/1/10 params=-1/1.2/1/-1.2/0/0 float=y maxiter=1200 bailout=25 inside=0 logmap=22 symmetry=none periodicity=10 colors=000b6H<2>V6DT6CP6BM6AI69G68I89L99PA9VC9Y6AYDL\ cJKfOF<3>qXG<6>V_bS_eO_h<3>C`t<2>I_b<5>QXoRWqTWs<2>X\ UyYUzZTz_Tz<3>IQz<3>PTzRUzSUz<2>QezPdz<2>Ocz<5>bczdc\ zgcz<3>pcz<3>Kcz<3>HczGczFcz<3>HczHczIczIczJczJcz<3>\ CczBcz9cz<3>3cz<6>KczMczOczRczTczVcz<3>jczhczEcz9cz<\ 3>IczKczNcz<3>Vez<4>LgzJhzHhz<3>Ajz<3>ClzDmzDmz<3>Fm\ zFmzFmzDmzBmz<2>smz<3>qmzqmzqmz<2>pmz<7>QmzMmzJmz<2>\ 9mz6mz5mz<7>4mz4mz3mz<3>3mz<5>PmzTmzWmz<3>imz<5>cmz<\ 3>_mz_mzRmz<6>`mzbmzcmz<3>hmz<3>Smz<7>Emzgmzdmz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: (fractint) sqr() function considered harmful. Date: 26 Apr 2000 18:37:50 +1200 I took some time out to do some speed tests of Fractint's formula parser - in particular, how it handles various ways of representing integer powers of a complex number. I was surprised by the results. I made these tests on the standard v20 distribution, after booting to DOS so that my timings wouldn't be blurred by Windows rearranging Fractint's memory in the background (though Fractint may not necessarily notice, it was just as easy to avoid the possibility as ignore it). I evaluated c^n using floating-point arithmetic about two million times in succession for random values of c, where n ranged from 0 to 16 using the following formula as a template: {z=0,c=rand:c=[c^n],|z|<4} c^n was evaluated in three different ways. First off was the obvious "c^n" construct itself, e.g., c=c^5. Second was to use repeated multiplication, e.g., c=c*c*c*c*c And third was to use sqr() as much as possible to avoid repeated expressions: e.g, c^5=sqr(sqr(c))*c, c^7=sqr(sqr(c)*c)*c, c^8=sqr(sqr(sqr(c))). I wrote an autokey script to do the boring work of running all these tests, saving each completed test as an image, then took the timing information from the resulting series of gifs. Anyhow, here are the timings: n power mult sqr 0 1:29.74 1:08.28 1:08.28 1 1:44.36 1:03.22 1:03.17 2 1:17.83 1:18.21 1:19.09 3 1:17.67 1:33.43 1:34.36 4 1:17.61 1:50.24 1:35.57 5 1:17.55 2:05.17 1:50.95 6 1:17.50 2:20.23 1:51.50 7 1:17.45 2:35.87 2:08.80 8 1:17.39 2:52.63 1:51.17 9 1:17.39 3:07.07 2:10.29 10 1:17.33 3:23.67 2:11.77 11 1:17.39 3:37.07 2:26.32 12 1:17.39 3:50.97 2:10.89 13 1:17.39 4:12.00 2:27.03 14 1:17.39 4:21.94 2:24.62 15 1:17.33 4:36.65 2:40.66 16 1:17.34 4:55.88 2:07.43 When n is equal to zero or one, both repeated multiplication and repeated squaring result in the same expressions, respectively "1" and "c". So the similarity in their timings for these two values of n is inevitable. The ^ operator has trouble with the special cases c^0=1 and c^1=c; otherwise, it consistently gave times of just over 1 minute 17.5 seconds. The fluctuations in the sqr() timings is to be expected, given the variations in the number of operations required for each n. But the surprise is that sqr() did so poorly against the others. Above n=3, the power function was far and away the fastest, and repeated multiplication equally obviously the slowest; but even for the case n=2 (in which you would expect to to shine), sqr(c) was still noticeably _slower_ than c^2, or even c*c. Of course, the timed difference between c^2 and sqr(c) is only a matter of about a second here, but remember that this is over the course of just a minute's work at a (trivial) image. Going by the above timings, it appears that if you're raising a number z to the power of some fixed integer n, the fastest way of doing it is to write "z^n" when n is 2 or more, and simply to write "1" or "z" if n is zero or one. Repeated multiplication appears to be pretty much guaranteed to be slower, and even sqr(z) is slower than z^2. These results appear to contradict the usual advice given - use sqr(z) when you're squaring, and repeated multiplication instead of exponentiation for small values of n. I would be interested in seeing similar timings made by others to see just which code is faster than which. Morgan L. Owens "Good grief - you do two _million_ complex exponentiations and you're complaining about a delay of _one second_??!" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) Mime-Version: 1.0 Date: 26 Apr 2000 19:28:23 +1200 At 14:32 25/04/2000 -0400, you wrote: >Hi Morgan, > >>> Here's a little lsystem idea I thought I'd try out after looking at >>> reptiles too long. > >>> Pentominoes{ ; What's the collective noun for reptiles? > > Wow!!! It's great! > > Cheers, > > - Sylvie > Thank you! Morgan L. Owens "Yes, boss ... Uh, would you believe me if I it's a Perl format string generator...?" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) minibrots / mandeloids (whatever-you-call-'ems) Date: 26 Apr 2000 22:23:01 +1200 At 17:44 25/04/2000 GMT, Rupert Millard wrote: >Hello all, > >I find it fascinating that the 'mandelbrot shape' (I really *don't* know >what to call it!) occurs in so many different formulae. I have tried looking >to see what mandel, magnet1m, magnet2m, mandellamba, nova etc. have in >common with each other but *I* can't see anything. <:-( > What they have in common with each other ... well, it's more a matter with what they have in common with the standard Mandelbrot set. Consider the graph of a function. Just a standard wiggly line on graph paper - no need at this point to worry about complex-valued functions of a complex variable :-). You'll notice that a typical graph has humps and hollows and things like that. Zoom in on one of these hollows and you can for the most part ignore the rest - they could easily be different and the hollow you're looking at could still look pretty much the same. This is a quick hint of what's described in Beauty of Fractals as "universality". Now broaden your view out into another dimension. Instead of just having a bumpy line, have a bumpy surface. Peaks, valleys, passes and all sorts of other topography. Different features in the landscape produce different structures in the resulting fractal. (If you really want, you can try imagining that height above sea level is actually a complex number - which adds yet another whole dimension to your catalogue of possible features and possible structures). But again, one hollow looks pretty much like another. In a (somewhat metaphorical) sense, the graph of z^2+c consists entirely of one single hollow - a bowl shape. So now you set your point wandering all over this surface, following whatever orbit its function (magnet, nova or whatever) describes. Now and then your point may find itself in a bowl. Now, since one bowl looks pretty much like another your point will act pretty much the same in each one (a distant peak has less influence than a bowl that's _right there_). Depending on how closely you zoom in and how little you care about the surrounding countryside, you can approximate the bowl your point finds itself in with something that looks more like your generic standard-issue z^2+c, and less like whatever wild construction you _really_ have. And we know how points in bowls behave, don't we? The distortions that inevitably creep into the Mandelbrot sets that pop up all over (stretching, colliding and worse) all these other functions is a consequence of the fact that the functions _aren't_ really z^2+c after all: if two fairly large bowls are close together, for example, their Mandelbrot-set wannabes might collide. And of course there are all the other structures being created by all the other features of the surface. In short, a Mandelbrot-set-like thing shows up whenever and whereever a function (however wild) looks _locally_ like something that could be approximated by z^2+c: what I've be describing as a "bowl". (Could probably explain this better. Want to know where it could be improved.) Morgan L. Owens "Who admits to speaking in parables on occasion." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Fliguer, Miguel" Subject: RE: (fractint) minibrots / mandeloids (whatever-you-call-'ems) Date: 26 Apr 2000 15:25:30 -0300 >In short, a Mandelbrot-set-like thing shows up whenever and whereever a >function (however wild) looks _locally_ like something that could be >approximated by z^2+c: what I've be describing as a "bowl". By the same token, a n-lobe-distorted-M-set (or a picture of Mona Lisa) should show up whenever the above wild chaotic function is calculated on an area where it can be approximated by the n-lobe-distorted-M-set formula (or the formula for the picture of Mona Lisa). Are you still with me ? After years of complex plane exploring, I can say I found a lot of standard M-sets on many different formulas, but not many n-lobe-distorted-M-sets, and still not a single Mona Lisa ;-) So I guess the simpler the formula (i.e. z*z+c ), the greater the probability for the associated shape (i.e the standard M-set) to appear in the middle of chaos. The above statements may be pure nonsense, of course. Anyway, I enjoyed writing them. Fetch me some aspirins, please. Just my $0.02 pesos Regards, Miguel Fliguer Franktal Gallery - Shut Up and Draw Yer Fractals http://members.xoom.com/fliguer/franktal.html Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Iain G. Stirling" Subject: Re: (fractint) sqr() function considered harmful. Date: 26 Apr 2000 20:37:49 +0100 Morgan L. Owens wrote: > I took some time out to do some speed tests of Fractint's formula parser - > in particular, how it handles various ways of representing integer powers > of a complex number. I was surprised by the results. > Morgan, This type of analysis is what I find most interesting about computing, so I quickly set about producing my own set of results. I used the following (clumsy) procedure: Step 1. Create formulas for each of the tests in a .FRM file, e.g: exp0 {z=0,c=rand,c=c^0,|z|<4} sqr3 {z=0,c=rand,c=sqr(c)*c,|z|<4} Step 2. Create a .PAR file, each entry testing one of the formulas, e.g: sqr3 { reset=2000 type=formula formulafile=test.frm formulaname=sqr3 passes=1 center-mag=0/0/0.6666667 float=y cyclerange=1/1 colors=00000e } Step 3. Create a .BAT file, running each PAR entry and saving the image, e.g: rem fractint @test.par/sqr2 BATCH=y VIDEO=AF2 SAVENAME=sqr2 rem fractint @test.par/sqr3 BATCH=y VIDEO=AF2 SAVENAME=sqr3 I used video mode AF2 (1600 x 1200 x 2 colours diskvideo), which tests each formula 1,920,000 times. I then read the times from the images after restoring them in Fractint. Here are my times: n power mult sqr 0 7:48.46 5:47.40 5:44.44 1 8:33.50 5:47.35 5:44.49 2 8:34.82 6:19.43 6:07.29 3 8:21.64 6:53.75 6:52.55 (I only ran to n=3, as I am supposed to be studying for my final exams at the moment!) So, this fits quite well with the conventional wisdom in this area... This begs the question ... What is going on here? I have been trying to think of reasons for this. Do you use an non-Intel processor, which might give a different performance for some FP instructions? If I have time (possibly at the weekend), I'll continue these tests. Iain Stirling. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Bill Jemison Subject: (fractint) anyone remember an old lady that looked like me? Date: 26 Apr 2000 16:00:07 -0400 Subject: RE: (fractint) Pretty mandel Date: 26 Apr 2000 16:43:04 -0400 Hi Miguel, >> If I understand it well, if I ever venture into the arbitrary precisio= n >> realm, I better switch to passes=3D1, ok ? Yes, and at least, with passes=3D1, you're sure to get the most accurat= e image. >> What about difussion mode ? It seems much slower than passes=3D1. >> And the hidden synchronous orbit mode ? (I tried to plot Lee's par wit= h >> this method, it finished in about 40 seconds but the image was just 4 >> purple squares, each in 1/4 of the screen) This mode doesn't work with arbitrary precision. I tried it with Lee's= par, and it just froze Fractint. Cheers, - Sylvie Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Sylvie Gallet Subject: Re: (fractint) MandelbrotMix4 lakes Date: 26 Apr 2000 16:43:06 -0400 Hi Guy, >> Oohhh.. thanks Sylvie, Jim! That's a b'ful playground for little >> animations (and tests)!! You're welcome! Have fun!!! Cheers, - Sylvie Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Fliguer, Miguel" Subject: RE: (fractint) MandelbrotMix4 lakes Date: 26 Apr 2000 17:57:36 -0300 Guy wrote : >> Oohhh.. thanks Sylvie, Jim! That's a b'ful playground for little >> animations (and tests)!! Check out "Mandelbrot SunSet" at http://members.xoom.com/fliguer/gallery5.html for a 570K AVI which features the "lake" effect. Regards, Miguel Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: davides Subject: RE: (fractint) MandelbrotMix4 lakes Date: 26 Apr 2000 18:52:08 -0400 At 05:57 PM 4/26/2000 -0300, you wrote: >Check out "Mandelbrot SunSet" at >http://members.xoom.com/fliguer/gallery5.html >for a 570K AVI which features the "lake" effect. > >Regards, >Miguel Very nice. davides@pipeline.com Back up my hard drive? How do I put it in reverse? Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Lee Skinner Subject: (fractint) anyone remember an old lady that looked like me? Date: 26 Apr 2000 20:23:13 -0400 Bill, >> Yes! I should have a few pars ready shortly. << GREAT!! I haven't played a new music par in a long time. Lee Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Harry Bissell Subject: Re: (fractint) Fractal Music : was old lady looked like me? Date: 26 Apr 2000 23:18:44 -0400 Yeah that reminds me... I've played a little bit with the music feature. Did someone have a way to save the sequences as MIDI files. Best would be direct to a std. midi file format I could run to a dedicated sequencer CPU (its a '286 so sound card is out...'eh?). What are your favorite file types for fractal music... H^) harry (hear for eye AND ear candy....) Bill Jemison wrote: > > Yes! I should have a few pars ready shortly. > > Bill > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 27-04-00 (Worth a Diamond [6]) Date: 27 Apr 2000 00:48:00 -0400 (EDT) FOTD -- April 27, 2000 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal is a picture of another . . . you guessed it . . . midget from the ever-changing land of MandelbrotMix4. This particular midget exists and always has existed in abstract form in the Mandeloid fractal created by the formula 0.95(Z^(-1.1)-Z^1.1)+C. But this is the first time that this midget, which has been hiding since before eternity, has been seen by the eyes of observers, human or otherwise. The midget is one of the more decorative ones that I have dredged up in recent days. My ability to ferret out these elusive objects seems to rise and fall in irregular cycles. In the more complex formulas such as those calculated by the M-Mix4 formula, the position of the midgets is not always apparent. Sometimes they appear in areas that seem totally hopeless. To find these most elusive midgets I rely on instinct -- I get a feeling that a midget lies buried at a certain location, and as often as not, it does. Change the magnification of today's FOTD to 100, change the logmap to 1, and observe the hopeless image. I can give no logical reason why I searched the center of that image for a midget, but I did, and today's FOTD is the result. I named the picture "Be a Good Sport" for no reason in particular. It just seemed like a nice name. The 8 minutes it takes to run the parameter file is enough time to make a download the better choice. The download may be done by going to: on Usenet, and looking for the "Fractal of the Day" subject line, or by going to: which is Paul Lee's site on the Web. The fractal weather today was mostly cloudy and chilly, with a few sprinkles of rain. The fractal cats chose to venture outside only briefly in the temperature of 56F (13C). Much to the sorrow of those waiting for enlightenment, the philosophy languished today. But hopefully tomorrow will bring the light. It must. If I don't bring light tomorrow, who will? Until then, take care, and did God create fractals, or did man invent them? Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Be_a_Good_Sport { ; time=0:08:04.88 on a P200, SF5 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.70258058382572460/+1.84578902125106600\ /1.159885e+011/1/-95.001/-0.006 params=-1/1.1/1/-1.1\ /-0.05/1000 float=y maxiter=1200 bailout=25 inside=0 logmap=142 symmetry=none periodicity=10 colors=000MAk<3>PAhQAgRAfSAeTAdUAc<3>ZAe_Af`AfaAf<5>\ gFfhGfiHf<3>mLfnMcoNZ<3>rbFrVAsK5PA4KA1oK2kY3ge4<3>T\ P6PK7LF8IC8KH7LN7NR6OX6Q`6Rf5ck5hp4hu4mz4mz5mz6hx7bu\ 8Op8<3>HkCFjCEhD<2>9eF7dP5cZ1di<6>HZZJYYLXX<3>UUR`UP\ dTOiSNmZL<2>umH<2>zmDwmErcFmKGhJHdII<10>J7SH6TF5U<3>\ 72X<11>WdcYgd_kd<3>gwf<3>UxmRxnOxp<3>Bxv<3>VgpZbncZm\ hVkmRjtMk<14>LZUJ_TG`R<3>7dN1fL<6>TWMXUM`TM<3>oNM<11\ >TYYRZZP__<3>HccFai<3>IiSJkOKmJLoFMs7<3>KwMKxQJyT<3>\ IzgHzjHznHzq<7>TzqVzqWzq<3>azqhzy<6>3zA } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) sqr() function considered harmful. Date: 27 Apr 2000 20:07:04 +1200 At 20:37 26/04/2000 +0100, you wrote: >Morgan L. Owens wrote: > >> I took some time out to do some speed tests of Fractint's formula parser - >> in particular, how it handles various ways of representing integer powers >> of a complex number. I was surprised by the results. >> > >Morgan, > >This type of analysis is what I find most interesting about computing, >so I quickly set about producing my own set of results. > >I used the following (clumsy) procedure: > >... > Substantially it's the same approach as mine - in particular the formulae are almost identical ("almost" - see below). Rather than create pars and run them from a batch file, though, I used an autokey script with lines like: "t" ENTER "power03" ENTER ENTER CALCWAIT "s" CALCWAIT to run Fractint in a single long run through all 51 formulae. The video mode I used was 1600x1200x256, with passes=g (which was easier than switching to a lower resolution) and a maxiter of 1023. That comes to round about 2000000 iterations per image (since only something like one in a thousand pixels would be evaluated). >Here are my times: > >n power mult sqr >0 7:48.46 5:47.40 5:44.44 >1 8:33.50 5:47.35 5:44.49 >2 8:34.82 6:19.43 6:07.29 >3 8:21.64 6:53.75 6:52.55 > >(I only ran to n=3, as I am supposed to be studying for my final exams >at the moment!) > This looks a lot more like what I'd expected to see. The much higher times overall than mine can be explained with a look at the formulae: exp0 {z=0,c=rand,c=c^0,|z|<4} sqr3 {z=0,c=rand,c=sqr(c)*c,|z|<4} The second comma should be a colon; as things stand all four statements are executed with every iteration, instead of only the last two. In fact, mine run far slower than they should - the final test need only be something guaranteed to be true: "1==1" (or even just "1", if the parser works the way I think it does) would be a lot faster, and so make for more accurate times. >So, this fits quite well with the conventional wisdom in this area... >This begs the question ... What is going on here? > >I have been trying to think of reasons for this. Do you use an non-Intel >processor, which might give a different performance for some FP >instructions? > Nope, it's a bog-standard Pentium 166. This sort of result is what I half-suspected, which is why I hoped someone else would run similar tests. I had got suspicious when some optimisations I was making to a few of my formulae didn't appear to have any result. But I surmised that conventional wisdom must have had some justification. When I find another spare hour or two I'll fiddle with the experimental conditions and make another run. > If I have time (possibly at the weekend), I'll continue these tests. > I'll be interested in the results, in particular where the breakovers occur - how high does n have to be before powers are cheaper than multiple multiplicatios? Incidentally, how does Fractint actually time a run? By comparing wall time at the start and end (or interruption) of a run, or does it use an internal timer? Calibrated how? Morgan L. Owens "Spend the time now, save it later. I wish I could do that with money." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: RE: (fractint) minibrots / mandeloids (whatever-you-call-'ems) Date: 27 Apr 2000 21:56:38 +1200 At 15:25 26/04/2000 -0300, Miguel Fliguer wrote: > >>In short, a Mandelbrot-set-like thing shows up whenever and whereever a >>function (however wild) looks _locally_ like something that could be >>approximated by z^2+c: what I've be describing as a "bowl". > I should have pointed out earlier that the _really_ important bits of the landscape are the flat points - like those at the bottom of the bowl. These so-called "critical points" are very sensitive to what goes on around them - jiggle them a tiniest bit and they're not flat any more! But since a bowl _has_ to have a critical point (assuming the surface is smooth), then if one is destroyed, another will appear to takes its place. The same thing happens on the tops of humps of course, but our orbiting points avoid them. > >So I guess the simpler the formula (i.e. z*z+c ), the greater >the probability for the associated shape (i.e the standard M-set) >to appear in the middle of chaos. > In more complicated formulas, the stability of critical points is by no means assured - they could split or merge even if the formula changes only a tiny bit. z^2+c survives because it's only got one critical point and while it can wander about it can't disappear. z^3+c has one critical point also - at z=0+0i - but in its case the slightest alteration to the formula (like adding 0.0000001z) causes this solitary critical point to split into two (in this case into +-1/30000000+0i.) Not a lot of difference, but play with these formulas and see what happens to the cubic as the perturbation gets larger. The perturbed Quadratic is just the M-set when p1=0. Note how well that stays together as p1 increases. Oh, and that z=sqrt...whatever business? Well, these things are supposed to start from a critical point, so... perturbedCubic{ z=sqrt(-p1/3),c=pixel: z=z^3+p1*z+c |z|<=4 } perturbedQuadratic{ z=-p1/2,c=pixel: z=z^2+p1*z+c |z|<=4 } Morgan L. Owens "Whew! And I did all that without once mentioning Morse's Theorem. Which is not necessarily a Good Thing." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Ricardo M. Forno" Subject: RE: (fractint) MandelbrotMix4 lakes Date: 27 Apr 2000 13:31:53 -0300 Miguel: After several attempts, I was unable to connect to your page. Do you know what is going on? ----- Original Message ----- Sent: Wednesday, April 26, 2000 5:57 PM > Guy wrote : > > >> Oohhh.. thanks Sylvie, Jim! That's a b'ful playground for little > >> animations (and tests)!! > > Check out "Mandelbrot SunSet" at > http://members.xoom.com/fliguer/gallery5.html > for a 570K AVI which features the "lake" effect. > > Regards, > Miguel > > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Iain G. Stirling" Subject: Re: (fractint) sqr() function considered harmful. Date: 27 Apr 2000 17:00:43 +0100 Morgan L. Owens wrote: > At 20:37 26/04/2000 +0100, you wrote: > >Morgan L. Owens wrote: > > > >> I took some time out to do some speed tests of Fractint's formula parser - > >> in particular, how it handles various ways of representing integer powers > >> of a complex number. I was surprised by the results. > >> > > > > >Here are my times: > > > >n power mult sqr > >0 7:48.46 5:47.40 5:44.44 > >1 8:33.50 5:47.35 5:44.49 > >2 8:34.82 6:19.43 6:07.29 > >3 8:21.64 6:53.75 6:52.55 > > > >(I only ran to n=3, as I am supposed to be studying for my final exams > >at the moment!) > > > This looks a lot more like what I'd expected to see. The much higher times > overall than mine can be explained with a look at the formulae: > > exp0 {z=0,c=rand,c=c^0,|z|<4} > sqr3 {z=0,c=rand,c=sqr(c)*c,|z|<4} > > The second comma should be a colon; as things stand all four statements are > executed with every iteration, instead of only the last two. This might account for the difference we see. With my formulae, c is reinitialised, and so takes on a fresh magnitude every iteration. With your formulae, c is repeatedly diminshed, through 150 iterations (assuming you have left the default maxiter value). Surely at some point, the value is diminshed until it cannot be represented in floating point any more, and it just takes the value zero. Then, perhaps the particular function (*, ^ or sqr()) has an optimisation for the zero case, allowing it perform very well? (This is just a hunch, mind you.) > This sort of result is what I half-suspected, which is why I hoped someone > else would run similar tests. I had got suspicious when some optimisations > I was making to a few of my formulae didn't appear to have any result. But > I surmised that conventional wisdom must have had some justification. > > When I find another spare hour or two I'll fiddle with the experimental > conditions and make another run. > > > If I have time (possibly at the weekend), I'll continue these tests. > > > I'll be interested in the results, in particular where the breakovers occur > - how high does n have to be before powers are cheaper than multiple > multiplicatios? > I have decided to take a break from studying (well-earned, I assure you) to continue my testing: n power mult sqr 0 7:48.46 5:47.40 5:44.44 1 8:33.50 5:47.35 5:44.49 2 8:34.82 6:19.43 6:07.29 3 8:21.64 6:53.75 6:52.55 4 8:08.23 7:36.43 6:53.92 5 8:00.59 8:22.08 7:38.73 6 7:55.55 9:03.76 7:43.02 7 7:52.08 9:48.80 8:35.86 8 7:49.45 10:55.59 7:46.27 9 7:47.36 12:09.47 8:45.15 10 7:53.95 13:39.32 8:53.05 So it can be seen that beyond n=4, multiplication is worst, and powers and sqr fight over it, with sqr being successful on n=5,6 and 8. What I will probably do next (on my next study break) is add that colon into the formulae and get a new set of results, which I presume will compare with yours. If you change the colon for a comma in your formulae, will your times agree with mine above...? For reference, I have a P133 and I am running Fractint from DOS, so the times we get should be quite similar for identical tests. Iain Stirling. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Fliguer, Miguel" Subject: RE: (fractint) MandelbrotMix4 lakes Date: 27 Apr 2000 15:10:31 -0300 It works from here. You can try using xoom's numerical ip address : http://206.132.163.167/fliguer/franktal.html (You can't see the graphics in this way) If you can connect to the page, that means your browser can't resolve xoom's address because of a local DNS problem. How's your book selling ? ;-) -----Mensaje original----- De: Ricardo M. Forno [mailto:rforno@afip.gov.ar] Enviado el: jueves 27 de abril de 2000 13:32 Para: fractint@lists.xmission.com Asunto: RE: (fractint) MandelbrotMix4 lakes Miguel: After several attempts, I was unable to connect to your page. Do you know what is going on? ----- Original Message ----- Sent: Wednesday, April 26, 2000 5:57 PM > Guy wrote : > > >> Oohhh.. thanks Sylvie, Jim! That's a b'ful playground for little > >> animations (and tests)!! > > Check out "Mandelbrot SunSet" at > http://members.xoom.com/fliguer/gallery5.html > for a 570K AVI which features the "lake" effect. > > Regards, > Miguel > > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Iain G. Stirling" Subject: Re: (fractint) sqr() function considered harmful. Date: 27 Apr 2000 21:30:02 +0100 Iain G. Stirling wrote: > Morgan L. Owens wrote: > > > At 20:37 26/04/2000 +0100, you wrote: > > >Morgan L. Owens wrote: > > > > > >> I took some time out to do some speed tests of Fractint's formula parser - > > >> in particular, how it handles various ways of representing integer powers > > >> of a complex number. I was surprised by the results. > > >> > > > > > > > > > > >Here are my times: > > > > > >n power mult sqr > > >0 7:48.46 5:47.40 5:44.44 > > >1 8:33.50 5:47.35 5:44.49 > > >2 8:34.82 6:19.43 6:07.29 > > >3 8:21.64 6:53.75 6:52.55 > > > > > >(I only ran to n=3, as I am supposed to be studying for my final exams > > >at the moment!) > > > > > This looks a lot more like what I'd expected to see. The much higher times > > overall than mine can be explained with a look at the formulae: > > > > exp0 {z=0,c=rand,c=c^0,|z|<4} > > sqr3 {z=0,c=rand,c=sqr(c)*c,|z|<4} > > > > The second comma should be a colon; as things stand all four statements are > > executed with every iteration, instead of only the last two. > > This might account for the difference we see. With my formulae, c is > reinitialised, and so takes on a fresh magnitude every iteration. With > your formulae, c is repeatedly diminshed, through 150 iterations > (assuming you have left the default maxiter value). Surely at some > point, the value is diminshed until it cannot be represented in floating > point any more, and it just takes the value zero. Then, perhaps the > particular function (*, ^ or sqr()) has an optimisation for the zero case, > allowing it perform very well? (This is just a hunch, mind you.) OOPS! I have just noticed that my _e-mail_ was the only place that the second comma had been introduced - a simple typo. on my part. My .FRM files all use the colon in the second position, and hence match your formulae. So, the above reasoning (which might be sound) is entirely unrelated to the testing we are performing. Therefore it must surely be connected with the fact that you are using passes=g whereas I am using passes=1. Consequently my next tests will be with passes=g... Sorry for the confusion, Iain Stirling. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Guy Marson Subject: RE: (fractint) MandelbrotMix4 lakes Date: 27 Apr 2000 23:17:48 +0200 At 17:57 26/04/00 -0300, you wrote: >Check out "Mandelbrot SunSet" at >http://members.xoom.com/fliguer/gallery5.html >for a 570K AVI which features the "lake" effect. > >Regards, >Miguel > yeh, very nice! cheers, Guy Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Ricardo M. Forno" Subject: RE: (fractint) MandelbrotMix4 lakes Date: 27 Apr 2000 17:43:16 -0300 I already was able to connect to your page at the end. Thanks a lot. Very beautiful fractals, especially the "glasses". My book is not selling very well. I gave it no charge to some "personalities" in the production of TV shows, etc. ----- Original Message ----- Sent: Thursday, April 27, 2000 3:10 PM > It works from here. > > You can try using xoom's numerical ip address : > > http://206.132.163.167/fliguer/franktal.html > > (You can't see the graphics in this way) > > If you can connect to the page, that means your > browser can't resolve xoom's address because of a local > DNS problem. > > How's your book selling ? ;-) > > -----Mensaje original----- > De: Ricardo M. Forno [mailto:rforno@afip.gov.ar] > Enviado el: jueves 27 de abril de 2000 13:32 > Para: fractint@lists.xmission.com > Asunto: RE: (fractint) MandelbrotMix4 lakes > > > Miguel: > After several attempts, I was unable to connect to your page. > Do you know what is going on? > > ----- Original Message ----- > From: Fliguer, Miguel > To: > Sent: Wednesday, April 26, 2000 5:57 PM > Subject: RE: (fractint) MandelbrotMix4 lakes > > > > Guy wrote : > > > > >> Oohhh.. thanks Sylvie, Jim! That's a b'ful playground for little > > >> animations (and tests)!! > > > > Check out "Mandelbrot SunSet" at > > http://members.xoom.com/fliguer/gallery5.html > > for a 570K AVI which features the "lake" effect. > > > > Regards, > > Miguel > > > > > > -------------------------------------------------------------- > > Thanks for using Fractint, The Fractals and Fractint Discussion List > > Post Message: fractint@lists.xmission.com > > Get Commands: majordomo@lists.xmission.com "help" > > Administrator: twegner@fractint.org > > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > > -------------------------------------------------------------- > Thanks for using Fractint, The Fractals and Fractint Discussion List > Post Message: fractint@lists.xmission.com > Get Commands: majordomo@lists.xmission.com "help" > Administrator: twegner@fractint.org > Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) sqr() function considered harmful. Date: 28 Apr 2000 16:49:10 +1200 At 17:00 27/04/2000 +0100, Iain G, Stirling wrote: >> >> The second comma should be a colon; as things stand all four statements are >> executed with every iteration, instead of only the last two. > >This might account for the difference we see. With my formulae, c is >reinitialised, and so takes on a fresh magnitude every iteration. With >your formulae, c is repeatedly diminshed, through 150 iterations >(assuming you have left the default maxiter value). Surely at some >point, the value is diminshed until it cannot be represented in floating >point any more, and it just takes the value zero. Then, perhaps the >particular function (*, ^ or sqr()) has an optimisation for the zero case, >allowing it perform very well? (This is just a hunch, mind you.) > By that argument, * and sqr() should work really well, as ^ doesn't get the opportunity to see that the expression is approaching zero (so to speak). But the vanishing towards zero does sound like something that could affect timings. I'll do that :<->, swap you suggest on the weekend. > >So it can be seen that beyond n=4, multiplication is worst, and powers >and sqr fight over it, with sqr being successful on n=5,6 and 8. > sqr would be at its best when n is a power of 2. I might try comparing ^ and sqr for these values of n and see just how much of a fight sqr puts up (assuming my timings start making sense). Morgan L. Owens "It's not an expense - it's an investment." Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: RE: (fractint) sqr() function considered harmful. Date: 28 Apr 2000 16:44:48 +1200 At 15:50 27/04/2000, Robin wrote: >As an aside while benchmarkings are being discussed: > >>then took the timing information >>from the resulting series of gifs. > >If you invoke fractint with the option "debugflag=1" >(or debugflag=any odd number actually) >it will write a text file with time stamps for all fractals generated with >sub-second precision. > I really should look at that .doc file one day :-). This will certainly make my monitor happy! Hey, that means I don't even need to save any gifs! Morgan L. Owens "clickclickclickclick" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 28-04-00 (Red Dwarf [5]) Date: 28 Apr 2000 01:20:26 -0400 (EDT) FOTD -- April 28, 2000 (Rating 5) Fractal visionaries and enthusiasts: I named today's average fractal "Red Dwarf", though perhaps "Green Dwarf" or "Lilac Dwarf" would be more appropriate. (No, it is not named after a sci-fi TV show.) The illustrated midget is actually a scene in the fractal that results when the expression 0.95Z-Z^101+C is iterated. These baby Mandelbrots are called midgets. I have never heard one referred to as a dwarf, though the name would be equally correct. Today's parameter file renders in a little more than two minutes on an average Pentium. Downloading the image from: or from: is still the faster way of viewing the scene. The cold, clammy, dreary and drizzly weather kept the cats indoors all day. The temperature of 45F (7C) kept the house heat going in what is normally a warm time of year. As can be gathered from the terseness of the discussion, the philosophy went nowhere today -- perhaps because my particular philosophy has nowhere it could go, but more likely because I was simply too busy. After all, anyone who spends as much time searching for fractals as I do can't have that much time left for deep thinking. Until next time, take care, and think about it. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Red_Dwarf { ; time=0:02:22.45, SF5 on a p200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=t center-mag=+0.10939053115958090/+0.00013913783754621\ /7534114/1/154.999 params=-1/101/0.95/1/0/0 float=y maxiter=1800 bailout=25 inside=0 logmap=45 symmetry=none periodicity=10 colors=00049K044034034014<3>004004013041081163364446\ 646848939B3BC1BE1CG1EH0GJ0GK0HM0JN0JT1PX4T<2>jEgnHkr\ KqvNtzQzzTzzWzzXzrWzYUnCTb0SQ<2>1XY6_`9`cEbfHcgMfj<3\ >_mtcnwfoyckrbgk`ce__YYWTMsnKvqKysKzvPKgTMkYMnbNrfNt\ jPynPzrSwvTszUozXm<2>z`bz0zz0zz0rz0j<2>z8MY0zT0zP3z<\ 2>9Hz4Mz0Qz4Wz8_sBcmEgfJkYMoSPsKSwCUz4Yy6`w6ct6<2>ko\ 6nm6rk6ti6wg6ze6zc6z`6z_6z`CzbHzbMwcQteUreYqfbnffkgj\ iinfircjvbjzcizcgzcfzefzeezeczebzfbzf`zf_zfYz<3>gWz`\ YrW`jQbcKeWEfN8iG1j60m00n00q0<3>0v00w00y0<3>6z08z19z\ 1Bz3Cz3Ez4Ez4<3>Ee4E`4Gc6He6Hf8Jg8Ki9Kk9MmBNnBNoCPqC\ QsEQtESvGTwGTyGYzJczKgzMmzN<2>zzSzzTzzUzzSqzPizNmzCo\ z1rz0Wzt`zofzjkzeqz_vzUzzPzzJzzEzzJzzNyzQvzUrzXnz`jz\ egzgczk_znWzrTztSzvSzvSzwSzwSzy<2>Szz<2>CzzEzzEzyEzt\ EzqEzmEzgEzcEz_GzWGzSGzMGzHSzTKzNCzH } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Tom Conally Subject: (fractint) Kaleidoscope Date: 28 Apr 2000 10:23:53 -0400 Hi Gang, My first new par in a while. This par when color-cycled looks as much like a kaleidoscope as any I've seen. kaleidoscope { ; Kaleidoscope (c)Tom Conally, 4/2000 ; cycle color for kaleidoscope effect ; t=26.04sec on p400 ; Version 2000 Patchlevel 9 reset=2000 type=julia(fn||fn) function=exp/sqr passes=1 center-mag=+0.31781005849828920/-1.32276153613428900/8.573609/1.0309 params=0/0/8 float=y maxiter=1000 bailout=128 bailoutest=manh fillcolor=1 outside=real logmap=yes decomp=32 colors=WWWXNM<3>XjKWpJYEN<11>mgYnjZol_<3>uwcXDN<12>KWMJXMIZM<3>EdLXCN<9>\ OIJNJJNKJ<3>JMHJMGING<3>EQEZCO<4>jBYlBZoA`<3>y9hQELJGIBJFXCN<6>aIHaJGbKF\ <3>dNBeNAfO9<2>hR6XEM<3>ZOIZQH_TGWCN<14>CENAEN9EN<3>3FOXEN<2>XKNWDNXMN<3\ >WUMWWMWYMV_LLVKAPJ<10>eHChGCkGB<3>wC8<4>aIPXJTTKW<3>AQj<4>AiW<2>AuN<4>C\ eQCbQC_R<3>EOTFLUFIVGEVGBW<3>KLKMNHNQEOSBPV8RY4<13>RhfRiiRik<3>SmwkbK<12\ >qYkrYmrXp<3>uVy<3>umqtrnvov<2>jos } Tom Conally In every boomerang there is a perfect throw. Your life, Grasshopper, is to practice till you find that throw and become one with that boomerang! http://fly.to/boomerangs " Flying Frog Boomerangs" http://www.vstore.com/vstorehardware/flyingfrogtools/ "Flying Frog Tools" http://www.netpath.net/~conally My greater internet index Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: comdotatdotcom@csi.com Subject: RE: RE: (fractint) sqr() function considered harmful. Date: 28 Apr 2000 20:05 0000 Hi Morgan, >I really should look at that .doc file one day :-). This will certainly >make my monitor happy! Hey, that means I don't even need to save >any gifs! Well if you really want to check out the effect of using different ways of raising to powers you could save those gifs and then use debugflag=50 to detect any differences in the images... though I guesss that the file size would be a good indicater too, you'd probably get differeces in the size as a few pixels difference would compress differently. If you do get differences then passes=g would be out as a valid benchmarking method too... Gets more compicated the more you think about it :-) Cheers, Robin. Then again, how do you tell which one's the right one? Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 29-04-00 (Sugar-Plum Midget [6]) Date: 29 Apr 2000 09:47:40 -0400 (EDT) FOTD -- April 29, 2000 (Rating 6) Fractal visionaries and enthusiasts: The discussion is a little late again today because I once again took a moment to relax after the day's work, and next thing I knew it was 7:30am. But all is not lost, for while dozing I dreamed of sugar-plums. Now I'm not sure that I would recognize a sugar-plum if I saw one. All I know about them is that they're found around nutcrackers. And how I know that the things I dreamed of were sugar-plums when I wouldn't recognize one is a secret that I will never reveal. (Actually, it might not be a bad idea to start writing my FOTD discussion in the morning, when I'm fresh and the ideas are plentiful, rather than late in the evening, when I'm groggy and want only a nice long rest.) I might have given the name "Sugar-Plum Midget" to another FOTD several years ago. The name seems vaguely familiar, but I don't remember for certain. Regardless, today's picture has been given the name because it reminds me of a midget surrounded by sugar plums. The formula behind all the candy is 1.4(Z^129)+1.05(Z)+(1/C), an expression that appears rather boring at first glance. But then Z^2+C also appears boring and too simple to do anything, and look what *it* started. I'm getting interested in mixing high and low powers of Z, so more images of this type are likely in the days to come. The parameter file takes over 22 minutes to render on an average Pentium. For relief, the image has been posted for over 12 hours to: It may also be found on Paul Lee's web site at: The fractal weather was cloudy and cool, with some sun in the afternoon, but not nearly enough to lure the fractal cats outdoors. The fractal temperature reached 60F (15.5C for the rest of the world) -- too cool to bring out the cats. As a result, the cats spent the day indoors. The fractal philosophy list needs another kick in the pants, which I might give it with a controversial statement or two in the near future. But for today, we've come to the end of the line. Until next time, take care, and enjoy the peace that only fractals bring. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Sugar-Plum_Midget { ; time=0:22:20.31, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-21.35172450881101000/+0.3544097800329110\ 0/1.516326e+007/1/-24.999 params=1/129/0.75/1/0.4/0 float=y maxiter=3600 bailout=25 inside=0 logmap=301 symmetry=none periodicity=0 colors=500ACK<2>3AK<2>CGKFIKIKI<6>bY8e_7ha5<3>th0<3>\ YbESaHM`L<3>0WY<13>5T`6T`6Sa<2>7Sa7Sa9Q`<14>VAWX9VY8\ V<3>c4U<12>kXdlZel`e<2>nfhnhhmge<10>lZFkYDkXA<3>kU1<\ 3>km3kr4kv4<8>OkRLjTIiW<3>8ed<5>YTXbRWfPV<3>wHQ<3>wE\ VwDWwCXv9V<3>xIdxKfyNjyPnyRszTwzVzzXzzVzzUxwTvuStsQr\ qNrpLqnIqmEqlCq<3>f7pe6pc5p<2>_5pZ5pX7q<3>RFrPHrNIr<\ 3>HLsGMtENt<3>8RuASuCTxESy<3>MPzOPzQOzSNz<6>_Jz`IzaH\ zbHzcGzdHzeGzfGz<3>mFzoFzqFzsFzuFz<2>yEzzEzzEz<3>zDz\ z9z<3>zNzzQzzIz<7>zCz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "J.P. Louvet" Subject: (fractint) Re: [fractal-art] Fractal art FAQ Date: 30 Apr 2000 00:20:04 +0200 Terry and all other fractal lovers, What you write is exactly what I think. I can write broad lines about some programs (being more experimented with some of them) but I have said several times that this attempt to have a fractal art FAQ needed a collective participation to be useful and objective. Unfortunately I have received only very few contributions and this goal doesn't seem to interest many people. I think that it is not a question of time when I see, for example the overabundant exchange of parameters and formulae in the UF list and, to a less extent in the Fractint list. Well, I will post also this reply in these 2 lists. I have some material to do a new version of the draft and I will take my responsibility, Tim, about the text describing the programs. But this effort will be more useful if I have more contributory feedbacks. Waiting for that I acknowledge in advance those who will accept to help the fractal community, specially the beginners (note that I don't say "those who will help me" because this is not what is important). ------------------------------------------------------------------------- J.P. Louvet | Phone : (33)05-56-84-58-35 IUT Universite Bordeaux I | 33405 Talence CEDEX France | email : louvet@hse.iuta.u-bordeaux.fr ------------------------------------------------------------------------- ----- Original Message ----- Sent: Saturday, April 29, 2000 11:22 PM > Tim, > > I agree entirely with this. I also have great respect for Jean-Pierre's > views. He's always been able to point out weaknesses in my programs without > 'inflaming my stys.' He's also provided insightful suggestions for > improvement. If he can't write a fair description for each fractal program > as it now exists, then I don't know who could. But he's also quite right > when he asks for "the opinions of many people." Jean-Pierre hasn't used > every program around, or to the same depth, so some omissions/inaccuracies > are unavoidable, unless... If J-P is to act as a moderator, so to speak, he > should have all the pertinent information about each program(in the broadest > scope of the FAQ), and what the authors/users see as strengths and > weaknesses. Finally, everyone should realize the license and responsibility > that Jean-Pierre takes in writing this version of the FAQ, and limit their > criticisms to constructive, rather than ***** feedback. > > Terry W. Gintz Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 30-04-00 (Double-Minus Brot [4]) Date: 30 Apr 2000 01:00:39 -0400 (EDT) FOTD -- April 30, 2000 (Rating 4) Fractal visionaries and enthusiasts: Today I trimmed the overgrown fractal lawn, giving myself a stiff back and a great excuse to do nothing but explore fractal land for the rest of the day. My fractal theme of the day was all negative parameters and no fractional powers. I started with -1(Z^(-2))-2(1/Z)+(1/C). I named the picture "Double- Minus Brot" because of the two negative exponents. It's another of those simple formulae that promise little but deliver much. In fact, the only change I made was to raise the bailout radius to 1400, which broke the fractal into interesting segments, separated by curious holes. The rating for this fractal effort can only be an honest somewhat-below-average 4, not quite worth the 15 minutes required to run the parameter file, but at least worth the minimal effort of downloading the pre-rendered image from Usenet at: or from the WWW at: The fractal weather today was unexpectedly bright and warm, with sunny skies and a temperature of 68F (20C), which brought out the little bit of friskiness left in the fractal cats. The philosophy is cooking right on schedule, so stay in touch with the philofractal list all you frustrated fractal philosophy fans for some fantastic philosophizing in the fairly near future. Right now it's time for my Saturday evening spell in front of the TV, watching some junky sci-fi. I think it's Dr. Who this evening in "Meglos". That's the one with the dodecahedron god and the cactus Doctor. I'll return tomorrow, same time same venue. Until then, take care, and keep a stiff upper fractal. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Double-Minus_Brot { ; time=0:15:10.72, SF5 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.350341334507803/+4.094891764521559/2.0\ 04851e+010/1/142.383/0.035 params=-1/-2/-2/-1/0/1300 float=y maxiter=1600 inside=0 logmap=171 symmetry=none periodicity=10 colors=000WDD<3>`3Ha1HZ0I<7>G0NE0OB0P<3>20R<9>bB`fCa\ jDb<3>xHe<7>RRMNSKITH<3>2X8<3>4PW4Na4Lf<3>PahUehZji<\ 3>rzj<3>dqp`oqYls<3>Kdx<9>UItVGsWEs<3>_5r<9>fcqgfqhj\ q<2>jtqjwqlsr<4>q_tsWutSu<3>xCxy8yt9z<7>ODzKDzGEz<3>\ 0Fz<3>9JzBKzALzFMz<2>LPzNPzOSz<3>QazQczKXz<3>08z<3>A\ MzCPzESzGVz<7>9Jz8Hz7Gz<3>4Az<6>4Lz4Mz4Oz<3>4Tz<3>II\ zMFzPCzSAz<7>J5zI4zH4z<3>D2z<4>aMz<2>pXz`azMfz<7>gkz\ ilzllz<3>vnz<5>bizZhzWhz<3>Jez<4>`qz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Morgan L. Owens" Subject: Re: (fractint) sqr() function considered harmful? Date: 30 Apr 2000 18:53:17 +1200 At 16:49 28/04/2000 +1200, I wrote: > I'll do that :<->, swap you suggest on the weekend. > The formulae I ended up with were things like: sqr05{z=0:c=sqr(sqr(pixel))*pixel,|z|<=4} I switched to pixel instead of rand so that I didn't have the RNG slowing things down. It also meant that I didn't need to explicitly initialise c to anything. The running conditions are as for my first experiment: a DOS boot, 1600x1200x256 resolution, 1023 iterations and passes=g (with passes=1 I'd be iterating something like a thousand times as many pixels). In all, roughly two million iterations per formula. (I'm only rough because passes=g is more thorough than one pixel per 1024-pixel block around the edges.) My new timings (in seconds are) n power mult sqr 0 15.16 14.22 14.23 1 14.83 14.50 14.50 2 14.72 14.83 14.83 3 38.34 16.37 16.26 4 38.56 17.52 15.87 5 38.50 18.51 17.30 6 38.45 20.05 17.30 7 38.50 21.26 18.35 8 38.50 21.20 16.75 9 38.50 22.30 18.34 10 38.51 23.07 18.18 11 38.50 26.20 18.95 12 38.56 27.19 18.29 13 38.56 25.98 19.34 14 38.55 26.86 19.00 15 38.61 27.84 20.44 16 38.56 32.08 17.96 Which does look a lot more sensible. One thing to notice is that repeated multiplication performs much better here against exponentiation: even z^16 appears to run slightly slower than z*z*z*z*z*z*z*z*z*z*z*z*z*z*z*z! Exponentiation is pretty much constant around 38 1/2 seconds, increasing only slowly, though treating n=0, 1, 2 as special cases. z*z also appears to be converted to sqr(z) when it appears. However, z*z*z and sqr(z)*z are slightly different. This suggests that Fractint doesn't spot the "z*z" in the cube expression; the extra time to look up 'z' _three_ times instead of two makes for an extra tenth of a second (out of two million iterations?! What are you complaining about?) Of the three methods, repeated squaring appears to be the fastest approach to writing hardwired integer powers; instead of saying z^9 or z*z*z*z*z*z*z*z*z, sqr(sqr(sqr(z)))*z offers clear speed advantages. These results are in conflict with those of Iain Stirling's, which say that repeated multiplication is slower than the other two, which are on a par with each other. I'm wondering if this may be a result of my switching to using pixel as the source for my test data instead of randomly-generated numbers? But in the quest for maximum speed in user formulae, the story doesn't end here. Consider this alternative method for writing z^15: z=sqr(sqr(z))*z,z=sqr(z)*z This saves an extra multiplication of the more straightforward repeated squaring method, which gives z=sqr(sqr(sqr(z)*z)*z)*z And if, as one often does, wish to calculate a number of powers of a variable, then it makes sense to reuse results as much as possible, rather than calculate them fresh each time; if you've calculated w=sqr(z)*z already, it makes more sense to calculate z^4 as w*z instead of sqr(sqr(z)). The ultimate in this field is still an open problem - in mathematics, not just in Fractint. Morgan L. Owens "Embarras de richesses" Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: "Iain G. Stirling" Subject: Re: (fractint) sqr() function considered harmful? Date: 30 Apr 2000 17:40:36 +0100 Morgan L. Owens wrote: > At 16:49 28/04/2000 +1200, I wrote: > > I'll do that :<->, swap you suggest on the weekend. > > > The formulae I ended up with were things like: > > sqr05{z=0:c=sqr(sqr(pixel))*pixel,|z|<=4} > > I switched to pixel instead of rand so that I didn't have the RNG slowing > things down. It also meant that I didn't need to explicitly initialise c to > anything. > > The running conditions are as for my first experiment: a DOS boot, > 1600x1200x256 resolution, 1023 iterations and passes=g (with passes=1 I'd > be iterating something like a thousand times as many pixels). In all, > roughly two million iterations per formula. (I'm only rough because > passes=g is more thorough than one pixel per 1024-pixel block around the > edges.) > > My new timings (in seconds are) > > n power mult sqr > 0 15.16 14.22 14.23 > 1 14.83 14.50 14.50 > 2 14.72 14.83 14.83 > 3 38.34 16.37 16.26 > 4 38.56 17.52 15.87 > 5 38.50 18.51 17.30 > 6 38.45 20.05 17.30 > 7 38.50 21.26 18.35 > 8 38.50 21.20 16.75 > 9 38.50 22.30 18.34 > 10 38.51 23.07 18.18 > 11 38.50 26.20 18.95 > 12 38.56 27.19 18.29 > 13 38.56 25.98 19.34 > 14 38.55 26.86 19.00 > 15 38.61 27.84 20.44 > 16 38.56 32.08 17.96 > > Which does look a lot more sensible. > > One thing to notice is that repeated multiplication performs much better > here against exponentiation: even z^16 appears to run slightly slower than > z*z*z*z*z*z*z*z*z*z*z*z*z*z*z*z! Exponentiation is pretty much constant > around 38 1/2 seconds, increasing only slowly, though treating n=0, 1, 2 as > special cases. z*z also appears to be converted to sqr(z) when it appears. > > However, z*z*z and sqr(z)*z are slightly different. This suggests that > Fractint doesn't spot the "z*z" in the cube expression; the extra time to > look up 'z' _three_ times instead of two makes for an extra tenth of a > second (out of two million iterations?! What are you complaining about?) > > Of the three methods, repeated squaring appears to be the fastest approach > to writing hardwired integer powers; instead of saying z^9 or > z*z*z*z*z*z*z*z*z, sqr(sqr(sqr(z)))*z offers clear speed advantages. > > These results are in conflict with those of Iain Stirling's, which say that > repeated multiplication is slower than the other two, which are on a par > with each other. I'm wondering if this may be a result of my switching to > using pixel as the source for my test data instead of randomly-generated > numbers? I'm sure that modification could have a large effect. That is the true difficulty of this issue - it really depends on precisely what is being calculated. > But in the quest for maximum speed in user formulae, the story doesn't end > here. Consider this alternative method for writing z^15: > > z=sqr(sqr(z))*z,z=sqr(z)*z > > This saves an extra multiplication of the more straightforward repeated > squaring method, which gives > > z=sqr(sqr(sqr(z)*z)*z)*z > > And if, as one often does, wish to calculate a number of powers of a > variable, then it makes sense to reuse results as much as possible, rather > than calculate them fresh each time; if you've calculated w=sqr(z)*z > already, it makes more sense to calculate z^4 as w*z instead of > sqr(sqr(z)). The ultimate in this field is still an open problem - in > mathematics, not just in Fractint. Indeed. I think what we have seen here is that the conventional wisdom of sqr being best is perhaps generally true, but your original tests results show that there _is_ a case where it is not true. However, that case may be degenerate and not apply in a realistic formula... On the other hand, the huge difference between this latest set of results and the two previous sets shows that there is no way to predict what is going to happen. Maybe it would be interesting as a final experiment to take some very realistic cases, such as a well-known formula (using various powers of z) with a good .PAR creating an image of it, and play about with it? I will probably give this a go at some point. Iain Stirling. Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------------------------------------------------------- From: Jim Muth Subject: (fractint) FOTD, 01-05-00 (Pseudo Pseudo Pseudo [5]) Date: 01 May 2000 01:06:06 -0400 (EDT) FOTD -- May 01, 2000 (Rating 5) Fractal visionaries and enthusiasts: I often envy the multi-layer images produced by those who use that new-fangled fractal program, the one with all the bells, whistles and doodads. They're the lucky ones, while here I am, still using Fractint, that aging relic of days gone by, still creating images that have only one layer, still searching and discovering like they did 13 years ago, when the Mandelbrot set was the entire world of fractals. How could anything possibly be more passe? Of course, nothing could. So today I decided to join the trendy set and get hip to the trend of the times by creating a pseudo- multilayered fractal image. My attempt to enter the world of the avant-garde resulted in today's image, which consists of only one layer, but still manages to capture the feeling of those images with the many layers. Perhaps a bit optimistically, I gave the effort a rating of 5. I named the picture "Pseudo Pseudo Pseudo" because everything about it is phony. To begin, I do not envy multi-layer images. In fact, I feel that the ability to pile one image on top of another is in danger of being used to the point of banality. Next, the appearance of multiple layers in today's FOTD is a total illusion. It is all done in one pass. Finally, I have no intention of taking part in anything that has become trendy. I live my life doing the things others do *not* do rather than repeating the things they *do* do. To be effective, today's image needs to be rendered at a very high resolution. The JPEG image has been posted at a resolution of 1280x1024, which is a good compromise between file size and picture quality. If you choose to run the parameter file, do so at the highest resolution available. It takes 12-1/2 minutes at a resolution of 1280x1024. As always, the JPEG image file has been posted to: and to: The fractal weather today was perfect -- sunny and 73F (23C). The cats approved by spending several hours outdoors. Still sore from yesterday's vigorous workout trimming the lawn, I spent the day searching for fractals. I also did a modicum of philosophizing, most of which has already been posted to the fractal philosophy list. Only one thing remains, and that thing is to shut down the fractal shoppe for another day and call it a night. Until tomorrow, when we'll go through the whole thing once again, take care, and don't forget that a fractal in time saves nine. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ PseudoPseudoPseudo { ; time=0:12:37.32, SF9 on a P200 ; Version 2000 Patchlevel 9 reset=2000 type=formula formulafile=mandnewt.frm formulaname=MandNewt07 passes=1 center-mag=0.0108678/0.0197287/10.63749/1/37.5 params=0.561/4.728/2.775/-2.18/0.633/-0.177 float=y maxiter=120 bailout=25 inside=bof60 logmap=28 symmetry=none periodicity=0 colors=000TCcW8`<3>k_fofgslh<3>Gen7do1GD<2>apw<3>aaS\ OdHAf6<3>eFVm8`hFc<3>PfkLlmKWoKFp<3>7CF4C67KH<2>FgmH\ owIlq<2>Ica<2>btRGSjDOYALM<3>Q28<3>RaeRimYbd<3>wF8tJ\ WrMr<3>sbbtfZtjVtnRtrN<2>tGS<3>QZZJb_0N_<2>2ddU`Q4bL\ 3fWHleCke7jewtJ<3>VoVNmYGl`9kc`CcJUdFp3AnG6lTjdR<3>H\ h`9icaeY<2>BicE8j<3>8Sg6Xf5af3fe`TJ<3>HcXCe_7hbMiE<3\ >CjS9jW7jZ4jbCZB<3>4h_dXW2Ab<3>2ceokx<3>Cjh5um<3>3oi\ 3nh2lg2kfJ2y<3>5ai7m5<3>3kU2j_Wgq<3>EijAjh6jfhuScHS<\ 3>LWZG_`Bcb6gdtgD<3>PiUHjY9jaC7H8LQ5YYSva<3>Dod9md5k\ e17M<3>2RW2WZ2``2ecl7r<3>Bbg2_c2edSuy<2>8lj`94<3>DZU\ 7d_Oa5<2>7hXNzHCrU_mR6yp<6>2kfKQlNLiQHf } frm:MandNewt07 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=3*z^2+c-1 z=z-p3*a/b .000000000000000000000000000001 <= |a| } END 20.0 PAR-FORMULA FILE================================== Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint"