From: owner-fractint-digest@lists.xmission.com (fractint-digest) To: fractint-digest@lists.xmission.com Subject: fractint-digest V1 #551 Reply-To: fractint-digest Sender: owner-fractint-digest@lists.xmission.com Errors-To: owner-fractint-digest@lists.xmission.com Precedence: bulk fractint-digest Wednesday, April 18 2001 Volume 01 : Number 551 ---------------------------------------------------------------------- Date: Fri, 13 Apr 2001 19:40:42 -0000 From: "Andrew Coppin" Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) >From: "Jonathan Osuch" >Reply-To: fractint@lists.xmission.com >To: >Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) >Date: Thu, 12 Apr 2001 19:54:54 -0500 > > The Ikenaga set is: Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C > where: Z(n) = x + yi and C = a + bi > >Jonathan Now *that* was what I was asking! Thanks. Andrew. _________________________________________________________________________ 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" ------------------------------ Date: Fri, 13 Apr 2001 15:35:36 -0500 From: DeBow Freed Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) Fellow Fractaliers:

FYI, what follows is a direct quote from Dr. Ikenaga's response to the second of a total of 4 messages I sent to him in September of last year attempting to inquire about "Ikenaga functions" in general, and the publication called "Self Similar Fractals" listed in his own Bibliograhy on his own Homepage in specific (addresss provided in PNL's earlier note):

"Dear Dr. Freed-

   "I wish I could be of help, but I have no idea what you're
  talking about [?????? - DBF]. If someone named something after me,
  they certainly never told me about it. :-)

    "And I've never written articles about fractals [??????- DBF]. Do you
  have references for them?

     "Also, are you sure that whoever is doing this [Jim Muth-DBF] got the name right?

     "(Thanks for mentioning fractint. I always enjoyed that program,
  but I'd thought they stopped developing it. Maybe I should go look
  again.)

  Bruce"

    After 2 more similarly confusing attempts to gain further information regarding the functions themselves or Dr. Ikenaga's publication entitled "Self-Similar Fractals" which was at that time also referenced in his own Homepage, I gave up further efforts at deciphering Dr. Ikenaga's courteous but paradoxical responses.

DeBow Freed (a/k/a DBF)

  -----
  Bruce Ikenaga                    bikenaga@marauder.millersv.edu
  Dept. of Math, P.O. Box 1002,    :::::::::::::::::::
  Millersville University,
  Millersville, PA 17551-0302

Andrew Coppin wrote:

>From: "Jonathan Osuch" <osuchj@qwest.net>
>Reply-To: fractint@lists.xmission.com
>To: <fractint@lists.xmission.com>
>Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7])
>Date: Thu, 12 Apr 2001 19:54:54 -0500
>
>           The Ikenaga set is:    Z(n+1) =Z(n)^3 + (C-1) * Z(n) - C
>           where:                      Z(n) = x + yi and C = a + bi
>
>Jonathan

Now *that* was what I was asking!

Thanks.
Andrew.

_________________________________________________________________________
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- -------------------------------------------------------------- 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" ------------------------------ Date: Fri, 13 Apr 2001 22:18:35 EDT From: JimMuth@aol.com Subject: (fractint) C-FOTD 14-04-01 (Squirt II [5]) Classic FOTD -- April 14, 2001 (Rating 5) Fractal visionaries and enthusiasts: Another busy and somewhat frustrating day has ended, to be replaced by a busy and equally frustrating evening. But at least the fractals were working right. Today's FOTD might have been named "Son of the Squirt", or "Return of the Squirt", or "Curse of the Squirt", or even "The Squirt Rises Again". All these names might have happened, but they did not. Instead I named today's image "Squirt II". I gave the fractal this unassuming name because it comes from the same Mandeloid as yesterday's image, though from a far different layer of the hyper-dimensional corkscrew caused by the multi-valued nature of the complex log function. The image, a picture of a rather gaudily colored midget in a valley of the Z^(sqrt2)+C figure, is as unassuming as its name. Because of several flaws, I could rate the image no higher than an average 5, but it's still an interesting view of things that exist in the unexplored depths of the Squirt fractal. The parameter file takes over 24 minutes to run on a 200mhz Pentium. All but the most hardy fractaliers will choose to download the GIF image file from Paul's web site at: or from Scott's site at: The fractal weather today started with a steady rain. But by 11am the rain ended and the sky cleared, leading to a sunny afternoon with a temperature of 77F (25C). The fractal cats found the conditions ideal, and showed their approval by spending the entire afternoon relaxing outdoors. My day was far from ideal, though the day's fractal partly made up for all the other things that went wrong. I'll try to have a better day tomorrow, when I'll also return with the next FOTD. Until then, take care, and perhaps I'll soon tackle the remote parts of the Zexpe (Z^2.71828...) fractal. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Squirt_II { ; time=0:24:48.96--SF5 on a P200 reset=2001 type=formula formulafile=branchct.frm formulaname=MandelbrotBC passes=1 center-mag=-0.72227094168292330/+0.175944088697707\ 90/1.898783e+007/1/-15 params=1.414213562373/0/33/0 float=y maxiter=4200 inside=0 logmap=630 periodicity=10 colors=000huIdsI`nGXjGUfFQbFM`EIXEESC9OC5KB3IB5K98\ M89N8CO7EQ5GR5IS4KU3MX3OY1QZ0S`0Va0Xb0Zd0`e0bh0di0\ fj0hl0jm0ln0np0pq0lm0hi8deI`bRXZ`SViORsKOzOSwRXqV`\ mYdh`hddlZfnVjsQmwMpzGtzCwz7yz3wz5uz7tz8szBqzCnyEm\ xGlwIjtJisMhqNenOdmRbjSaiU`hXYeYXdZVbaU`bSZdRYeSXd\ SVbSUbSSaSRaSQ`SO`SNZSMZSKYSJYSIXSGXSFVSEVSCUSBUS9\ SS8SS7RS5RS4QS3QS1OS0OS0NS0NS0MS0MS0KS0KS0JS0IS0GR\ 0GR0FR0ER0CR0BR09Q09Q08Q07Q05Q04Q03O03O01O00O00O00\ O00O00R00S01U03V35X57Y89ZBB`EEaGFdJIeMKfOMhROiUQjX\ SlZUmaXndYqf`sibtldunfwqhytjzwlzynzzpzymzwjztizqfz\ nezlbziazfZzdYzaVzZSzXRzUOzRNzOKyMJuJGtGFtECtB9s88\ s55s34q01q00q00q00n00m00l00j00h00f00e00d11a31`41Z5\ 3Y75X78U8BS9ERBGQCJNEMMFOKFRJGUGIXFJZEKaCMdBMf9Ni9\ Nl9Nn8Nq8Nt8Nw7Ny7Oz7Qz7Rz5Sz5Uz5Vz4Xz4Yz4Zz3`z3az\ 3bz3dz1ez1fz1fz0fz0fz0fz0fz0fz0fz0fz0fz1fz3fz4fz5f\ z4fz4fz3fz3fz3fz3fz3fz3fz } frm: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|<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" ------------------------------ Date: Sat, 14 Apr 2001 16:11:17 +1200 From: "Morgan L. Owens" Subject: Re: (fractint) Re: C-FOTD 11-04-01 (Veiled Objects [7]) At 05:20 14/04/2001, you wrote: >To all- > >Before I disseminate more misinformation than usual, Dr. Ik's "classnotes" >[his phrase] on "Self-SimilarFractals" are available at the homepage >address provided by PNL in the form of a Mathematica 2.1 Notebook [not >Adobe, as I previously stated], which I did not have the ability to >convert to legible text at the time. Most of them are Postscript documents, there's only the occasional Mathematica file there (and of course "Fractals.ma" is one of them). >When I heard nothing further from Dr. Ikenaga, I (obviously mistakenly) >assumed he knew his own work better than I ever would, gave up the search >for archaic versions of Mathematica software with which to translate his >2.1 Notebook, and took the man at his word. Not that an "archaic version" would have been needed - all subsequent versions of Mathematica are capable of reading and converting pre v.3 notebooks, as can the downloadable MathReader software. >Funny, wonder what the real genesis of the functionals was. Before learning of the Dewedney reference I did a wee bit of a search - "Ikenaga" seemed fairly common, and I came up with a topologist in named Shogo Ikenaga. That looked promising, but I can't read Japanese. There was also a roboticist, who may have been another Bruce - I forget, but that didn't look very likely. Morgan L. Owens. "Most of the pages found were about Fractint's Ikenaga function." - -------------------------------------------------------------- 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" ------------------------------ Date: Sat, 14 Apr 2001 21:04:51 EDT From: JimMuth@aol.com Subject: (fractint) C-FOTD 15-04-01 (Deep in Hyperspace [7]) Classic FOTD -- April 15, 2001 (Rating 7) Fractal visionaries and enthusiasts: I love vast open spaces filled with tiny distant objects, and today's image fits that description perfectly. I named the picture "Deep in Hyperspace", though the scene pictured exists obviously in everyday 3-dimensional space. It still rates a 7 however. The image is one that cries out for truecolor, but that feature is not yet available, at least in Fractint. If and when it does become available, I'll probably re-render this image as well as a batch of earlier images which suffer from the unavoidable bands. Normally, I am not bothered by bands, especially the equal-iteration bands that make a fractal a classic fractal, but occasionally, as in today's image, I would like to have perfect smoothness. I first thought of a name like "Flying Spectacles" for today's FOTD, but that name has no class whatsoever. Then I pictured myself in the vicinity of a very hot star deep in a cloud of dust. The bits and pieces floating in the foreground could only be protoplanets, so I decided on the name "Stellar Nursery". But that name has nothing to do with fractals. After a few more minutes thought, I arrived at the present name, which conveys the surreal feeling of the image quite well. The formula that created the image is number 8 in my series of 12 MandNewt formulae, which are based loosely on the Ikenaga function, the function with apparently no author to claim it. The parameter file renders in 9 minutes, making a download of the GIF file of the image more efficient. The download may be found on the W.W.Web at: and at: The fractal weather today was once again ideal, with sunny skies and a temperature of 70F (21C). The fractal cats however spent little time in the yard due to noisy sidewalk repair work at the house next door. I'm leaving now, but I shall return in 24 hours, more or less. The backlog of work is finally beginning to shrink, so the enlightening philosophy can't be too far off. Until tomorrow, take care, and don't get lost in hyperspace. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Deep_in_Hyperspace { ; time=0:08:56.89--SF5 on a P200 reset=2001 type=formula formulafile=mandnewt.frm formulaname=MandNewt08 passes=1 center-mag=0.0465338/0.0891693/27.49057/1/-82.5 params=2.945/-3.071/3.082/1.704/-3.535/2.935 float=y maxiter=250 inside=bof60 logmap=yes periodicity=0 colors=000zzzy_zx`zw`zv`zu_ztZzsYzrXzqWzpVzoUynTxm\ SwlRvkQujPtiOshNrgMqfLpeKodJncImbHlaGk`Fj_EiZDhYCg\ XBfWAeV9dU8cT7bS6aR5`Q4_P3Z7DH8EG9FFAFFBGEBHECHDDI\ DEJCEJCFKBGLAHLAIM9IN9JN8KO8LP7LP7MQ6MR6MS5MT5MU4M\ V4MW3MX3MY2MZ2M_1M`1Ma0Mb0Mc0Kd3Jd6Ie9HeCGeFEfIDfL\ CgNBgQAgT8hW7hZ6ia5id4if5hd6gb7f`8eZ9dXAcVBbTCaRD`\ PE`OF_MGZKHYIIXGJWEKVCLUAMT8NS6MT4NS5NR5OQ6OP6PO7P\ N7QM8QL8RK9RJ9SIASHATGBTFBUECUDCVCDVBDWAEW9EX8FX7F\ Y6GY5GZ4HZ3H_2I_1I`0J`0J`0Ja0Kb0Lb0Mc0Md0Nd0Oe0Pf0\ Pf0Qg0Rg1Sh1Si1Ti1Uj1Vk1Vk2Wl2Xl2Ym2Yn2Zn3_o3`p3`p\ 3aq3bq3bo9anE`lJ_kOZiTYhYXfbWegVdlVbiTagS`eQ_bPZ`N\ YZMXXKWUJVSITQGSNFRLDQJCPHAOE9NC7MA6L85OA7RC8TEAWG\ BYHC`JEbLFeNHgPIjQJlSLoUMqWOtYPvZQtYPsXPqWOpVOoUNm\ TNlTNkSMiRMhQLfPLeOKdOKbNKaMJ_KJXIIVGIVEHTDITFIUHI\ UJIVMIVOIVPIUQIURITTITUISVISWIRYIRZIQ_IQ`IPaIPcIOd\ IOeINfINhIMiIMjILkIJmJKlI } frm:MandNewt08 {; Jim Muth z=c=(pixel*p1): a=z^p2+(c-1)*z-c b=p3*z^2+c-1 z=z-1*a/b 0.000000000000000000000000000001 <= |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" ------------------------------ Date: Sat, 14 Apr 2001 23:00:30 -0500 From: "Paul N. Lee" Subject: Re: (fractint) C-FOTD 15-04-01 (Deep in Hyperspace [7]) JimMuth@aol.com wrote: > > The bits and pieces floating in the foreground..... > ..... The download may be found on the W.W.Web at: > > and at: > I have noticed over the past week or so, that the images created from Scott's running the "X" version of FractInt does not reproduce the level of detail with which is found in the DOS version. I usually compare the images and there was a considerable difference between several of them, especially on FOTD 13-04-01 "Squirt" (that is until Scott copied over the one from my site). But the latest image, FOTD 15-04-01 "Deep in Hyperspace" will show some of what I am talking about. My question is this, why is there so much variance between the two versions of FractInt all of a sudden?? I don't believe it was this much of a problem several months ago. 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" ------------------------------ Date: Mon, 16 Apr 2001 08:59:28 EDT From: JimMuth@aol.com Subject: (fractint) C-FOTD 16-04-00 (Remotely Mandeloid [3]) Classic FOTD -- April 16, 2001 (Rating 3) Fractal visionaries and enthusiasts: A very busy easter Sunday left little time for fractal activity. I found time only for a quick trip to the classic Mandelbrot set, where, not surprisingly, I found a midget. The midget is located on the north shore of the bud located around -1.31, in a spiral in the third valley of a sub-radical - -- a very remote location -- which is the reason I named the image "Remotely Mandeloid". Since I put next to no effort into the image, settling on the first FOTD candidate that appeared, I can rate it at only a 3. But even at a 3, it's still a midget in the M-set, almost certainly one never before seen. The area of the midget is one of near chaos, though a broad color palette reveals the familiar pattern seen in the shallow parts of valley spirals. With a render time of over 13 minutes on an old Pentium machine, the parameter file tries ones' patience. A faster way of satisfying curiosity is to download the GIF image from Paul's web site at: or from Scott's site at: And this time both sites will display the same rendered image. The fractal weather today was very pleasant most of the day, with clear skies and a temperature of 68F (20C), which lured the cats into the yard. Late in the afternoon however, clouds moved in and a chilly rain set in, cutting the cats' outdoor activities short. I've been thinking much philosophy lately. I simply have no time to write it. But eventually the wisdom or nonsense (depending on one's view of my ideas), will appear. So stay posted for more than I've had to say lately. (We really need to wake up that sleeping philofractal list.) For now it's 8:30am and back to work time. The next FOTD, a return to the MandelbrotMix4 formula, will appear in around 16 hours. Until then, take care, and from simple complex numbers mighty fractals come. Jim Muth jamth@mindspring.com START 20.0 PARAMETER FILE================================== Remotely_Mandeloid { ; time=0:13:39.72--SF5 on a p200 reset=2001 type=mandel passes=1 center-mag=-1.31202873989414700/+0.067685741726728\ 05/5.82079e+010/1/-52.492/-0.004 params=0/0 float=y maxiter=100000 bailout=25 inside=0 logmap=-11450 symmetry=none periodicity=10 colors=000UUgUUgUUhUUiUUjUUkUUlUUmUUnVUoTUpRVqPXrO\ YsM_tK`tIbsHcsIeoIflIgiIifIjcJk`JlYJnVJoSJpPJqMMrO\ OrQQrRTrTVrUXrWZrXasZcs_esagsbjsdlsensgpshoqjooknm\ lnkmnjnmhomfqldrlcslatk_ukYvkXwn_ykWsiSmfOhdKbaGX_\ CSX8MV5HS8FQAEOCDMECJGAHI9FK8DN7BP68R46T34V22X10Z0\ 4b87fGAjNGgNLdNQbNV_N`XNeVNjSNoPNtNNpMPmLRjKTgJUdI\ WaHYZG_WG`TFbQEdNDfKCgHBiEAkB9m89nGAlOBjWChcCgdFfe\ IefLegOdhQciTcjWbkZal`akc`je_ihZhjZglYgoXfqWesWdvV\ cxUczUbzVazV`zV_zVZzVYzVXzVWzVVzVUzVTzVSzVRzVtz4tz\ 4tz4tz4sz6rz7qz9qzApzCozDnzEnzGmzHlzJkzKkzLjzNizOh\ zQhzRgzSfzUezVezXdzYczZbz`bzaazc`zd_ze_zgZzhYzjXzk\ XzlYzjZzh_zf`zdazcbzacz_dzYezWfzVgzThzRizPjzNjzMiz\ LhzKgzKfzJezIdzIczHbzGazG`zF_zEZzEYzDXzCWzCVzBUzAT\ zASz9Rz8Qz8Pz7Oz6Nz6Mz5Lz4Lz4Lz4Lz4Lz4Lz4Lz5Lz5Mz5\ Mz5Mz5Mz5KzUNzRPzOSzLUzJXzIZzH`zGbzFdzEfzDizCkzBmz\ Aoz9qz8sz7tzRuzQuzPuzPuzO } 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" ------------------------------ Date: Mon, 16 Apr 2001 22:07:42 EDT From: JimMuth@aol.com Subject: (fractint) C-FOTD 17-04-01 (Fractal Celebration [5]) Classic FOTD -- April 17, 2001 (Rating 5) Fractal visionaries and enthusiasts: Today was a day of playing catch-up here at Fractal Central. Luckily, the work actually is catching up, and though the end is not quite in sight, it is lurking just around the next corner. While catching up, I somehow managed to find time for one fractal. That image is the one that appears as today's FOTD. It's only a 5-rated image, but still worth the effort of downloading the GIF file from: or from: The iterated formula combines 15 parts of Z^(-1.1) with 1.5 parts of Z^(-13), and then adds 1/C. I named the image "Fractal Celebration" mostly in memory of my recent enjoyment of the festivities of the religious season. The fractal weather today featured cold 48F (9C) air and occasional rain. The cats tried to go outdoors, but when they saw the conditions, their noses were back inside before their tails were out. And now it's time to quickly shutter down the fractal shoppe and call it a night. But I'll return in approximately 24 hours with more fractal things. Until then, take care, and if fractals had never been discovered, I would still have faith in them. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ FractalCelebration { ; time=0:13:04.22--SF5 on a p200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.22981160230094/+1.682986998869586/3.\ 658132e+008/1/-147.5 params=15/-1.1/1.5/-13/0/300 float=y maxiter=1200 inside=0 logmap=172 periodicity=10 colors=000QX`PY_PYYPYXPYVVXT`XSdVSjVQoTPuTPySOzSMz\ SMzPPxMSrLTmIXgFYaD`XAaS7dM6fL3iA0jF0m00o00r00s03v\ 0Dy0Oz0Yz1ao3rz4jnIsyzc`fddzYVuXYxX_zX`zXczXdzXfz_\ aza_zdXzgTyjQxmOvpLssIrvFpyCoz9ixDdvI_sLVrPQpSSlOT\ gLVdIX`FXXCYT9_P4`M1`I0aD0cA0d60d30c10Y0CQ0OG0FG0F\ 40A90DC0FF3II9JMFLPJOSPPVTS__TadVdiYgo_js`lvcmxdoy\ gozipzlrzmszpszruzuvzvvzxpzrlzlgzfaz`YzVTzPOzJJzDF\ z79z14z00z0Dz0Pm0``0mM0y90z00z00m4DVGSCSfzFJzCPyAT\ u9Yp6al4fg3jc0o_0sV0xX1vX4uX7sYArYFpYIp_Lo_Om_Sl`V\ j`Yj``iadgagfajdamdYg_VaVSYQOSMLOIIIDDC9A747104009\ 01C17F4DJ6JM9PPAVSC`XFf_GlaJrfLxiOzlPzoQzi`zdis`ri\ Xz_SzQPzVOzYMz`LzcJzfIyiLvjMslOpmQomSloTipXfpYdr_a\ sa_scXudVvgSviPxjMylLydGr_MjTTcM`XGgPAiI3jA0l30m00\ o10p40r71sA4uD7vGAvJCvMFvPIxSLyVMzYGzSAzO4zJ0zF0zA\ 0z61zMFzaSzrdzzczzczzazxazvazs`zp`zm`zlazlczlczldz\ ldzlfzlfzldziczgazdazc`z` } 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" ------------------------------ Date: Tue, 17 Apr 2001 23:10:15 EDT From: JimMuth@aol.com Subject: (fractint) C-FOTD 18-04-01 (Fractured Fractal [6]) Classic FOTD -- April 18, 2001 (Rating 6) Fractal visionaries and enthusiasts: For today's fractal wonder, we turn once again to the MandelbrotBC formula, which works wonders with Mandeloids of fractional orders. I'll be using this formula often in the days to come, but unfortunately I have lost track of the formula's author. I believe the author is Andrew Coppin, though I'm not sure. Perhaps the author will claim his authorship. I noticed a flurry of mail on the fractal-art list when I opened my virtual mailbox this afternoon. The flap appears to be about another case of fractal thievery. It appears that someone was caught with someone else's fractals on their web page, and might be making money from fractals that are not theirs. Of all the things I have to worry about, copyright infringement is pretty far down the list. Maybe my lack of concern is because I feel that my fractals are not worth stealing. After all, they're only one-layered 256-color images of midgets, in a world of more colors than the eye can distinguish, and multiple layers piled on top of one another. Actually, I simply accept that my images and discussion might be stolen. If they are stolen and used for profit, and I don't know about it, I'll have nothing to get upset about. I have no time to worry about all the things that might be happening that I don't know about. If I find out about blatant profiteering from my work, then I'll know what to do and who to do it to. The mere act of posting something on the internet makes it available to anyone in the world with an online computer. And it's nearly impossible to prevent thievery. It's the artistic quandary. We want as many as possible to admire our work, yet we don't want the admirers to admire it so much that they steal it and make more money from our work than we make ourselves. While I'm trying to think of a solution to this unsolvable problem, I'll draw attention to today's FOTD, which I have named "Fractured Fractal", and which I have rated a respectable 6. The name arises from the fractured nature of the elements surrounding the mis-shapen midget. The iterated expression behind the image is Z^(2.05)+C. I have used the MandelbrotBC formula to draw a remote part of the infinite fractal created by this expression, a part that is quite chaotic and filled with almost-but-not-quite perfect midgets. The attached parameter file is slow -- 20 minutes slow. A download of the GIF image file is fast. I leave it up to the reader to decide which way to go. If they decide to take the download, the image file will be posted shortly to: and to: The fractal weather today was partly cloudy breezy and chilly, with a sunshine shower of small hail just before sunset. The temperature of 46F (8C) permitted the fractal cats only 15 minutes out of doors, leaving them testy. Well, I see it's time to shut down. I'm just starting to get things back into their familiar state of dis-organization, and I want to do a bit more of my style of organizing before I totally run out of steam. Until tomorrow, take care, and exist in peace. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Fractured_Fractal { ; time=0:20:05.34--SF5 on a P200 reset=2001 type=formula formulafile=critical.frm formulaname=MandelbrotBC passes=1 center-mag=+1.35355495637857600/-0.015397043802760\ 70/475604.2/1/-52.499 params=2.05/0/56/0 float=y maxiter=5000 inside=0 logmap=295 periodicity=10 colors=000olLQfJPdJPcIOaIM`GL_GJYFIXFIVDGTDFSCDQCC\ PAAOAAM99L97J76I74G63F64D33D63D73DA3DC3DF1DG1DJ1DL\ 1DO1DP1DS0DT0DX0DY0D`0Da0Dd0Df0Di0Dj0Dm0Do0Dr0Ds0D\ v0Dx0Dz0Fz0Dz0Dy0Cx0Cu0As0Ap09o09l09i07g07d06c06`0\ 4_04X04V03S03P01O01L00J00G00F00C009007004003000000\ 0000000000000000100410630960A70D90GC0ID0LF0MG0PJ0S\ L0TM0XP0YQ0`S0cV1dX1gY1i_1lY1mV1oT7rQFsOMvMTxJ`zId\ zFizDmzArz9vz6vz4vz7rz9ozAvzCzzDzzFzzGzxIzvJzuMzsO\ zrPvpQyoSzlTzjVziXzgYzf`zdavccoadg_f`YgXXiYVj_Tl`S\ oaQpcOrdMsfLugJviIxjGylFzjFzlDzlCylAvmAslArlCplCol\ DmlDllFjjGijIgjJfjLdjMcjOajPajQajSaiQaiPagOagMagJa\ fIafGadFadDadAcc9cc7ca6ca3ca1c`0c`0c_0c_0c_0cY0cY0\ cX0dY0c_0c_0c`0ca0aa0ac0ac0ad0af0`f0`g0`g0`i0_j0_j\ 0_l0_l0_m0Yo0Yo0Yp0Yp0Yr0Xs0as0fu0jv0ov0sx1xx1zy1z\ z3zz3zz3zz3zz4zz4zz4zz6zz6zz6zz7zz7zz7zz7zz7zz9zzA\ zzAzzCzzDzzDzzFzzFzzGzzIz } frm:MandelbrotBC = { ; formula written by ? ? 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" ------------------------------ Date: Wed, 18 Apr 2001 00:08:41 -0500 From: "Paul N. Lee" Subject: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) JimMuth@aol.com wrote: > > ....we turn once again to the MandelbrotBC formula.... > ....but unfortunately I have lost track of the formula's > author. I believe the author is Andrew Coppin, though > I'm not sure. Yes, it was Andrew that first started the conversation on "Branch Cuts" back on April 07, 2000. Within about three to four days, he was able to come up with the following, as quoted from his email: _______________________________________________________________________ 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... _______________________________________________________________________ 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" ------------------------------ Date: Wed, 18 Apr 2001 17:56:35 -0000 From: "Andrew Coppin" Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) Thankyou paul. Yes, it was indeed I who thought of it, and [eventually] came up with the .frm text. It seems only fair to mention that I had help from others on this list thought... (Wish I could remember whom, but I definitly had help!) Thanks. Andrew >From: "Paul N. Lee" >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >CC: philofractal@lists.fractalus.com >Subject: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) >Date: Wed, 18 Apr 2001 00:08:41 -0500 > >JimMuth@aol.com wrote: > > > > ....we turn once again to the MandelbrotBC formula.... > > ....but unfortunately I have lost track of the formula's > > author. I believe the author is Andrew Coppin, though > > I'm not sure. > >Yes, it was Andrew that first started the conversation on "Branch Cuts" >back on April 07, 2000. Within about three to four days, he was able to >come up with the following, as quoted from his email: > >_______________________________________________________________________ > > >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... > > >_______________________________________________________________________ > > >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" _________________________________________________________________________ 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" ------------------------------ Date: Wed, 18 Apr 2001 16:33:04 -0400 From: "Zorba the Hutt" Subject: (fractint) The specter of schoolwork, and really really big fractals Finally I managed to beat down the looming demon of Far Too Much Homework That You've Been Putting Off, You Slacker, And Why Are We Paying For You To Go To College Anyway If All You Do Is Play Computer Games? I Mean, It's Not Like The Ones You Play Are Educational Or Anything, and managed to eke out some time for myself, which I spent updating my Really Big Fractals page. Today (this week? this month? this year?), I provide for you all those Fractal-Swarm-inspired images that Sylvie Gallet posted a while back. Yes, all of them. All 9. Done in beautiful 1600x1280, and do they ever look good. And, sigh, I really should have asked *before* this, but if I ask, wait for an answer, and *then* post 'em, I'll never get around to it. Sylvie, do you mind if I put those up? They're all credited to you and everything :) I just wanted to provide them for people who might not have the CPU power (or desire) to render them on their own. If you say you do mind, I'll take 'em off immediately, or if there's modifications you want me to make or anything. Anyway, the website is http://www.geocities.com/zorbathut - may you find a new desktop wallpaper . . . - -Zorba - -------------------------------------------------------------- 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" ------------------------------ Date: Wed, 18 Apr 2001 15:53:44 -0500 From: Programmer Dude Subject: Re: (fractint) The specter of schoolwork, and really really big fractals Zorba the Hutt wrote: > ...which I spent updating my Really Big Fractals page. Cool! Wonderful!! Delightful!!! Thanks! p.s. Unexpected Fractal's link is ge-broken. ;-( - -- |_ CJSonnack _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________| - -------------------------------------------------------------- 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" ------------------------------ Date: Wed, 18 Apr 2001 17:43:56 -0400 From: Sylvie Gallet Subject: (fractint) The specter of schoolwork, and really really big fractals Hi Zorba, >> And, sigh, I really should have asked *before* this, but if I ask, wai= t >> for an answer, and *then* post 'em, I'll never get around to it. Sylvi= e, >> do you mind if I put those up? They're all credited to you and >> everything :) I just wanted to provide them for people who might not >> have the CPU power (or desire) to render them on their own. If you say= >> you do mind, I'll take 'em off immediately, or if there's modification= s >> you want me to make or anything. I am not favorable to making high resolution images available on the we= b, and I would definitely have preferred you to ask before doing it. Since = I have a slow internet connection, I haven't downloaded any of them, but th= e size of some of the PNGs make me think that anti-aliasing made some of th= em lose their particular texture (at least two of them: 18 and 27). I'll make an exception and let you keep them but please, change the copyright notice so that it makes clear people are not allowed to print them, put them on a web site, etc. Best regards, - 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" ------------------------------ Date: Thu, 19 Apr 2001 00:16:05 -0500 From: "Paul N. Lee" Subject: Re: (fractint) Re: C-FOTD 18-04-01 (Fractured Fractal [6]) Andrew Coppin wrote: > > Thankyou paul. Just thought credit should be mentioned where due. :-) > > It seems only fair to mention that I had > help from others on this list thought... > (Wish I could remember whom, but I definitly > had help!) You first started discussing the "Branch Cuts" on Fri, 07 Apr 2000. And some of the individuals involved with that topic on the List were as follows: Barry N. Merenoff (Collin Merenoff) Morgan L. Owens Tim Wegner Jim Muth Kenneth Childress Damien M. Jones This went on until Tue, 18 Apr 2000. I am sure that the archives will show the details of who did what. 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" ------------------------------ End of fractint-digest V1 #551 ******************************