From: owner-fractint-digest@lists.xmission.com (fractint-digest) To: fractint-digest@lists.xmission.com Subject: fractint-digest V1 #124 Reply-To: fractint-digest Sender: owner-fractint-digest@lists.xmission.com Errors-To: owner-fractint-digest@lists.xmission.com Precedence: bulk fractint-digest Saturday, March 7 1998 Volume 01 : Number 124 ---------------------------------------------------------------------- Date: Fri, 6 Mar 1998 17:27:08 EST From: Nature102 Subject: Re: (fractint) Out of my depth In a message dated 98-03-06 16:50:06 EST, elmont@cdsnet.net writes: << Joined the listserver about ten days ago and have been reading all the messages that are being sent out. WOW!!! Am I over my head. >> Trust me, you're not the only one. :-P - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 6 Mar 1998 17:33:06 EST From: HWeber8606 Subject: Re: (fractint) February's pars Hi Les, I have the same problem as Bob. My AOL-browser refuse to d/l your 02.98 par- collection and your frm-file. What have you done in an other way than before?Please post it to my compuserve adress. Thanks. Cheers --Jo-- - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 06 Mar 1998 14:54:48 PST From: NOEL_GIFFIN Subject: Re: (fractint) February's pars HWeber8606 wrote: > Hi Les, > > I have the same problem as Bob. My AOL-browser refuse to d/l your 02.98 > par- > collection and your frm-file. What have you done in an other way than > before?Please post it to my compuserve adress. Thanks. I've loaded the available parameter collections from Les's webpage onto the Spanky database. You may (or may not) find that you can download from there if you have problems with Les's site. I think Les's webpage should be everyones first choice for downloading these formulae. He is after all, the one doing all the work, and his site will always be more up-to-date. I will keep them there if this is alright with Les and as long as everyone acknowledges him as the person who has done the great job compiling them. You can find them for now at: http://spanky.triumf.ca/pub/fractals/params/ and put the formula file in http://spanky.triumf.ca/pub/fractals/formulas/FML_FRM.ZIP Cheers, Noel Giffin P.S. Let me know if this is okay with you Les. - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 6 Mar 1998 16:23:30 -0700 From: Ray Montgomery Subject: (fractint) Continuation But not long, I promise. (I feel that I almost know most of you who are posting because I downloaded so many of the 'Gallery'-combi-bios-&-images.) The final 'gist' of my posting is, - it takes a special type of person who can put up with teaching a 'kindergartner' of 'first-grader' - "Shoe?" "Yes, you're right, shoe!" But if anybody out there has the patience to put up with it, I'd like to start asking some very basic and fundamental questions. I promise they will be spaced appropriately far apart. But, I would beg anyone who would be willing to answer to phrase the answer so that an 'Old-man' kindergartner' would be able to understand. There! I've done it. Dared to step into the room with the big-boys! Mercy! Mercy!! Mercy!!! Bob Carr has been gracious enough to reply already and I am already so grateful. Thanks Ray Montgomery - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 6 Mar 1998 19:54:44 -0500 From: "Peter Gavin" Subject: Re: (fractint) Fractais in Brazil What about English to English? :) [snip] >Now if they just had C++ to English, Advanced Math to English, or even >better: >English to Fractint frm, English to Fractint par, English to Fractint map Pete - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 6 Mar 1998 19:56:39 -0500 From: "Peter Gavin" Subject: Re: (fractint) Fractais in ???? Sounds like something from Star Wars.... hmmm... :) - -----Original Message----- From: Jason Hine To: fractint@lists.xmission.com Date: Thursday, March 05, 1998 6:56 AM Subject: Re: (fractint) Fractais in ???? >Gedeon asks: >>Kivancsi vagyok, hogy vannak e magyarok? > >Hmmm... from somewhere on the greater Asian continent? This is definitely >tougher than Spanish to guess at! >Jason > > >- >------------------------------------------------------------ >Thanks for using Fractint, The Fractals and Fractint Discussion List >Post Message: fractint@xmission.com >Get Commands: majordomo@xmission.com "help" >Administrator: twegner@phoenix.net >Unsubscribe: majordomo@xmission.com "unsubscribe fractint" - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 6 Mar 1998 20:09:34 -0500 From: "Peter Gavin" Subject: Re: (fractint) Fractint as prototype society ><< - what's happening to Fractint now? Has it reached perfection? :) >> > > Nope. Not until it can calculate images at zoom levels of 10^(10^12) in five >seconds and generate realtime 3-D walkthroughs of fractal worlds. :-P > On an 8086 with only 1K of Ram and no HD, one 5.25" floppy drive, and a monochrome monitor. Oh, yeah, in 32-bit True color. Pete - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 6 Mar 1998 19:15:50 -0600 (CST) From: pjcarlsn@ix.netcom.com (Paul and/or Joyce Carlson) Subject: (fractint) Texture and Inflation Formula This formula and pars explore four areas of the classic Mandelbrot set using a rendering method that creates, in pars mndatm01, 03 and 04, images with a nice "texture" that almost make you want to run your fingers over them. Par mndatm02 creates an image that looks inflated (makes you want to stick a pin in it). Paul Carlson frm:Mand_Atan_Mset {; Copyright (c) Paul W. Carlson, 1998 w = z = iter = range_num = bailout = 0 c = pixel num_ranges = real(p2) colors_in_range = imag(p2) : prev_w = w w = w * w + c IF (abs(real(w)) > p1) bailout = 1 angle = abs(atan((imag(w)-imag(prev_w))/(real(w)-real(prev_w)))) index = 2 * colors_in_range * angle / pi z = index + range_num * colors_in_range + 1 ENDIF range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter bailout == 0 } mndatm01 {; Copyright (c) Paul W. Carlson, 1998 ; Nice texture. reset=1960 type=formula formulafile=mndatan.frm formulaname=Mand_Atan_Mset passes=t center-mag=-0.81638668446488240/+0.19987647824278850/306\ 89.28/1/-170 params=1.5/0/2/125 float=y maxiter=2000 inside=253 outside=summ colors=000zqa<123>WRFz88<123>O00000<3>000 } mndatm02 {; Copyright (c) Paul W. Carlson, 1998 ; The "inflated" look. reset=1960 type=formula formulafile=mndatan.frm formulaname=Mand_Atan_Mset passes=t center-mag=+0.30078202224390480/+0.02039060482684493/2638\ 81.6/1/3.199 params=0.8/0/2/125 float=y maxiter=2000 inside=253 outside=summ colors=000zqa<123>WRFz88<123>O00000<3>000 } mndatm03 { ; Copyright (c) Paul W. Carlson, 1998 ; Another nice texture. reset=1960 type=formula formulafile=mndatan.frm formulaname=Mand_Atan_Mset passes=t center-mag=-1.27902461721017400/+0.07031146780659604/2318\ 6.32/1/156.5 params=1.5/0/2/125 float=y maxiter=2000 inside=253 outside=summ colors=000zqa<123>WRFz88<123>O00000<3>000 } mndatm04 { ; Copyright (c) Paul W. Carlson, 1998 ; Still another nice texture. reset=1960 type=formula formulafile=mndatan.frm formulaname=Mand_Atan_Mset passes=t corners=-1.429323736733/-1.4293206462961/0.001621210035598\ 3/0.001622949268712/-1.4293234590076/0.0016208397351079 params=2/0/2/125 float=y maxiter=2000 inside=253 outside=summ colors=000zqa<123>WRFz88<123>O00000<3>000 } - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 6 Mar 1998 20:17:00 EST From: Nature102 Subject: Re: (fractint) Fractint as prototype society In a message dated 98-03-06 20:11:43 EST, pgavin@mindspring.com writes: << ><< - what's happening to Fractint now? Has it reached perfection? :) >> > > Nope. Not until it can calculate images at zoom levels of 10^(10^12) in five >seconds and generate realtime 3-D walkthroughs of fractal worlds. :-P > On an 8086 with only 1K of Ram and no HD, one 5.25" floppy drive, and a monochrome monitor. Oh, yeah, in 32-bit True color. >> And it has to be able to do it in a Win95/NT DOS box! :-P ::Looks at the Stone Soup Group:: Well, guys, get on it! :-P - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 07 Mar 1998 12:53:33 +1100 From: Andrew Plukss Subject: Re: (fractint) Fractais in ???? Peter Gavin wrote: > > Sounds like something from Star Wars.... hmmm... :) > > -----Original Message----- > From: Jason Hine > To: fractint@lists.xmission.com > Date: Thursday, March 05, 1998 6:56 AM The fractint newgroup generates a lot of mail and threads such this, in my opinion, are just unnecessary clutter. Please have consideration for those with limited email access. Andrew Plukss > Subject: Re: (fractint) Fractais in ???? > > >Gedeon asks: > >>Kivancsi vagyok, hogy vannak e magyarok? > > > >Hmmm... from somewhere on the greater Asian continent? This is definitely > >tougher than Spanish to guess at! > >Jason > > > > > >- > - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 06 Mar 1998 20:10:55 -0600 From: Carolyn Subject: (fractint) Out of my depth These two messages have been such an encouragement to me. I thought I was out here all alone just reading and never understanding but enjoying the results of other's work. Nature102 wrote: > In a message dated 98-03-06 16:50:06 EST, elmont@cdsnet.net writes: > > << Joined the listserver about ten days ago and have been reading all > the messages that are being sent out. WOW!!! Am I over my head. >> > > Trust me, you're not the only one. :-P > - -- Carolyn car34slmo@worldnet.att.net Jesus is the Light of the world, the Bread of life and the Salvation of your soul. - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 06 Mar 1998 18:42:57 -0800 From: Wizzle Subject: Re: (fractint) Out of my depth Carolyn... Welcome!!! Many of the things posted to the list I don't have a clue about either. I'm part of the "pretty picture" contingent. But I do have a web page with lots of VERY basic information. The info that got me going was Linda Allison's lessons....you will find the link at http://wizzle.simplenet.com/fractals/fractalintro.htm I'm going to re-organize my hints and lessons, including a section for the q&a postings from this list, this week end (she says...sure!!! maybe). I think Fractint is wonderfully documented, but examples helped me at first soooooo much.....and that is where a web page can fill a gap. Besides, we all learn in different ways. Anyone else with lessons type pages posted...please email me the url wizzle@cci-internet.com ciao Angela aka wizzle At 08:10 PM 3/6/98 -0600, you wrote: > These two messages have been such an encouragement to me. I thought I >was out here all alone just reading and never understanding but enjoying >the results of other's work. > > >Nature102 wrote: > >> In a message dated 98-03-06 16:50:06 EST, elmont@cdsnet.net writes: >> >> << Joined the listserver about ten days ago and have been reading all >> the messages that are being sent out. WOW!!! Am I over my head. >> >> >> Trust me, you're not the only one. :-P >> > >-- >Carolyn - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 06 Mar 1998 19:40:11 -0800 From: Wizzle Subject: Re: (fractint) gravijul-a1 >comment { 3/6/1998 Mark "Bud" Christenson > >Okay, here's my first effort. > Yup yup...works great!!! Another gravijul winner. In thanks, I've modified your sil&gld map in the second par by replacing the red with teal..... wizgravi1 { ; wizzle from a Bud Christensen formula 3/6/98 reset=1960 type=formula formulafile=*.frm formulaname=gravijul-a1 function=asin/atanh/atan center-mag=0.0103628/0.0154305/0.2575853/1/-19.999 params=1.1/0/0/0.93/0.966/2.2 float=y inside=111 outside=real decomp=256 colors=000000000<5>D67F79H8AKACLBD<32>xxkzzmyyl<25>KC2IA0G90<5>000<5>336\ 000437<21>JGTKHUKHT<8>ECKDBICAHBAGB9FA8E<12>111000000000<3>000<2>A05D06F\ 27<5>REITGKVILWJM<12>tggviixkkzmmyllwjj<22>I2AG08C06<2>000<2>000000123<1\ 8>SpwUszTqw<16>234000000<2>000 cyclerange=0/255 } wizgravi2 { ; wizzle 3/6/98 from Bud's new formula ; and a gift of teal for bud's fav map too!! budteal.map reset=1960 type=formula formulafile=*.frm formulaname=gravijul-a1 function=sqr/atanh/asinh center-mag=0.0103628/0.0154305/0.5488324/1.3333/-19.999 params=1.1/0/0/0.93/0.966/2.2 float=y inside=111 outside=real decomp=256 viewwindows=1/1/yes/0/0 colors=MJB<20>zsX<31>000<3>800<2>2770AA0CC<5>0PP0RR0SS<14>0rr<13>0``0__0\ YY0WW<10>0CC0AA077044000<8>FFFHHHJJJLLLMMMOOO<17>sss<30>222000012<30>0kz\ <30>022000221<8>KIA cyclerange=0/255 } Hint for anyone else....bud's map will look great with endless variations if you leave the silver and gold as is and fiddle with the other two colors....try purple and green....magenta....oooooooorange......browns...go for it!!! Just remember to find the darkest versions of the other colors and replace them....then find the lightest versions and replace them.......use the old = and voila!!! new map. Bud's map has black (r0, g0, b0) in strategic places.....don't cross those boundaries. Have fun!! - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 6 Mar 1998 22:35:54 -0700 From: Ray Montgomery Subject: (fractint) .par & .frm files Hi Linda Just left your Gumbycat page and down-loaded the .par and .frm instructions. Had to. Otherwise too much for old brain to remember. It was an enormous help, but brought two questions to mind. (Far more than two, but two is all that I can handle right now.) In order to save the two files, do I have to type them all into a directory - or is there a way to use the existing typed paragraphs? Second question; can I down-load the color-map instructions - and if so will the B.G. black come out all black, or will there be some kind of transformation that I know naught of? Enormous help, in that all of a sudden I realize just what the two phrases refer to, and ALMOST how to use them. Thanks a lot. A whole bunch of fractals worth. Ray Montgomery - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 7 Mar 1998 01:25:28 -0500 From: "Philip DiGiorgi" Subject: (fractint) Gravijul Mania My first post to the list, and I've really been enjoying all the great images you folks are posting. And here's just what everyone needs..., yet another variation of the Gravijul formula. Will post some more pars in another message. --Phil D. grav2u01 { ; t= 0:01:38.16 (c) P. DiGiorgi - Mar '98 ; Generated on a K6-266 at 1600x1200 reset=1960 type=formula formulafile=grav.frm formulaname=gravijul_2u function=cabs/acosh/abs/log passes=1 center-mag=0/4.44089e-016/0.3854591/1/180 params=0.6/0.9/1/0/0.15/1 float=y maxiter=300 inside=0 decomp=256 periodicity=0 colors=B36<10>UAHWBIYDK<24>zzz<21>000801<22>801801A44<12>Umc<5>zzz<6>Yof\ UmcSi`<10>A55812812<9>634634533<14>00000S<21>77u<7>zzz<15>55f<12>22L11K1\ 1I00G00G10G000<8>000000100201<2>412513513513<13>513613824A25 cyclerange=0/255 } grav2u02 { ; t= 0:03:10.04 (c) P. DiGiorgi - Mar '98 ; Generated on a K6-266 at 1600x1200 reset=1960 type=formula formulafile=grav.frm formulaname=gravijul_2u function=cabs/acosh/abs/log passes=1 center-mag=0/4.44089e-016/0.3854591/1/180 params=0.5/0.8/1/0/0.15/1 float=y maxiter=300 inside=0 decomp=256 periodicity=0 colors=OOO<5>000<29>000<3>C0GG0LI0P<6>e2rh2vi8r<5>nfV<3>000<21>g8D<6>zVF\ <7>jBEg8De8D<3>V69S59R59Q59P58<8>000754000EB8<6>zpa<7>A66000<5>000000200\ <20>hCEkDFmGF<4>zVF<5>kDEhAEd9D<10>000<2>000000202<20>j2y<18>000<7>zzzzz\ zzzz<8>SSS cyclerange=0/255 } grav2u03 { ; t= 0:05:05.23 (c) P. DiGiorgi - Mar '98 ; Generated on a K6-266 at 1600x1200 reset=1960 type=formula formulafile=grav.frm formulaname=gravijul_2u function=cabs/atanh/tan/atanh passes=1 center-mag=0.345663/0.886304/2.898551/1/-90 params=0.95/0/0.03/0/0.03/2.5 float=y maxiter=300 inside=0 decomp=256 periodicity=0 colors=000823412000<2>000000202<20>j2y<18>000<7>zzzzzzzzz<15>000<29>000<\ 19>zpa<4>000<21>g8D<6>zVF<7>jBEg8De8D<3>V69S59R59Q59P58<8>000<8>zpa<7>A6\ 6000<5>000000200<20>hCEkDFmGF<4>zVF<5>kDEhAEd9D<7>C34 } grav2u04 { ; t= 0:02:14.57 (c) P. DiGiorgi - Mar '98 ; Generated on a K6-266 at 1600x1200 reset=1960 type=formula formulafile=grav.frm formulaname=gravijul_2u function=exp/recip/abs/acosh passes=1 center-mag=0/0/0.6945411 params=0/1.5/-2.8/0.05/-0.077/1.9 float=y maxiter=300 inside=0 decomp=256 colors=B36CCi99g55f<10>22O22N22L11K11I00G00G10G000<8>000000100201<2>4125\ 13513513<13>513613824A25D47<9>UAHWBIYDK<24>zzz<21>000801<22>801801A44<12\ >Umc<5>zzz<6>YofUmcSi`<10>A55812812<9>634634533<14>00000S<21>77u<7>zzz<6\ >bbqZZpVVoRRnNNmKKkGGj } grav2u05 { ; t= 0:02:13.41 (c) P. DiGiorgi - Mar '98 ; Generated on a K6-266 at 1600x1200 reset=1960 type=formula formulafile=grav.frm formulaname=gravijul_2u function=cabs/atanh/atanh/atanh passes=1 center-mag=-9.99201e-016/-8.88178e-016/1.397102/1/-90 params=0.91/0/0.05/0/0.03/2.5 float=y maxiter=300 inside=0 decomp=256 periodicity=0 colors=000B60740310001<3>00P00V00Z11c11h<3>11v12w12y<2>12y12x11v<2>11m11\ i11d00_00W<2>00E00700200B<2>I8COBCUDCZFDcIDhKDmLEpNEsOEvQExQFyRFzRFzRFyR\ FxQFvQE<2>mMEiKDdID<3>J9CD6B63B11B332<3>PHKVLPZOScSWgW_k_bobeqfgtjivmkwq\ lwtlxtlwqlvmktjirfhobel_c<2>_OTWLQQHL<3>432<31>000<15>zWF<15>000<12>`Fw<\ 6>D5L000<3>000300<11>M03O04R15U16<2>Z18_18`19a1Aa1A`19`18<3>U16S15P04<2>\ F03C02801401100310<5>QG1TI1YL2<6>wa3wa3tZ3pX3lV3hS2dP2`N2YL2TI1<3>E90 } frm:gravijul_2u { ; Variation of gravijul formula - PD 3/98 ; Original formula by Mark Christenson bailout = imag(p3), k = real(p3) z = abs(pixel): x = real(z), y = imag(z) w = fn1(x) + k*y, v = fn1(y) + k*x u = fn2(w + flip(v)) z = fn4(p1/fn3(u*u)) + p2 |z| < bailout } - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 7 Mar 1998 01:43:30 -0500 From: "Philip DiGiorgi" Subject: (fractint) More Gravjul Mania Here are some more pars. Many of these use an interesting striped map I've been fooling around with. Have fun! --Phil grav2u06 { ; t= 0:00:28.72 (c) P. DiGiorgi - Mar '98 ; Generated on a K6-266 at 1600x1200 reset=1960 type=formula formulafile=grav.frm formulaname=gravijul_2u function=tan/recip/sqr/acosh passes=1 center-mag=3.10862e-015/-8.88178e-016/0.2121325 params=-1.5/0.5/-2.1/0.02/-0.2/2 float=y maxiter=300 inside=0 logmode=fly decomp=256 colors=000vWEvXFwYG<14>xjdykfykgylh<12>ytwzuyzuy<2>zuyzuxztv<25>wYGvXEvW\ DuVBuUA<4>uS3uR1uQ1<5>sN0sM0rL0rK0qJ0<3>pH0pG0pF0pE0oE0<3>mB0mA0m90m90k9\ 0<20>310000000<71>000000200<7>L40O50P50<13>lA0nB0nB0<13>rM0sN0sN1sO2<10>\ vVD } grav2u07 { ; t= 0:45:49.16 (c) P. DiGiorgi - Mar '98 ; Generated on a K6-266 at 1600x1200 reset=1960 type=formula formulafile=grav.frm formulaname=gravijul_2u function=ident/atanh/atanh/atanh passes=1 center-mag=0/0/0.5534543/1/-90 params=1/0/0.1/0/0/5 float=y maxiter=255 inside=0 outside=summ logmode=fly periodicity=0 colors=610Z70<4>nB0<13>uVEvWFwYHwZJ<14>zuy<14>x_KwYHwXG<13>oD2nB0kB0<14>\ 000<159>000300920<6>V60 } grav2u08 { ; t= 0:00:06.48 (c) P. DiGiorgi - Mar '98 ; Generated on a K6-266 at 1600x1200 reset=1960 type=formula formulafile=grav.frm formulaname=gravijul_2u function=cabs/atanh/ident/atanh passes=1 center-mag=0.0103448/0.0199618/0.4435881/1/-90 params=0.9399999999999999/0/0.13/0.025/-0.003/3.75 float=y maxiter=300 inside=0 outside=summ logmode=fly periodicity=0 colors=A04000JArzVFJApkJCJ6beFAJ4XaBAJ3TY89J2QV68J1MR38S48J1K522XQJ633bV\ N733h_Q744lcT844pgW855tkY955xn_955zpaA66301<19>`5Ba5Cc5Ce6Dg8DiAD<10>zVF\ <10>hAEg8Dd8C<10>000<16>_2a<3>N8mJApI9kG7e<16>000<4>bbbjjjssswwwzzzuyzmw\ z<2>lvykuyktyjsyirx<2>fnwdlwckvaiv`gu<5>QUrORqLOp<2>EGnCDmA9mAAmAAmAAm99\ l99k99i88f88d<2>66U55Q44L<3>000000fzzeyydxwbvu<2>WojTlfQiaMeWIaR<3>0J00K\ 0<4>0H00G00E0<2>1A0190270250230321321zzmyylxwkwuivrgtoerlb<2>kZShUOeOK<2\ >V66W66<3>S55Q55P44N44K33<6>000 } grav2u09 { ; t= 0:05:31.64 (c) P. DiGiorgi - Mar '98 ; Generated on a K6-266 at 1600x1200 reset=1960 type=formula formulafile=grav.frm formulaname=gravijul_2u function=cabs/ident/log/log center-mag=0/1.77636e-015/0.4656563 params=0.5/1/1.5/0/0.155/4.2 float=y maxiter=300 fillcolor=0 logmode=fly decomp=256 periodicity=0 colors=R38J4TXQJJ3RbVNJ3Ph_QJ2NlcTJ1KpgW855<7>855955B55<19>e7Cg8DhAE<10>\ zVF<10>hAEg8Dd8C<10>000<16>_2a<3>N8mJApI9kG7e<16>000<2>NNNA04VVV<2>sssww\ wzzz<2>zzzqqq<2>iiigggfff<2>aaa```___ZZZZZZQQQNMMKKJIHH<2>DCBBAAA98887<6\ >h2rwqUd2ltnT_2fpjSV2`lgQQ1VhcPL1Pe`OG1JaXMB0DYULF0IUQJJ0NQNIN0SNJHS1YJG\ FW1bFCE_1gB9Cc1l75Bh2r319321<14>321E54J65<2>T87W98YA9<6>jDClEDlED<4>zVF<\ 3>rLFJApnGEJAnlFEJ9ljEDJ9jgDCJ8heCCJ8ebBBJ7c`AAJ6aY89J6_V68J5YR38J5V cyclerange=0/255 } frm:gravijul_2u {; Variation of gravijul formula - PD 3/98 ; Original formula by Mark Christenson bailout = imag(p3), k = real(p3) z = abs(pixel): x = real(z), y = imag(z) w = fn1(x) + k*y, v = fn1(y) + k*x u = fn2(w + flip(v)) z = fn4(p1/fn3(u*u)) + p2 |z| < bailout } - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 7 Mar 1998 19:33:19 +1000 From: "D&J Pitman" Subject: (fractint) another out -of -depth-er I was so glad to read that I am not the only "Granny" on this list. Since I saw my first fractal I have been fascinated by the amalgamation of science and art that they represent, the ideas of visible mathematics and colour, and that first viewing was a long time ago. My study of maths was limited altho' science interests me greatly so I have been very grateful to the many listers who explain the various concepts, altho' I don't C but QB. Thanks to you others who got me out of lurkdom Cheers ,Pat. - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 7 Mar 1998 07:59:18 -0500 From: Les St Clair Subject: Re: (fractint) February's pars Hi Noel, >>I've loaded the available parameter collections from Les's webpage onto the Spanky database.<< >> P.S. Let me know if this is okay with you Les. << That's fine by me, placing them on Spanky is an excellent idea. The reaso= n for doing the compilations is just to keep these fine postings for posterity (of course, if I get new visitors to my fractal pages that's go= od too! :) - - Les - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 7 Mar 1998 08:45:06 EST From: Bill at NY Subject: (fractint) Fractint Tutorial There seems to be a surprising number of people who subcribe to this newsletter who are very new to fractals and Fractint. At my website's Links page, I have a step-by-step tutorial that can be downloaded that can help get any beginner started with Fractint. Please stop by and check it out. No Math Required! http://members.aol.com/billatny/links.htm Bill - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 07 Mar 1998 13:02:16 -0600 From: Bob Margolis Subject: (fractint) Fractal Formulas Hi Team Fractals: Recently I downloaded an important fractal technical/reference paper from the Internet that was chock full of formulas and other reference material. I've excised all but the formulas that one can use in Fractint (and other fractal programs) formula writing. If you're interested in downloading the entire paper--it's 23 pages of 8.5 x 11-inch paper--surf over to http://www.lifesmith.com/technical.html#anchor254229 . Happy formula writing! Bob Margolis ============================================================ Important Formulae for Complex Numbers 1) z = x + iy where x = Real part of z and y = Imaginary part of z 2) c = a + ib where a = Real part of c and b = Imaginary part of c 3) z = re^iq = (sqrt(x^2 + y^2)) (cos q + i sin q) where q = arctan (y / x), r = sqrt(x^2 + y^2) and "sqrt" means square root 4) z^n = r^n*e^inq = (sqrt(x^2 + y^2))^n (cos nq + i sin nq) ; r and q as above 5) sqrt(z) = (sqrt(r)sqrt(e^iq)) = (sqrt(sqrt(x^2 + y^2))) [cos (.5 arctan (y / x)) + i sin (arctan (y / x))] 6) ln z = ln[sqrt(x^2 + y^2)] + i arctan (y / x) 7) e^z = e^x(cos y + i sin y) 8) sin z = sin x cosh y + i cos x sinh y = -i sinh iz = (e^iz - e^-iz) / 2i 9) cos z = cos x cosh y - i sin x sinh y = cosh iz = (e^iz + e^-iz) / 2 10) sinh z = - i sinh iz = (e^z - e^-z) / 2 11) cosh z = cos iz = (e^z + e^-z) / 2 12) sin^2(z) + cos^2(z) = 1 13) cosh^2(z) - sinh^2(z) = 1 14) tan z = (sin 2x + i sinh 2y) / (cos 2x + cosh 2y) 15) cot z = (sin 2x - i sinh 2y) / (cosh 2y - cos 2x) 16) nth root of z = [nth root of (x^2 + y^2)](cos (q / n) + i sin (q / n)) 17) Newton's Method z(n+1) = z(n) - [f(z(n)) / f '(z(n))] 18) Henon Attractor: (for z(n) = x(n) + iy(n)) , x(n+1) = ax(n) + y(n) and y(n+1)= bx(n) 19) Halley Map: z(n+1) = z(n) - L[(2f(z(n))f '(z(n))) / (2(f '(z(n)))^2 - - f' '(z(n))f(z(n)))] 20) Lorenz Attractor: dx / dt = a(y - x) dy / dt = x(r - z) - y dz / dt = xy - bz Complex Equations Researched Here are the equations that we have used during the past nine years to generate well over 300,000 Mandelbrot and Julia sets. We have over 3 terabytes of fractal data! Feel free to continue to delve into them using whatever software (your own or canned) you have available. Because I wrote my own code in C language and a complex math library was not available, I had to resolve each of these equations into real, f(x), and imaginary, f(y), parts. Many, many long (but fun) hours doing just the basic algebra were spent in order to bring you the majestic beauty of these incredible forms. 1--F(Z) = Z^2 + C 2--F(Z) = Z^3 + C 3--F(Z) = (Z^2 + C) / (Z - C) 4--F(Z) = Z^2 - Z + C 5--F(Z) = Z^3 - Z^2 + Z + C 6--F(Z) = (1 + C)Z - CZ^2 7--F(Z) = Z^3 / (1 + CZ^2) 8--F(Z) = (Z - 1)(Z + .5)(Z^2 - 1) + C 9--F(Z) = (Z^2 + 1 + C) / (Z^2 - 1 - C) 10--F(Z) = Z^1.5 + C 11--F(Z) = exp(Z)-C 12--F(Z) = Z - 1 + Cexp(-Z) 13--F(Z) = CZ - 1 + Cexp(-Z) 14--F(Z) = (4Z^5 + C)/5Z^4 15--F(Z) = (6Z^7 + C)/7Z^6 16--F(Z) = Z^2 * exp(-Z) + C 17--F(Z) = Z^2 * Z^(-2) + C 18--F(Z) = Z * exp(-Z) + C 19--F(Z) = C * exp(-Z) + Z^2 20--F(Z) = Z^3 + Z + C 21--F(Z) = Z^4 + Z + C 22--F(Z) = Z^4 + CZ^2 + C 23--F(Z) = Z^2sin(Re Z) + CZcos(Im Z) + C 24--F(Z) = 2^Z * CZ^2 25--F(Z) = Z^5 - Z^3 + Z + C 26--F(Z) = (Z^2 + C)^2 + Z + C 27--F(Z) = (Z + sin(Z))^2 + C 28--F(Z) = Cexp(Z) 29--F(Z) = Z^2 + C^3 30--F(Z) = Cexp(CZ) 31--F(Z) = Z^2cos(ReZ)+CZsin(ImZ)+C 32--F(Z) = CZ^2 + ZC^2 33--F(Z) = exp(cos(CZ)) 34--F(Z) =(1 + Jo(Re Z))^2 + (Jo(Im Z) + C)^2 (Here Jo represents the Bessel function) 35--F(Z) = C(sin Z + cos Z) 36--F(Z) = Z^(-.5) + C 37--F(Z) = CZ(1 - Z) 38--F(Z) = C^2Z(1 - Z) 39--F(Z) = ((Z^2+C)^2)/(Z-C) 40--F(Z) = (Z + sin Z)^2 + Z^-.5 + C 41--F(Z) = C*(sin Z + cos Z)*(Z^3+Z+C) 42--F(Z) = Cexp(Z) * exp(cosCZ) 43--F(Z) = (Z^3+Z+C)*C*(sinZ + cosZ) 44--F(Z) = ((1+C)Z-CZ^2)*((Z+sinZ)^2+C) 45--F(Z) = Z^2 + Z^1.5 + C 46--F(Z) = Z^2 + ZexpZ + C 47--F(Z) = (Z+sinZ)^2+Cexp(-Z)+Z^2+C 48--F(Z) = ((Z^3)/(1+CZ^2))+expZ-C 49--F(Z) = (Z^2*sin(ReZ) + CZ(ImZ) + (Z^2*cos(ReZ)+CZsin(ImZ)+C 50--F(Z) = (Z+sinZ)^2+Cexp(Z)+C 51-- F(Z) = Z^2 + 1/Z + C 52-- F(Z) = (Z^3 + C) / Z 53-- F(Z) = (Z^3 + C) / Z^2 54-- F(Z) = ((Z+1)^2 + C) / Z 55-- F(Z) = (Z + C)^2 + (Z + C)* 56-- F(Z) = (Z + C)^3 - (Z + C)^2 57-- F(Z) = (Z^3 - Z^2)^2 + C 58-- F(Z) = (Z^2 - Z)^2 + C 59-- F(Z) = (Z + ln Z)^2 + C 60-- F(Z) = (Z - sqrt(Z))^2 + C 61-- F(Z) = (Z + sqrt(Z))^2 + C 62-- F(Z) = Z^2exp(Z) - Zexp(Z) + C 63-- F(Z) = (exp(CZ) + C)^2 64-- F(Z) = Z * exp(Re Z/Im Z) + C 65-- F(Z) = exp(X^2*Y^2) + Im Z + C 66-- F(Z) = exp(Re Z)*(X-a) + exp(Im Z)*(Y-b)i 67-- F(Z) = X^2*exp(Y+b) + iaexp(Y+b) 68-- F(Z) = (a-X^2+Y^2)exp(b+X^2-Y^2) + i(b+X^2-Y^2)exp(a-X^2+Y^2) 69-- F(Z) = [(2X-Y^2+a)/(2X^2+Y-b)] + i[(2X^2+Y-a)/(2X-Y^2+b)] 70-- F(Z) = [(X^2+Y^2+a)/cos(X^2+Y^2)] + i[(X^2+Y^2+b)/sin(X^2+Y^2)] 71-- F(Z) = Z^5 + C 72-- F(Z) = Z^6 + C 73-- F(Z) = Z^7 + C 74-- F(Z) = (3Z^4 + C) / 4Z^3 75-- F(Z) = (2Z^3 + C) / 3Z^2 76-- F(Z) = Z^5 + CZ^3 + C 77-- F(Z) = Z^6 + CZ^4 + CZ^2 + C 78-- F(Z) = Z^8 + C 79-- F(Z) = Z^9 + C 80-- F(Z) = Z^8 + CZ^4 + CZ^2 + C 81-- F(Z) = Z^9 - CZ^6 + CZ^3 + C 82-- F(Z) = (Z^4 + C) / (Z - C) 83-- F(Z) = (Z^3 + Z + C) / (Z^2 - Z - C) 84-- F(Z) = (Z^3 + Z + C) / (Z - C) 85-- F(Z) = (Z^3 + Z + C) / Z 86-- X = X^2+XY+A ; Y = Y^2-XY+B 87-- X = X^3-(X^2)Y+XY^2-XY+A; Y = Y^3-XY^2+(X^2)Y+XY+B 88-- X = (X^2)sin Y + A ; Y = (Y^2)cos X + B 89-- X = X^4-3X^3+3X^2(Y^2)+A ; Y = Y^4+3XY^3-3X^2(Y^2) 90-- X = X^2(1+exp(-Y))+A ; Y = Y^2(1+exp(-X)+B 91-- F(Z) = C(Z^2 + 1)^2 / Z(Z^2 -1) 92-- F(Z) = CZ^2 93-- F(Z) = CZ^3 94-- F(Z) = CZ^4 95-- F(Z) = C*cos Z 96-- F(Z) = C*sin Z 97-- F(Z) = CZ*ln Z 98-- F(Z) = C*tan Z 99-- F(Z) = C*exp(CZ) / (exp(C) - 1) 100-- F(Z) = C*exp(Z)*sqrt(Z) /n 101 -- F(Z) = (Z^2(1+Z^2))/(Z+C) 102 -- F(Z) = Z(1+Z^2)/(Z+C) 103 -- F(Z) = (Z^5+C)/(Z^3+Z^2+Z+1) 104 -- F(Z) = (Z^3+C)/3Z^2 105 -- F(Z) = (Z^3+Z^2+Z+C)/(Z-C) 106 -- F(Z) = exp(Z^2+C) 107 -- F(Z) = Z^2*exp(Z^2)+C 108 -- F(Z) = exp(Z^2)/(Z+C) 109 -- F(Z) = (Z+exp(Z))^2+C 110 -- F(Z) = (Z^2+C)^2-exp(Z)+C 111 -- F(Z) = (1+iC)sin(Z) 112 -- F(Z) = (1+iC)cos(Z) 113 -- F(Z) = Z*tan(ln Z)+C 114 -- F(Z) = sqrt(Z^4+1)+C 115 -- F(Z) = sqrt(Z^4+C) 116 -- F(Z) = C^Z 117 -- F(Z) = C*arctan(Z) 118 -- F(Z) = (ZlnZ)/exp(C) 119 -- F(Z) = exp(Z)/lnZ+C 120 -- F(Z) = sqrt(Z^3+C) 121 -- F(Z) = sqrt(Z^3+1)+C 122 -- F(Z) = cubrt(Z^6+1)+C 123 -- F(Z) = (Z+exp(Z)+ln Z)^2+C 124 -- F(Z) = (Z^2+C+1)^2 / (2Z+C+2)^2 125 -- F(Z) = Z ^ 10 + C 126 -- F(Z) = Z ^ 11 + C 127 -- F(Z) = Z ^ 12 + C 128 -- F(Z) = Z^12 - Z^11 - Z^10 + C 129 -- F(Z) = Z ^ 13 + C 130 -- F(Z) = Z ^ 14 + C 131 -- F(Z) = Z ^ 15 + C 132 -- F(Z) = Z ^ 16 + C 133 -- F(Z) = Z ^ 17 + C 134 -- F(Z) = Z ^ 18 + C 135 -- F(Z) = Z ^ 19 + C 136 -- F(Z) = Z ^ 20 + C 137 -- F(Z) = Z ^ 21 + C 138 -- F(Z) = Z ^ 22 + C 139 -- F(Z) = Z ^ 23 + C 140 -- F(Z) = Z ^ 24 + C 141 -- F(Z) = Z ^ 25 + C 142 -- F(Z) = Z ^ 26 + C 143 -- F(Z) = Z ^ 27 + C 144 -- F(Z) = Z ^ 28 + C 145 -- F(Z) = Z ^ 29 + C 146 -- F(Z) = Z^30 + C 147 -- X=X^2+Y+A+X^2/Y ;Y=Y^2+X+B+Y^2/X 148 -- X=X^3+Y^2-X+A ;Y=Y^3-X^2+Y+B 149 -- X=X^2+2XY-Y+A ;Y=Y^2-2XY+X+B 150 -- X=X^3+AX^2+BY ;Y=Y^3+BY^2+AX 151 -- X=2X^2-3ABY+A ;Y=3Y^2+2ABX-B 152 -- X=X^4lnX+Y^2sinY+A; Y=Y^4lnY+X^2cosX+B 153 -- X=sqr(ln(X^2))+YsinX+A; Y=sqr(ln(Y^2))-XcosY+B 154 -- X=.5(X^2-Y^2)+.5(X+Y)+A; Y=.5(Y^2-X^2)-.5(X+Y)+B 155 -- X=sqr(X^3)+sqr(Y^3)+A; Y=sqr(Y^3)-sqr(X^3)+B 156 -- X=Y/sqrX+X/sqrY+A; Y=XsqrY+YsqrX+B 157 -- F(Z) = Z^30 - 30Z^29 - 870Z^28 + C 158 -- F(Z) = Z^27 - 27Z^26 - 702Z^25 + C 159 -- F(Z) = Z^24 - 24Z^23 - 552Z^22 + C 160 -- F(Z) = Z^21 - 21Z^20 - 420Z^19 + C 161 -- F(Z) = Z^18 - 18Z^17 - 306Z^16 + C 162 -- F(Z) = Z^15 - 15Z^14 - 210Z^13 + C 163 -- F(Z) = Z^30 - 30Z^29 - 870Z^28 + Z^27 - 27Z^26 - 702Z^25 + C 164 -- F(Z) = Z^27 - 27Z^26 - 702Z^25 + Z^24 - 24Z^23 - 552Z^22 + C 165 -- F(Z) = Z^24 - 24Z^23 - 552Z^22 + Z^21 - 21Z^20 - 420Z^19 + C 166 -- F(Z) = Z^21 - 21Z^20 - 420Z^19 + Z^18 - 18Z^17 - 306Z^16 + C 167 -- F(Z) = Z^18 - 18Z^17 - 306Z^16 + Z^15 - 15Z^14 - 210Z^13 + C 168 -- F(Z) = Z^30 - 30Z^29 - 870Z^28 + Z^27 - 27Z^26 - 702Z^25 + Z^24 - 24Z^23 - 552Z^22 + C 169 -- F(Z) = Z^27 - 27Z^26 - 702Z^25 + Z^24 - 24Z^23 - 552Z^22 + Z^21 - 21Z^20 - 420Z^19 + C 170 -- F(Z) = Z^24 - 24Z^23 - 552Z^22 + Z^21 - 21Z^20 - 420Z^19 + Z^18 - 18Z^17 - 306Z^16 + C 171 -- F(Z) = Z^21 - 21Z^20 - 420Z^19 + Z^18 - 18Z^17 - 306Z^16 + Z^15 - 15Z^14 - 210Z^13 + C 172 -- F(Z) = Z^30 - Z^29 + Z^28 - Z^27 + Z^26 - Z^25 + C 173 -- F(Z) = Z^24 - Z^23 + Z^22 - Z^21 + Z^20 - Z^19 + C 174 -- F(Z) = Z^18 - Z^17 + Z^16 - Z^15 + Z^14 - Z^13 + C 175 -- F(Z) = Z^15sinX - Z^14cosY - Z^13tanX + C 176 -- F(Z) = Z^12cosX - Z^11sinY - Z^10tanY + C 177 -- F(Z) = Z^15sinA - Z^14cosB - Z^13tanX - Z^12tanY + C 178 -- F(Z) = Z^12cosA - Z^11sinB - Z^10tanY - Z^9tanX + C 179 -- F(Z) = Z^30sinX - 30Z^29cosY + C 180 -- F(Z) = Z^28cosX - 28Z^27sinY + C 181 -- F(Z) = (Z^3+3Z(C-1)+(C-1)(C-2))^2 182 -- F(Z) = (3Z^2+3Z(C-2)+C^2-3C+3)^2 183 -- F(Z) = (Z^3+3Z(C-1)+(C-1)(C-2))^2 / (3Z^2+3Z(C-2)+C^2-3C+3)^2 184 -- F(Z) = Z ^ pi + C 185 -- F(Z) = pi ^ Z + C 186 -- F(Z) = Z ^ 4 + C 187 -- F(Z) = Z ^ pi + pi ^ C 188 -- F(Z) = C * Z ^ pi 189 -- F(Z) = Z ^ pi - Z ^ 3 + C 190 -- F(Z) = Z ^ pi - Z ^ 2 + C 191 -- F(Z) = Z ^ 2.5 + C 192 -- F(Z) = (5Z^6 + C)/6Z^5 193 -- F(Z) = Z ^ e + C 194 -- F(Z) = Z ^ (C * e) 195 -- F(Z) = (Z ^ e) ^ C 196 -- F(Z) = C * Z ^ e 197 -- F(Z) = Z ^ (pi * e) 198 -- F(Z) = Z * (C ^ e) 199 -- F(Z) = cbrt(Z ^ 7 + 1) + C 200 -- F(Z) = Z ^ 4.669 + C 201 -- F(Z) = (Z ^ 8 + 1) ^ 1/4 + C 202 -- F(Z) = (Z ^ 9 + 1) ^ 1/4 + C 203 -- F(Z) = ((Z ^ 2 * (ReZ - (ImZ)^2))/(1 - Z)) + C 204 -- F(Z) = (Z ^ 10 + C) ^ 1/4 205 -- F(Z) = (Z ^ 10 + 1) ^ 1/4 + C 206 -- F(Z) = (Z ^ 11 + C) ^ 1/4 207 -- F(Z) = (Z ^ 11 + 1) ^ 1/4 + C 208 -- F(Z) = (Z ^ 12 + C) ^ 1/4 209 -- F(Z) = (Z ^ 12 + 1) ^ 1/4 + C 210 -- F(Z) = YZ^2sinX - XZcosY + C 211 -- F(Z) = XZ^3cosY + YZ^2sinX + C 212 -- F(Z) = Z^4 - Z^2cosX + YsinY + C 213 -- F(Z) = XYZ^2 + C 214 -- F(Z) = Z^2 + X^2*Y^2 + C 215 -- F(Z) = Z^3 + X^2sinY + Y^2cosX + C 216 -- F(Z) = (Z ^ 13 + C) ^ 1/6 217 -- F(Z) = (Z ^ 5 + C) ^ 1/3 218 -- F(Z) = (Z ^ 4 + C) ^ 1/sin X 219 -- F(Z) = Z ^ 2 + iZ ^ 2 + C 220 -- F(Z) = Z ^ 3 + iZ ^ 3 + C 221 -- F(Z) = Z ^ 4 + iZ ^ 2 + C 222 -- F(Z) = (Z ^ 4 / Z + 1) + C 223 -- F(Z) = (Z ^ 6 / Z + 1) + C 224 -- F(Z) = (Z ^ 4 / Z + i) + C 225 -- F(Z) = (Z ^ 6 / Z + i) + C 226 -- F(Z) = (Z ^ 2 / (lnZ)^2) + C 227 -- F(Z) = (Z ^ 2 / (ln(Z^2)) + C 228 -- F(Z) = (Z ^ 3 / (lnZ)^3) + C 229 -- F(Z) = (Z ^ 3 / (ln(Z^3)) + C 230 -- F(Z) = (Z ^ 4 / (lnZ)^4) + C 231 -- F(Z) = (Z ^ 4 / (ln(Z^4)) + C 232 -- F(Z) = Z ^ 2 + Z / ln Z + C 233 -- F(Z) = Z ^ 2 + ln Z / Z + C 234 -- F(Z) = Z ^ 6 + Z ^ 4 + Z ^ 2 + C 235 -- F(Z) = Z ^ 6 - Z ^ 4 - Z ^ 2 + C 236 -- F(Z) = Z ^ (1/Z) + C 237 -- F(Z) = Z ^ 2 + sin Z / Z + C 238 -- F(Z) = Z ^ 2 + Z / sin Z + C 239 -- F(Z) = Z ^ iZ + C 240 -- F(Z) = Z ^ 2 * exp(X) + C 241 -- F(Z) = Z ^ 2 * exp(X ^ 2) + C 242 -- F(Z) = Z ^ 3 * exp(X) + Z ^ 2 * exp(Y) + C 243 -- F(Z) = exp(Z ^ Z) + C 244 -- F(Z) = (Z ^ 3) / (Z + 1) + C 245 -- F(Z) = Z ^ 2 / C 246 -- F(Z) = (Z ^ 4 + 1) / (Z + C) 247 -- F(Z) = (Z ^ 4 + C) / (Z ^ 2 + 1) 248 -- F(Z) = (Z ^ 4 + C) / (1 - Z ^ 2) 249 -- F(Z) = Z ^ 2 * exp(Z) / (Z + C) 250 -- F(Z) = Z ^ 2 - exp(Z) + sin(Z) + C 251 -- F(Z) = (Z ^ 4) / (Z ^ 2 + C) 252 -- F(Z) = Z ^ 2 + sqrt(Z ^ 2 + C) 253 -- F(X) = X^2 - Y^2 + XsinY + A; F(Y) = Y^2 - B 254 -- F(X) = X^2 + atan(Y/X) + A; F(Y) = Y^2 - A 255 -- F(X) = 1 - X - Y^2 + A; F(Y) = 1 - Y + X^2 + B 256 -- F(X) = exp(sqrt(X)) - exp(sqrt(Y)) + A; F(Y) = exp(XlnY) + B 257 -- F(Z) = C ^ 2 * ln(Z ^ 2) 258 -- F(Z) = Z ^ 2 ln(C) 259 -- F(Z) = Z ^ 2 ln(C) + C 260 -- F(Z) = Z ^ 2 ln(Z + C) 261 -- F(Z) = Z ^ -2 + C 262 -- F(Z) = ((X^2 + Y^2 + A) / (X^2 - Y^2)) + i[((X^2 - Y^2 - B) / (X^2 + Y^2))] 263 -- F(Z) = (X^3 - iY + C) / (X + Y + 1) 264 -- F(Z) = [(X^2 + A^2) / Y] + i[(Y^2 + B^2) / X] 265 -- F(Z) = [(X^3 + X^2 + X + A) / (Y^3 - Y^2 - Y - 1)] + i[(Y^3 + Y^2 + Y + B) / (X^3 - X^2 - X - 1)] 266 -- F(Z) = [(X^4 - Y^2) / (X + Y + A)] + i[(X^2 + Y^4) / (X - Y - B)] 267 -- F(Z) = C ^ 3 / Z ^ 2 268 -- F(Z) = [Z^(1/2) / Z^(1/3)] + C 269 -- F(Z) = (Z ^ 2 + C) / (1 - C) 270 -- F(Z) = (exp(Z ^ 4)/ Z ^ 4) + C 271 -- F(Z) = (Z ^ 6 + 1) ^ (1/5) + C 272 -- F(Z) = Z ^ 2 + CZ + C * sin Y - Z * cos X + C 273 -- F(Z) = Z ^ 6 - Z ^ 5 - Z ^ 4 - Z ^ 3 - Z ^ 2 - Z + C 274 -- F(Z) = Z ^ 2 * (sin C / C) 275 -- F(Z) = exp(- Z ^ 2 / 2) + C 276 -- F(Z) = (Z ^ 3 + 3 * Z - 1) / (2 - Z) 277 -- F(Z) = Z ^ 3 * sin C + Z ^ 2 * cos C + XY + C 278 -- F(Z) = (Z ^ 2 + 1) ^ 2 / (Z + C) ^ 2 279 -- F(Z) = (Z ^ 2 + C + 1) ^ 2 / (Z - C - 1) ^ 2 280 -- F(Z) = Z ^ 4 * sin Y + Z ^ 2 * cos X + XY + C 281 -- F(Z) = Z * cos (XY) + C 282 -- F(Z) = Z ^ 2 * cos (X ^ 2 + Y ^ 2) + C 283 -- F(Z) = Z ^ (2 + ln C) 284 -- F(Z) = Z ^ (9/7) + C 285 -- F(Z) = Z ^ 5 * (1 - Z - (Z + C) ^ 2) + C 286 -- F(Z) = Z ^ 6 + Z ^ 5 + C 287 -- F(Z) = Z ^ 6 + Z ^ 4 + C 288 -- F(Z) = Z ^ 6 + Z ^ 3 + C 289 -- F(Z) = Z ^ 6 + Z ^ 2 + C 290 -- F(Z) = Z ^ 6 + Z + C 291 -- F(Z) = Z ^ 2 + cos Z + C 292 -- F(Z) = Z ^ 2 + cos 2Z + C 293 -- F(Z) = Z ^ 2 + cos 3Z + C 294 -- F(Z) = Z ^ 2 + cos 4Z + C 295 -- F(Z) = Z ^ 2 + cos 5Z + C 296 -- F(Z) = (Z ^ 7 + C) / Z ^ 5 297 -- F(Z) = (Z ^ 7 + C) / Z ^ 4 298 -- F(Z) = (Z ^ 7 + C) / Z ^ 3 299 -- F(Z) = (Z ^ 7 + C) / Z ^ 2 300 -- F(Z) = (Z ^ 7 + C) / Z 301 -- F(Z) = Z ^ 3 - Z ^ 2 - Z + C 302 -- F(Z) = Z ^ 4 - Z ^ 3 - Z ^ 2 + C 303 -- F(Z) = Z ^ 5 - Z ^ 4 - Z ^ 3 + C 304 -- F(Z) = Z ^ 6 - Z ^ 5 - Z ^ 4 + C 305 -- F(Z) = Z ^ 7 - Z ^ 6 - Z ^ 5 + C 306 -- F(Z) = Z ^ 2 * (cos(Z)) ^ 2 + C 307 -- F(Z) = Z ^ 2 * (cos(XY)) ^ 2 + C 308 -- F(Z) = Z ^ 4 * (sin(Z)) ^ 2 + C 309 -- F(Z) = Z ^ 3 * (sin(XY)) ^ 2 + C 310 -- F(Z) = Z ^ 3 * (cos(Z)*sin(Z)) + C 311 -- F(Z) = (Z ^ 2 / sin(Z)) + C 312 -- F(Z) = (Z ^ 4 / cos(Z)) + C 313 -- F(Z) = (Z ^ 6 + C) / (sin(Z) * cos(Z)) 314 -- F(Z) = (Z ^ 3 + Z ^ 2 + Z + C) / (Z + cos(Z) 315 -- F(Z) = (Z ^ 2 * ln Z + Z + C) / (sin(Z)) ^ 2 316 -- F(Z) = Z ^ 4 + (cos X) ^ 2 + (sin Y) ^ 2 + C 317 -- F(Z) = Z ^ 3 + cos X * sin Y + C 318 -- F(Z) = Z ^ 4 + Z + cos C 319 -- F(Z) = Z ^ 2 + Z + tan C 320 -- F(Z) = Z ^ 3 + Z ^ 2 + exp(1 + sin X) + C 321 -- F(Z) = sqrt(Z ^ 4 + cos(theta) + C); theta = arctan (Im Z / Re Z) 322 -- F(Z) = sqrt(Z ^ 5 + Z ^ 3 + Z + C) 323 -- F(Z) = sqrt(Z ^ 4 + Z ^ 3 + Z ^ 2 + Z + C) 324 -- F(Z) = sqrt(Z ^ 6 - Z ^ 3 + C) 325 -- F(Z) = sqrt(ln (Z ^ 2) + Z ^ 2 * ln Z + C) 326 -- F(Z) = cos((Z ^ 2 + C) / XY) 327 -- F(Z) = cos((Z ^ 3 + C) / XY) 328 -- F(Z) = cos((Z ^ 4 + C) / XY) 329 -- F(Z) = ((Z ^ 4 + C) / XY) + cos((Z ^ 3 + C) / XY) 330 -- F(Z) = cos((Z ^ 4 + C) / XY) + cos((Z ^ 3 + C) / XY) + cos((Z ^ 2 + C) / XY) 331 -- F(Z) = Z ^ 3/2 + Z ^ 4/3 + C 332 -- F(Z) = Z ^ 4/3 + Z ^ 5/4 + C 333 -- F(Z) = Z ^ 5/4 + Z ^ 6/5 + C 334 -- F(Z) = Z ^ 5/2 + Z ^ 7/3 + C 335 -- F(Z) = Z ^ (pi/e) ^ 2 + C 336 -- F(Z) = Y * sin X * cos Y * exp(-X) + C 337 -- F(Z) = Z ^ 2 * cos X * cos Y * exp(-Y) + C 338 -- F(Z) = XYZ * sin X * sin Y * exp(Z) + C 339 -- F(Z) = Z ^ 3 + X ^ 2 * Y ^ 2 * cos X * sin Y + C 340 -- F(Z) = Z ^ 2 + X ^ 2 * sin Y + Y ^ 2 * cos X + C 341 -- F(Z) = 1 / Z + 1 / Z ^ 2 + C 342 -- F(Z) = Z ^ 2 / Z' + Z ^ 3 / Z' ^ 2 + C 343 -- F(Z) = Z ^ 3 / C' + Z ^ 2 + C 344 -- F(Z) = Z ^ 2 + Z' ^ 2 + C 345 -- F(Z) = Z ^ 3 + Z ^ 2 * Z' + Z * Z' ^ 2 + Z' ^ 3 + C 346 -- F(Z) = Z ^ 4 - Z ^ 3 * Z' + Z ^ 2 - Z' + C 347 -- F(Z) = Z ^ 5 - C * Z ^ 3 - C' * Z ^ 2 + Z' + C 348 -- F(Z) = Z ^ 4 * Z' ^ 2 - Z ^ 3 * Z' + C 349 -- F(Z) = Z ^ 6 + Z' ^ 5 + Z ^ 4 + Z' ^ 3 + Z ^ 2 + Z' + C 350 -- F(Z) = Z ^ 4 + Z ^ 2 / Z' + Z' ^ 3 / Z ^ 2 + C 351 -- F(Z) = arcsin(ln(Z)) + C 352 -- F(Z) = arctan(ln(Z)) + C 353 -- F(Z) = (arcsin(ln(Z))) ^ 2 + C 354 -- F(Z) = e ^ (1 + cos(ln(Z))) + C 355 -- F(Z) = e ^ (2 - e ^ cos(Z)) + C 356 -- F(Z) = XY * Z^2 - X^2 * YZ + X * Y ^ 2 * Z ^ 3 + C 357 -- F(Z) = X ^ 3 * Y ^ 4 + X ^ 2 * Z ^ 5 + C 358 -- F(Z) = XY^2Z^3 - X^3Y^2Z + X^2Y^2Z^2 + C 359 -- F(Z) = Z ^ 4 - X ^ 2 * cos(Y) + Y * sin(X) + C 360 -- F(Z) = Z ^ 3 - Y ^ 2 * cos(XY) - X ^ 2 * sin(X) - Y * cos(Y) + C 361 -- F(Z) = (Z ^ 3 + C) / (Z ^ 3 - C) 362 -- F(Z) = (Z ^ 3 + C ^ 2 + 1) / (Z ^ 3 - C ^ 2 - 1) 363 -- F(Z) = (Z ^ 3 + Z + C) / (Z ^ 3 - Z - 1) 364 -- F(Z) = (Z ^ 2 - Z ^ 3 + 1) / (Z ^ 4 + C) 365 -- F(Z) = (Z ^ 4 + C) / (4Z ^ 3 + 1) 366 -- F(Z) = (Z ^ C) / (Z + 1) 367 -- F(Z) = (Z ^ (1 + C)) / (1 + C) 368 -- F(Z) = (2 ^ Z) / C 369 -- F(Z) = 2 ^ Z + C 370 -- F(Z) = 2 ^ Z + (2 ^ Z) / C + C 371 -- F(Z) = XYZ ^ 2 - X ^ 2YZ + C 372 -- F(Z) = X ^ 4 * Y ^ 3 * Z ^ 2 + C 373 -- F(Z) = X^3*Y^3*Z^3 - X^2*Y^2*Z^2 + XYZ + C 374 -- F(Z) = XY^2Z + X^2YZ^4 + C 375 -- F(Z) = Z^2*sqrt(XY) + XY^2Z^4*sqrt(XY) + C 376 -- F(Z) = Z ^ (2XY) + C 377 -- F(Z) = X ^ (2YZ) + C 378 -- F(Z) = Y ^ (Z^2) + X + C 379 -- F(Z) = X ^ (2YZ) + Z ^ (2XY) + C 380 -- F(Z) = (XY) ^ (Z - C) 381 -- F(Z) = Z ^ 2C + C 382 -- F(Z) = Z ^ 2 + C ^ 2Z + C 383 -- F(Z) = X^Y + Z^X + Y^Z + C 384 -- F(Z) = Z ^ 2 + A ^ X + B ^ Y + C 385 -- F(Z) = Z ^ 3 + X ^ (AB) + Y ^ C 386 -- F(Z) = Z ^ 9 - Z ^ 8 - Z ^ 7 + C 387 -- F(Z) = Z^9 - 9Z^8 - 8Z^7 + C 388 -- F(Z) = Z^9 - 9Z^8 - 8Z^7 - 7Z^6 - 6Z^5 - 5Z^4 + C 389 -- F(Z) = Z^9 - 9Z^8 - 8Z^7 - 7Z^6 - 6Z^5 - 5Z^4 - 4Z^3 - 3Z^2 - 2Z +C 390 -- F(Z) = Z^9 + C^9 391 -- F(Z) = Z^3 + Z^2 + CsinX + C 392 -- F(Z) = Z^4 + X^2 - Y^2 - C^2*cosZ + C + A 393 -- F(Z) = Z^5 + Im(Z^4 + Z^3 + Z^2) + CZRe(Z^2 + C) + C 394 -- F(Z) = Z^3 + Z^2*cosY + ZsinX + C 395 -- F(Z) = Z^4 + (Z^2 / sinY) + (CZ^3 / cosX) + C 396 -- F(Z) = (Z + ln Z)^4 + C 397 -- F(Z) = Z + (ln Z)^4 + C 398 -- F(Z) = Z^2 + (ln Z)^3 + C 399 -- F(Z) = Z^3 + (ln Z)^2 + C 400 -- F(Z) = (ln Z)^2 + C^2 + C Lissajous Figures A 3-D Lissajous figure is created using three parametric equations, one each for the x, y, and z coordinates. These equations are functions of sin and cos, so they are periodic, with the actual period depending on what values you enter. The values you input in these functions are: a, b, and exponents x, y, and z. The value of t, the parametric "time" parameter, ranges from 0 to the number of spheres plotted minus one. Thanks to Aaron C. Caba for the info. We used five different sets of equations. Here they are: Set 1) x = r * (sin(a*t) * (cos(b*t)^x)) y = r * (sin(a*t) * (sin(b*t)^y)) z = r * (cos(a*t)^z) Set 2) x = r * (sin(a*t) * (cos(b*t)^x)) y = r * (cos(a*t) * (cos(b*t)^y)) z = r * (sin(a*t)^z) Set 3) x = r * (sin(a*t) * (sin(b*t)^x)) y = r * (sin(a*t) * (cos(b*t)^y)) z = r * (sin(a*t)^z); Set 4) x = r/4 * (a * sin(2*(t-pi/13))^x) y = r/4 * (-b * cos(t)^y) z = r * (sin(a*t)^z) Set 5) x = r * (sin(a*t) * (cos(a*t)^x)) y = r * (sin(b*t) * (sin(b*t)^y)) z = r * (sin(t)^z) Spherical Harmonics Spherical harmonics are expressions in three-dimensional spherical coordinates which are primarily used to describe the theoretical hybrid electron orbital shapes in molecules. The three coordinates are r (for radius), theta (degrees in the traditional x-y plane), and phi (degrees in the y-z plane). You may also recognize this way of laying out spatial coordinates from Star Trek's "210 mark 45" designation for navigation as the degrees in theta and phi. As with the rectangular coordinates, x, y, and z, we can describe any point in three dimensional space using such a coordinate system. All types of scientists use spherical and cylindrical (rho, theta, and z) coordinate systems to analyze various physical phenomena. Here are a few of the examples we have used to produce our mathematical "flying saucers:" r = (cos (theta))^2 + (cos(2 * theta))^4 + sin(4 * phi) r = (cos(12 * theta))^5 + (cos(8 * theta))^3 + cos(6 * theta) r = 2 * (cos(6 * theta))^6 - 4 * (cos(4 * theta))^4 - 2 * (cos(2 * theta))^2 rho = (sin(theta))^4 + (sin(2 * theta))^2 + e ^ (1 - sin(z)) rho = 4 * (cos(4 * theta))^4 - 2 * (cos(2 * theta))^2 + (1 + cos (z))^2 You can experiment with an infinite number of possibilities. You will soon discover what each coefficient, exponent, and function does to the overall shape of the object. Happy Hunting! Affine Transformations (Due to the limitations of web publishing, our notation of matrices, symbols, subscripts etc. will be clumsily laid out...please bear with us...as our tools improve, so will our presentation.) As given by Barnsley in "Fractals Everywhere," an affine transformation is a manipulation of a geometric set of points (here x1 and x2, or just x) using matrices and column vectors such that: w(x1,x2) = (ax1 + bx2 + e , cx1 + dx2 + f) A general affine two-dimensional transformation, is given by: w(x) = Ax + t where A is a 2 x 2 real matrix and t is the column vector: A = (a b) (c d) t = (e) (f) In graphic terms, the A matrix transforms x by a linear transformation, which deforms space relative to the origin (involving rotation and rescaling), whereas the t vector merely translates (moves) the points once the deformation is complete. The matrix A can always be written as: A = (r1 cos g -r2 cos h) (r1 sin g r2 sin h) where r1 and r2 are scaling factors and g and h are rotation angles. Barnsley continues in his book to describe Iterated Function Systems, a way of describing objects created by affine transformations. Using the letters w, a, b, c, d, e, and f as defined above, he offers a typical a typical fern designation in tidier "IFS code:" IFS code for a Fern (Barnsley) w a b c d e f p 1 0 0 0 .16 0 0 .01 2 .85 .04 -.04 .85 0 1.6 .85 3 .2 -.26 .23 .22 0 1.6 .07 4 -.15 .28 .26 .24 0 .44 .07 Notice he provides a number p which corresponds to the probability that each of the four "w" transformations will be used given each point (x1,x2) that is to be manipulated. All of the p's must add up to one. Because of this probability factor, each time you generate a fern, it will be a slightly different fern. Thus we are not producing a "deterministic fractal," as are Mandelbrot and Julia sets (which are exactly reproducible), but more of a "random iteration" fractal. - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ End of fractint-digest V1 #124 ******************************