February 2005 - Fractint - mailman.xmission.com

FOTD 05-02-05 (Fractal Thomas [5])
by Jim Muth 05 Feb '05

05 Feb '05

FOTD -- February 05, 2005 (Rating 5) Fractal visionaries and enthusiasts: I was doing a bit of casual exploring in the fourth dimension yesterday, when I suddenly saw on the screen the face of Thomas, one of the fractal cats, peering out at me. It immediately reminded me of the way Thomas actually peers from the bushes before coming into the open to check that everything is in order and no danger is about. The name "Fractal Thomas" came to mind almost at once. The actual scene is a view of the Seahorse Valley of a tiny midget deep in East Valley of the large midget on the main stem of the classic Mandelbrot set. Yes, I realize that it looks nothing at all like either a Seahorse Valley or an East Valley. This is because the image is oriented in one of the oblique directions through the four-dimensional Julibrot. The resemblance to one of the fractal cats is striking enough, but I have seen such images many times, and could rate today's image no higher than an average 5. This is not to say that Thomas is an average cat. Quite the contrary. He is tied with Tippy for number one cat in the world. It is just that today's representation of him does not do him justice. Only a real photograph could do that, and even then it would be difficult to capture his full personality. Speaking of photographs, I still am planning on getting a brand- new digital electronic camera to replace my old film-loaded Pentax that stopped working sometime during the 15 or so years that have passed since I found fractals and stopped using it. The fractal cats will not be around forever, and I would like to have some pictures of them before they go where good cats go. Taking their pictures seems such a simple thing, and there appears to be so much time in which to do it, that I never get motivated to go out shopping for a digital camera. This is curious, for I really enjoy photography. At one time I was an avid photographer who did my own black-and-white as well as color darkroom work. I was most interested in infrared and ultraviolet photography, which showed the familiar everyday surroundings in a new light. Using infrared film, I even caught some pictures of the things that ghost hunters now call orbs -- moving balls of light that are sometimes photographed in locations said to be haunted by ghosts. At the time I thought the spots on the film were flaws in the film or specks of dust floating very near the lens. I am far from convinced that I caught glimpses of an unknown energy on film, but I have never understood why such spots appeared only in the infrared photo- graphs and on so many different batches and brands of infrared film. Well, I see that we are again wandering from the topic, which is fractals and not photographic oddities, so it's time to remind everyone that seven minutes may be saved if today's fractal is downloaded from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday brought little sun, but the temperature reached 46F 8C, which was just into the comfort range of the dynamic cats. They spent several hours in the yard, peeping from the bushes much as we see Thomas doing in today's image. When evening arrived, they came indoors ready to settle down without complaint. I gave them their regular treat of tuna to be sure they didn't complain. Today is starting warmer with full sun. The duo should have another fine day. For me, the work is mostly caught up. A few minor chores remain, but they can be done in less than an hour. Then it will be time for fractals and philosophy. The next fractal will appear in 24 hours; the next chapter of philosophy will take a day or two longer. Until tomorrow's FOTD, take care, and isn't it wonderful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fractal_Thomas { ; time=0:07:40.28--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=0/0/1.975315e+008/6.144e-006 params=90/6.22/2/0/0/0/-1.749699879151/0 float=y maxiter=50000 inside=0 logmap=380 symmetry=yaxis periodicity=10 colors=000NVINVKOVLOVNOVPPVRPVSQVUQVWRVYRVZRV`SVbS\ VdTVeTVgUViUVkUVlPUgKUbFTYATT4VM5TO5RQ5PR5NT5LU5JW\ 5HX6IW7IV8IU9ITAISBIRBIQCJPDJOEJNFJMGJLHJKFKGHJKJI\ NLIRNHUOHXQG`eMcaR_ZXWVbSRgONmKKrGbpVunitmjsmjsmkr\ mkrmlqmlqmmpmmomnomnnmonmommpmmplmqlmqkjrkhrjerjcr\ jasiZsiXsiVshSthQtgNtgLtgJufGufEufCugFsgHrgJqhLphN\ ohPmhRliTkiVjiXiiZgj`fjbejddjfciibhlbgnbgqbfsbevbe\ xbawWZvQWuJTtDQtIOkMM_QKbUIYYFUbDPfBLj9Gn7CrCoVDdW\ GsZEqXDoWBnUAlTQIKSNJVLJXPI_RIaRHdVHfVGfVHhVGjYGlY\ FmYFoYEq`Er`Es_EscEscEsaEscEscEscEtcEscEvcDvcEscEp\ cEo`EjYEgVEdUEaQFZKFWPFTIFQBFN8FK5F13B9ADHGFPMHXSJ\ dYLecOhcRncNtcIzcBycExcGwcIvcKtcMscOraQq_SoYUnWWnU\ ZmS`kQbjOdiMfhMhgMjfMleMndMpPG`dMrcOqcQpbSpbUobWoa\ YnaZna`m`bm`dl`fk_hk_jj_kjZmiZoi_qhashcugeylgvgisc\ kp_mmWokSqhOseKubGw_CxY8yX9zz9zz9zzAzzAzzAzzBzzBzz\ BzzCzzCzzCzzbzzPzzCzzEzzG } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 04-02-05 (The Drunkard's Walk [5])
by Fr. Jim Lacasse 04 Feb '05

04 Feb '05

Fractint fellows, I continue to get bounce messages and also the FOTD. I'm confused. Can one of you provide me with the name and address of the owner so I can email him directly. Thank you. Fr. Jim P.S. When I display some of Jim's work my Geometry students always enjoy them. >>> jamth(a)mindspring.com 02/04/05 06:53AM >>> FOTD -- February 04, 2005 (Rating 5) Fractal visionaries and enthusiasts: With today's image we return to the MandelbrotMix4 formula and the unlimited goodies therein. We examine the fractal that results when negative Z^1.5 is combined with Z^0.5 and straight C is added. This fractal is shaped much like a classic M-set that has been rotated 180 degrees, with the main exception being the area of East Valley, which is now on the west side of the main bay. Instead of jutting sharply into the bay, the valley has degenerated into a large area of chaos that extends some distance inland. This chaotic area is filled with quadratic- shaped midgets, one of which appears at the center of today's image. I named the image "The Drunkard's Walk". The midget at the center is surrounded by radiating filaments that remind me of a path a very tipsy drunkard might take when he leaves the bar and starts taking steps in random directions as he begins his walk hopefully toward home. This random path appears quite often in nature and is known to mathematicians as the drunkard's walk. A drunkard could never be expected to produce a worthy fractal simply by taking steps in random directions, but today's image rates a 5, and lesser images have made it to the lofty heights of Fractal of the Day. Our drunkard finally made it home, and does not appear in the image. The path he took on his trip is still visible however, and may be seen by running the included parameter file or by downloading the GIF image in completed form from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The latest chapter of philosophical musing appears in the philofractal version of today's FOTD discussion. Thursday failed to live up to its promise here at Fractal Central, as an unexpected wet snow began at 2:30pm and cut short the cats' time in the yard. Extra tuna was needed to ease their frustration. Today is again starting partly cloudy and mild. Hopefully, the day will turn out better than yesterday. For me it looks like a rather slow day coming up. This could mean a great fractal for tomorrow, or it could mean a lazy day for me. Regardless, the next FOTD will appear right here in 24 hours. Until then, take care, but don't forget the fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Drunkards_Walk { ; time=0:02:50.93--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident center-mag=-0.86634515270768200/+0.265248736118700\ 60/1.378352e+009/1/-92.4997801961145996/-0.0003971\ 32291258053827 params=1/0.5/-1/1.5/0/0 float=y maxiter=500 inside=0 logmap=69 periodicity=10 colors=0004SP1QQ4PQ7OQAMPDLPFJOIGOLDMO9MS4LX1LaCIg\ MGfXKjfQomUsuYxzcszcpzZlxUiuPdpKalFYfDVaDQXFOSFLPF\ QTIX_JadMgjOmpPooMpmLrlJsjGsiFugDvfAxd9xc7vd4vf3vg\ 1vi0vj0vl0vm0vo0vp0vr0xs0yu0yv0zx0zy0zy0zz0zz0zz0z\ z0zz0yz0ux1ou6jr9foCYiLPdSI__9Vg1Po0Lv0Gz0Iz0Jz4Lz\ ALyGMxMOxSPvYPucQuiSsoTruTrfJoSAlD0i00gC7SMMCPPGQS\ JSVOTYQV`VXcYYfa_id`liaolcpodmmflmgiligljdllcjm`jm\ _joYipVirTgsQguPgvMfxLfxJfuIirGloGomFpjDsgDvfCxcAz\ `AzY9zX7zT7zQ6zP6zO9zMCzLFvJIoILiGOcFQXDTQCXLA_D9a\ 79c1QY7dODgSCiVAj_Ala9md7oi7rl6sp6us4vv3xz3yz1zz1s\ z7lzDdzJYzPSyVLx`Dvf6ul0sp0lv9sxPzxdzxuzxozyiuzcjz\ Y`zTSzOIzI7zC0z70zG0yPAsYLmdVgmfavpXzzQzzLzzMzzOzz\ PzzQzzSzzTzzVzzXzzYzz_zz`zz`uzamzcfzd`zfTzgMzgFzi9\ zj1zl0zm0zm0zf4z`DzVLzPTzI`zCiz6pz0xz0Xz74zL7zI9zF\ AzDDzAFz7Gz6Iz3Lz0Mz0Oz0Qz0Sz0Tz0Vz0Yz0`z0cz0fz1gz\ 4jz7mzCpzFrzIuzMxzPCzT7zT } 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 PARAMETER FILE========================================= _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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FOTD 04-02-05 (The Drunkard's Walk [5])
by Jim Muth 04 Feb '05

04 Feb '05

FOTD -- February 04, 2005 (Rating 5) Fractal visionaries and enthusiasts: With today's image we return to the MandelbrotMix4 formula and the unlimited goodies therein. We examine the fractal that results when negative Z^1.5 is combined with Z^0.5 and straight C is added. This fractal is shaped much like a classic M-set that has been rotated 180 degrees, with the main exception being the area of East Valley, which is now on the west side of the main bay. Instead of jutting sharply into the bay, the valley has degenerated into a large area of chaos that extends some distance inland. This chaotic area is filled with quadratic- shaped midgets, one of which appears at the center of today's image. I named the image "The Drunkard's Walk". The midget at the center is surrounded by radiating filaments that remind me of a path a very tipsy drunkard might take when he leaves the bar and starts taking steps in random directions as he begins his walk hopefully toward home. This random path appears quite often in nature and is known to mathematicians as the drunkard's walk. A drunkard could never be expected to produce a worthy fractal simply by taking steps in random directions, but today's image rates a 5, and lesser images have made it to the lofty heights of Fractal of the Day. Our drunkard finally made it home, and does not appear in the image. The path he took on his trip is still visible however, and may be seen by running the included parameter file or by downloading the GIF image in completed form from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The latest chapter of philosophical musing appears in the philofractal version of today's FOTD discussion. Thursday failed to live up to its promise here at Fractal Central, as an unexpected wet snow began at 2:30pm and cut short the cats' time in the yard. Extra tuna was needed to ease their frustration. Today is again starting partly cloudy and mild. Hopefully, the day will turn out better than yesterday. For me it looks like a rather slow day coming up. This could mean a great fractal for tomorrow, or it could mean a lazy day for me. Regardless, the next FOTD will appear right here in 24 hours. Until then, take care, but don't forget the fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Drunkards_Walk { ; time=0:02:50.93--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident center-mag=-0.86634515270768200/+0.265248736118700\ 60/1.378352e+009/1/-92.4997801961145996/-0.0003971\ 32291258053827 params=1/0.5/-1/1.5/0/0 float=y maxiter=500 inside=0 logmap=69 periodicity=10 colors=0004SP1QQ4PQ7OQAMPDLPFJOIGOLDMO9MS4LX1LaCIg\ MGfXKjfQomUsuYxzcszcpzZlxUiuPdpKalFYfDVaDQXFOSFLPF\ QTIX_JadMgjOmpPooMpmLrlJsjGsiFugDvfAxd9xc7vd4vf3vg\ 1vi0vj0vl0vm0vo0vp0vr0xs0yu0yv0zx0zy0zy0zz0zz0zz0z\ z0zz0yz0ux1ou6jr9foCYiLPdSI__9Vg1Po0Lv0Gz0Iz0Jz4Lz\ ALyGMxMOxSPvYPucQuiSsoTruTrfJoSAlD0i00gC7SMMCPPGQS\ JSVOTYQV`VXcYYfa_id`liaolcpodmmflmgiligljdllcjm`jm\ _joYipVirTgsQguPgvMfxLfxJfuIirGloGomFpjDsgDvfCxcAz\ `AzY9zX7zT7zQ6zP6zO9zMCzLFvJIoILiGOcFQXDTQCXLA_D9a\ 79c1QY7dODgSCiVAj_Ala9md7oi7rl6sp6us4vv3xz3yz1zz1s\ z7lzDdzJYzPSyVLx`Dvf6ul0sp0lv9sxPzxdzxuzxozyiuzcjz\ Y`zTSzOIzI7zC0z70zG0yPAsYLmdVgmfavpXzzQzzLzzMzzOzz\ PzzQzzSzzTzzVzzXzzYzz_zz`zz`uzamzcfzd`zfTzgMzgFzi9\ zj1zl0zm0zm0zf4z`DzVLzPTzI`zCiz6pz0xz0Xz74zL7zI9zF\ AzDDzAFz7Gz6Iz3Lz0Mz0Oz0Qz0Sz0Tz0Vz0Yz0`z0cz0fz1gz\ 4jz7mzCpzFrzIuzMxzPCzT7zT } 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 PARAMETER FILE=========================================

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FOTD 03-02-05 (Final Beast [4])
by Jim Muth 03 Feb '05

03 Feb '05

FOTD -- February 03, 2005 (Rating 4) Fractal visionaries and enthusiasts: Today's image gives us one last, and perhaps one too many glimpses of the fractal beast. We have now distorted the beast almost beyond recognition. The colors are still the same, but even with the aid of the colors, the spirals and converging arms are nearly impossible to pick out. There are only spirals that try to get started but never quite succeed, and arms that set out promisingly, but lead nowhere. Because the center of rotation of all the 'Beast' images lies in the open area at the center of the original Mandelbrot midget, the hole that once appeared as that midget is still in the picture. It has been stretched beyond recognition however, and now exists as a narrow slit in the bottom-center part of the frame. Curiously enough, this slit still retains some of its original Mandelbrot character, needing only some stretching in the right direction to return it to its recognizable, though somewhat warped, Mandelbrot shape. The rating of a humble 4 is all I could do for the image. Actually, I expected better things from the beast when I started the series. I guess my disappointment shows. The name "Final Beast" is a simple statement that after today we shall see no more of this beast. Th render time of under 2 minutes on my machine is the fastest of the 'Beast' series. But for the convenience of those who dislike hunting and rendering, the beast has been captured and caged, and is being kept on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> from where it may be safely downloaded. No philosophy is ready today, but the next batch should be included in the philofractal version of tomorrow's FOTD. A nearly perfect mid-winter day here at the Fractal Central on Wednesday made for near perfect fractal cats. With warm sun, a temperature of 41F 4C, and melted snow waiting for them, the duo enjoyed several peaceful hours in the yard. Even the crows that raided a neighbor's trash can failed to disturb the dynamic duo. In the evening I gave them their tuna treat just to make the day perfect. Today is starting cloudy, but it is milder and no more snow is expected. The cats' day will likely be another good one. For me, the work is moderate. I should be finished by early afternoon, leaving me plenty of time to shape up the latest installment of philosophy, which, unless something unexpected goes wrong, will appear in 24 hours. Until then, take care, and just wait. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Final_Beast { ; time=0:01:56.06--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 center-mag=-0.000046448\ 18451324/-0.00001890775131802/337663.9/0.01552/\ 158.981743903266619/85.1656595908049638 float=y params=51.916/-157.216/-82.429/166.391/0.288136932\ 805/0.482645405409/0.288136932805/0.482645405409 maxiter=5000 inside=0 logmap=288 periodicity=10 colors=000SYrSXrSWqSVpSUoSTnSSmSQlTOkUMjVKiWIhXGgY\ Ef_CeaAdcAceAbgAaiA`kC_mEZoGYqIXrKWsMTrOSqQRpSQpUP\ oWOnXNnYMmZLl_KlaJkcIjeHjgHkhGkgFlfEldDmbCm`BnZAnX\ 9kV8hT8eR8bP7_N7XL7UJ6RH6OF6LD5IB5FC5CC49D46D43D45\ E57F59G6AH6CI6EJ7FK7HL8JM8KN8MO9OP9QQARRATSAVTBWUB\ YVC_WC`XCaYEbZGbZHc_Jd`Kd`MeaNebPfbQgcSgdThdVheWif\ YjgZjh`kiakjclkdmlfmlgmmimminmjomjpmjqnjrojtpjuqjv\ rjwsjxtlxujwtivshurgtqftpdsocrmbqlapk`oj_oiYnhXmgW\ lfVkdUjcTjbRiaQh`Pg_OfZNfYMgXKgVJgUHhTGhREhQDiPBiN\ AiM8jK7jJ5jI4kG2kF1kE0gH1dJ1aM2ZO2WR3TT3QY4Na4Kf5U\ o5cs2mz5mz8mzBhtEcrHZqKUoNPnQLmTMkWNjZOiaPidQhgRhj\ SgmTgpShsTgrTfrTfqTeqUepUbpU_pUZoUUoVTnVTnVSnVSmVR\ mWRnWQoWQpWPqWPsXOuXOwXNxXNzXMzYMzYLzYLzYKzYKzVOzS\ SzQWzN_zLczPgzUkzZozcszhvzmuzmwzmvzmvzmuzmuzmtzmtz\ mszmszmrzmrzmrzmqzmqzmpzmpzmozmozmnzmnzmmzmmzmmzml\ zmlzmkzmkzmjzmjzmizmizmiz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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multifractal!
by david lowenstein 02 Feb '05

02 Feb '05

thank you! I didn't see much pictures of multifractals before! -david ----- Original Message ----- From: <fractint-request(a)mailman.xmission.com> To: <fractint(a)mailman.xmission.com> Sent: Wednesday, February 02, 2005 6:53 AM Subject: Fractint Digest, Vol 24, Issue 2 > Send Fractint mailing list submissions to > fractint(a)mailman.xmission.com > > To subscribe or unsubscribe via the World Wide Web, visit > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > or, via email, send a message with subject or body 'help' to > fractint-request(a)mailman.xmission.com > > You can reach the person managing the list at > fractint-owner(a)mailman.xmission.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of Fractint digest..." > > > Today's Topics: > > 1. Fractint_Multifractal (Albrecht Niekamp) > 2. FOTD 02-02-05 (Triple Beast [5]) (Jim Muth) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Wed, 2 Feb 2005 05:00:50 +0100 > From: Albrecht.Niekamp(a)t-online.de (Albrecht Niekamp) > Subject: [Fractint] Fractint_Multifractal > To: <Fractint(a)mailman.xmission.com> > Message-ID: <002301c508db$c9256ba0$78b4fed9@homerwq09jetk> > Content-Type: text/plain; charset="iso-8859-1" > > Hi, > > IÂ´m back again. > There are several reasons. The first one is that I managed > to boot Windoze98 as additional OS. As you know this OS > has a perfect DOS support and allows switching between DOS and > windows vv. Also I like it because it is compact and easy to handle. > All the hardware, AGP, USB, DVD, Firewire etc is there. > For Fractint I use an ancient Nvidia G-force 4 video card which has > full Vesa support, also 1600/1200. > The second reason is that I have some ideas how to improve and > complete my multifractal formula. > There is another one not mentioned today. > > In my email archive dated July19 I found a request by David > Lowenstein asking for multifractals composed of different fractals > at the same time. Maybe this is an answer, although possibly not > the one you expected. > > Multifractal_10 composes images using max 5 different formulas > simultaneously. There are 9 frms to choose from. There are five > "channels": basic shape, outside and inside 1-3.The transitions > are controlled by an iteration counter or by border (z) values, > in and out (bigger or smaller), or iteration and border > simultaneously. > At the transition points optional resets are provided, either of the > iteration counter or the z-value (or both), which affect the coloring > and further iteration. > Five different bailout values can be applied, ranging from 1 to > one million. The effect is compression or expansion of the colours. > > A unique programmable "warp-effect" can be applied to each channel. > It changes the behaviour and looks of the channels, pending on > previous iterations, a choosable function and a "warp" factor. Maybe > this just means a distortion, maybe a 3d effect. > > Sylvie GalletÂ´s lake effect is optional, fully integrated and > works with all formulas, inside3 is shut off if activated. > > There now is a second basic "Double mandel" which allows the creation > of "mandscapes", 2 samples with different insides, symmetric or > asymmetric are provided. > > The par-files are demos for the contributing formulas to give you > an impression about their looks, mostly with activated lake effect. > "Pandemonium" is a basic image with lots of zooming spots. I gave it > that name because so many different structures are hidden somewhere. > > "Debugflag=322" must be deactivated. Please check your SS-tools.ini. > > Any questions are welcome, of course. > > Attached is a printable wordpad file which is handy if you should > want to compose your own image. If it does not get through, please > paste the following part to an editor, using size9 to make it small > enough for one sheet of paper. > > Sincerely, Al. > ---------------------------------------------------------------------------- > - > > Multifractal_10 Inputs > > > Real P2 > First Input (before the dot) > 5 Digits : Channels : 1_Basic Shape 2_Outside 3_Inside1 4_Inside2 > Inside3 > Frms: 1_Secant 2_Mandel(2) 3_Bees 4_Julia 5_Many Mods 6_Phoenix > 7_Newton 8_Spider > Second Input (after the dot) > 2 Digits_Many Mods_Number of sides 2 Digits_Phoenix 2 Digits_Spider > 1 Digit_Reset on Transitions (Shape) 0_no 1_Dble Mandel 2_Iter-reset > 3_both +5_warp > 4 Digits_Reset Channels 2-5 0_no 1_z-reset 2_Iter-reset 3_both > +5_warp > > Imag P2 > First Input > 5 Digits_Colour (Bailout) Number for each channel (5 available) > Second Input > Variables : 4 Digits_Mand/Jul (2 var) 2 Digits_Secant 4 Digits_Bees > > Real P3 > First Input > 2 Digits_Newtonvariable 4 Digits_Colour1 > Second Input > 5 Digits_Colour2 5 Digits_Colour3 > > Imag P3 > First Input > Basic Shape : Warp-factor (fn1 is used) > Second Input > 5 Digits_Colour4 6 Digits_Colour5 > > Real P4 > First Input > Outside : Warp-factor (fn2 is used) > Second Input > Outside : 4 Digits+1fractal digit_Border-out 4 Digits+1 > fractaldigit_Border-in > > Imag P4 > First Input > Inside1_Maxiter > Second Input > Inside1 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin > +5_maxiter+border > 5 Digits_warp factor (fn2 is used) 4 Digits+1 > fractaldigit_border1 > > Real P5 > First Input > Inside2_Maxiter > Second Input > Inside2 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin > +5_maxiter+border > 5 Digits_warp factor (fn3 is used) 4 Digits+1 > fractaldigit_border2 > > Imag P5 > First Input > Inside3_Maxiter > Second Input > Inside3 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin > +5_maxiter+border > 5 Digits_Warp factor (fn4 is used) 4 Digits+1 fractal > digit_border3 > Alternate Input Imag P5 > First Input : 1_Lake effect enabled (Inside3 disabled) > Second Input : 2 Digits_Frequency 2 Digits_Waterlevel 2 > Digits_Amplitude > > > ------------------------start-pars----------------------------------------- > > Secant_basic { ; Lake effect active > ; Time 0.42.00.86 > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_10 function=sin/sin/exp/sin passes=t > center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 > params=-0.05825983458967864/0.3785210730307932/10000.32595700022/55234.0\ > 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ > 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter > outside=tdis logmap=4 periodicity=0 rseed=-2436 > colors=200A85<17>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ > 0s00<3>z00<25>C00A00800<3>000<12>NNNPPPQQQ<8>fffgggiiijjjlll<3>sss<25>BB\ > B999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<2>864 > } > > Bees_Basic { ; Lake effect active > ; Time 0.09.10.85 > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_10 function=sin/sin/exp/sin passes=t > center-mag=1.00827/0.00308737/0.6630435/1/-90/3.88578058618804789e-016 > params=-0.05825983458967864/0.3785210730307932/30000.32595700022/35234.0\ > 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ > 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter > outside=tdis logmap=4 periodicity=0 rseed=-2436 > colors=200A85<17>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ > 0s00<3>z00<25>C00A00800<3>000<23>fffgggiiijjjlll<3>sss<25>BBB999777<2>22\ > 2000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<2>864 > } > > Julia_Basic { ; Lake effect active > ; Time 0.31.26.42 > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_10 function=sin/sin/exp/sin passes=t > center-mag=0.0659115/0.0324086/1.087898/1.0222/90/3.88578058618804789e-0\ > 16 > params=-0.05825983458967864/0.3785210730307932/40000.32595700022/25234.0\ > 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ > 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter > outside=tdis logmap=4 periodicity=0 rseed=-2436 > colors=000047049<5>0BL0DN0DP<4>0KZ0L`0Mb0Nd0Of0Qh<3>0Up4Yr8atCgvGkxKqz<3\ > >4_s0Vq0Uo<12>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R0LT0NV0PX0P<3>\ > d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y0SW0RU0O<5>I0F\ > G0EE0CC0A<3>304102010<4>0B10D10F10H20J20L20N2<2>0T40V40X3<3>0d40f50h5<3>\ > 0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>\ > 0000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_\ > Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<5>121000\ > 001023025 > } > > Phoenix_basic { ; Lake effect enabled > ; Time 0.19.25.24 > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_10 function=exp/sin/exp/sin passes=t > center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 > params=-0.05825983458967864/0.3785210730307932/60000.32565700023/25234.0\ > 506030602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ > 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter logmap=5 > periodicity=0 rseed=-2436 > colors=200432<20>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ > 0s00<3>z00<25>C00A00800<3>000<7>FFFHHHJJJ<9>___aaaccc<3>iiijjjlll<3>sss<\ > 25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211 > } > Newton_Basic { ; Lake effect active > reset=2004 type=formula formulafile=mfr9n.frm > formulaname=multifractal_10 function=exp/sin/exp/sin passes=t > center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 > params=-0.05825983458967864/0.3785210730307932/70000.32595700023/55234.0\ > 506030602/152048.0404808048/384.1604894048/384.00482000595/256.1007683/5\ > 12.1007683001/1.244062 float=y maxiter=1024 inside=maxiter > outside=tdis logmap=2 periodicity=0 rseed=-2436 > colors=200432<20>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ > 0s00<3>z00<25>C00A00800<3>000<9>IIIKKKLLL<9>bbbdddfffgggiiijjj<3>qqqsssq\ > qq<24>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211 > } > > Spider_Basic { ; Lake effect active > ; Time 0.09.42.76 > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_10 function=exp/sin/exp/sin passes=t > center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 > params=-0.05825983458967864/0.3785210730307932/80000.32595700023/25234.0\ > 506030602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ > 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter > outside=tdis logmap=4 periodicity=0 rseed=-2436 > colors=2000NU<8>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7\ > A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<11>LLLNNNPPPQQQSSS\ > UUU<6>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<\ > 15>0OW > } > Many_mods_basic { ; Lake effect active > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_10 function=sin/sin/exp/sin passes=t > center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 > params=-0.05825983458967864/0.3785210730307932/50000.16595700022/55234.0\ > 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ > 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter > outside=tdis logmap=yes periodicity=0 rseed=-2436 > colors=20009C<19>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3\ > >unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ > 0<23>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<3>07A > } > Pandemonium { ; Time 0.21.15.48 > ; > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_10 function=sin/exp/exp/sin passes=t > center-mag=-0.489028/0/0.6666667 > params=-0.05825983458967864/0.3785210730307932/21225.64595718025/21235.0\ > 311030602/150056.0204808192/384.32768524288/384.00482000595/256.10076830\ > 01/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter > outside=tdis periodicity=0 rseed=-2436 > colors=2000gt<22>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB\ > 7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>fffgggiiijjjll\ > l<3>sss<25>BBB999777<2>222000012<22>0_k0am0bo0cq<4>0kz0jx0hv > } > Mandscape2 { ; asymmetrical inside > ; Time 0.14.07.06 > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_10 function=exp/exp/exp/sin passes=t > center-mag=-0.504822/4.44089e-016/0.9463538 > params=-0.05825983458967864/0.3785210730307932/20227.32595710661/25255.1\ > 111020602/151024.0204808192/384.32768524288/384.00482000595/128.10076800\ > 01/512.10076800005/768.10076800002 float=y maxiter=1024 > inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 > colors=000376<2>121000001023025047049<5>0BL0DN0DP<4>0KZ0L`0Mb0Nd0Of0Qh<3\ > >0Up4Yr8atCgvGkxKqz<3>4_s0Vq0Uo<12>0FQ0DO0DM<3>08E06C06A0480460240120001\ > 00<12>R0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_\ > e0Z<3>Y0SW0RU0O<5>I0FG0EE0CC0A<3>304102010<4>0B10D10F10H20J20L20N2<2>0T4\ > 0V40X3<3>0d40f50h5<3>0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>\ > 0I20G20E20C20A1081<3>0000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM\ > <3>DdTDfVEhWFjYFlYGn_Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK\ > <3>7KE6IC5GB5DA4B9497 > } > > Mandscape1 { ; symmetrical inside > ; Time 0.14.02.12 > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_10 function=exp/exp/exp/exp passes=t > center-mag=-0.504822/-3.9968e-015/1.1027/0.8582 > params=-0.05825983458967864/0.3785210730307932/20222.32595710666/25234.1\ > 111020602/151024.0204808192/384.32768524288/384.00482000595/128.10076800\ > 01/384.10076800005/512.10076800002 float=y maxiter=1024 > inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 > colors=200A85<17>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ > 0s00<3>z00<25>C00A00800<3>000<23>fffgggiiijjjlll<3>sss<25>BBB999777<2>22\ > 2000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<2>864 > } > Lite_Zoom { ; Different outside > ; Time 1.51.37.67 > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_10 function=sin/exp/exp/sin passes=t > center-mag=-1.50466/1.66533e-016/4.219409/1/-90/3.88578058618804789e-016 > params=-0.05825983458967864/0.3785210730307932/21225.64595767025/13234.0\ > 311030602/151024.0204808192/384.32768524288/384.00482000595/256.10076830\ > 01/512.1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter > outside=tdis periodicity=0 rseed=-2436 > colors=2000LS<11>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3\ > >unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ > 0<11>LLLNNNPPPQQQSSSUUU<6>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012\ > <11>0JQ > } > > Multimix { ; Lite zoom > ; Time 3.23.44.07 > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_9 function=sin/exp/exp/sin passes=t > center-mag=-1.22699/8.32667e-017/13.33333/1/90/3.88578058618804789e-016 > params=-0.05825983458967864/0.3785210730307932/21225.64595718025/23434.4\ > 911030602/152048.0409608192/384.3276898304/384.00482000595/256.100768300\ > 1/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter > outside=tdis periodicity=0 rseed=-2436 > colors=2000KQ<6>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7\ > A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<9>IIIKKKLLL<9>bbbd\ > ddfffgggiiijjj<3>qqqsssqqq<24>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<1\ > 7>0LS > } > Hades { ; The gate to the underworld > ; Time 2.09.12.02 > reset=2004 type=formula formulafile=mfr10.frm > formulaname=multifractal_10 function=cos/sin/sin/sin passes=t > center-mag=-0.188053/0.00113846/24.61324/1/-90/3.88578058618804789e-016 > params=-0.05825983458967864/0.3785210730307932/21222.32595700021/22222.0\ > 506020602/551024.0204808192/384.32768524288/384.0048000545/256.100768555\ > 55/512.10076855555/768.10076855555 float=y maxiter=3072 > inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 > colors=200222<24>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3\ > >0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3\ > >000400<23>o00q00s00<3>z00<31>000 > } > > -----------------------------------------start > frm--------------------------- > FRM:Multifractal_10 { ; Albrecht Niekamp Jan2005 > ;p1 (spider)julia-seed > ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 > ;0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider > ; input2: 2digits_many-mods 2digits_phoenix 2digits_spider > ; 1digit_shapereset:0_no 1_dblmandel 2_iter-reset 3_both +5_warp > ; 4digits reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp > ;imag(p2)(-) 5digits_colour(bailout) number > ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees > ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 > ;imag(p3) shape : factor (fn1), 5digits_colour4 6digits_colour5 > ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in > ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in > ; 5digits_factor1 (fn2) 4digits+fract_border1 > ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in > ; 5digits_factor2 (fn3) 4digits+fract_border2 > ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in > ; 5digits_factor3 (fn4) 4digits+fract_border3 > ; optional: 1_lake effect, 2digits_frquency 2digits_level 2digits_ampl > ;fn(1) shared by many-mods+bees > ; > le=0 > z=pixel > da=real(p2) > dd=trunc(da) > da=round((da-dd)*100000000000)+11111 > dd=dd+11111 > d=trunc(dd/10000) > dd=dd-d*10000 > d3=(d==4)+(d==5)+(d==8)+(d==9) > d4=d3==0 > vb=d>5 > sc=d==2 > mo=d==6 > px=d==7 > ab=px+(d==3)+(d==5)+(d==9) > d=trunc(dd/1000) > dd=dd-d*1000 > ex1=d>1 > sc1=d==2 > mo1=d==6 > px1=d==7 > v1m=mo1+px1 > v1j=d>7 > dd1=v1j+(d==4)+(d==5) > ab1=px1+(d==3)+(d==5)+(d==9) > d=trunc(dd/100) > dd=dd-d*100 > ex2=d>1 > sc2=d==2 > mo2=d==6 > px2=d==7 > v2m=mo2+px2 > v2j=d>7 > dd2=v2j+(d==4)+(d==5) > ab2=px2+(d==3)+(d==5)+(d==9) > d=trunc(dd/10) > ex3=d>1 > sc3=d==2 > mo3=d==6 > px3=d==7 > v3m=mo3+px3 > v3j=d>7 > dd3=v3j+(d==4)+(d==5) > ab3=px3+(d==3)+(d==5)+(d==9) > d=dd-d*10 > ba=imag(p5) > mi3=trunc(ba) > dd=(d>1)+(mi3>1) > ex4=dd==2 > sc4=d==2 > mo4=d==6 > px4=d==7 > v4m=mo4+px4 > v4j=d>7 > dd4=v4j+(d==4)+(d==5) > ab4=px4+(d==3)+(d==5)+(d==9) > ; > mm=trunc(da/1000000000) > da=da-mm*1000000000 > ph=trunc(da/10000000)/100 > da=da-ph*1000000000 > sp=trunc(da/100000)/100 > da=da-sp*10000000 > d=trunc(da/10000) > ex0=d>4 > da=da-d*10000 > d=d-5*ex0 > dm=(d==2)+(d==4) > ir0=(d==3)+(d==4) > d=trunc(da/1000) > w1=d>4 > da=da-d*1000 > d=d-5*w1 > rs1=(d==2)+(d==4) > ir1=(d==3)+(d==4) > d=trunc(da/100) > w2=d>4 > da=da-d*100 > d=d-5*w2 > rs2=(d==2)+(d==4) > ir2=(d==3)+(d==4) > d=trunc(da/10) > w3=d>4 > da=da-d*10 > d=d-5*w3 > rs3=(d==2)+(d==4) > ir3=(d==3)+(d==4) > d=round(da) > w4=d>4 > d=d-5*w4 > rs4=(d==2)+(d==4) > tt=ex1+ex0+ex2+ex3+ex4 > ; > d=real(p3) > dd=trunc(d) > da=(d-dd)*10000000000 > pp=trunc(dd/10000) > ba1=dd-10000*pp > ba2=trunc(da/100000) > ba3=da-100000*ba2 > ; > d=imag(p3) > sfac=trunc(d) > da=(d-sfac)*100000000000 > ba4=trunc(da/1000000) > ba5=da-ba4*1000000 > ; > d=real(p4) > ofac=trunc(d) > da=(d-ofac)*10000000000 > bh=trunc(da/100000)/10 > bl=(da-bh*1000000)/10 > bs=bl/2 > ; > d=imag(p2) > t=d<0 > if (t) > d=-d > endif > dd=trunc(d) > da=round((d-dd)*10000000000) > d=trunc(dd/10000) > dd=dd-d*10000 > bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) > d=trunc(dd/1000) > dd=dd-d*1000 > bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) > d=trunc(dd/100) > dd=dd-d*100 > bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) > d=trunc(dd/10) > dd=dd-d*10 > bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) > d=round(dd) > bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) > ; > d=da > p0=trunc(d/100000000)/10 > d=d-p0*1000000000 > p6=trunc(d/1000000)/10 > d=d-p6*10000000 > if (t) > p6=-p6 > endif > p7=trunc(d/10000)/10 > d=d-p7*100000 > dp=p6+p0/100 > p8=trunc(d/100)/100 > d=d-p8*10000 > p9=d/100 > ; > d=imag(p4) > mi1=trunc(d) > da=(d-mi1)*100000000000 > d=trunc(da/10000000000) > bt1=d>6 > da=da-d*10000000000 > d=d-5*bt1 > dt1=d>1 > iv1=d==3 > fac1=trunc(da/100000) > da=da-fac1*100000 > bo1=(da/100000)/10 > ; > d=real(p5) > mi2=trunc(d) > da=(d-mi2)*100000000000 > d=trunc(da/10000000000) > bt2=d>6 > da=da-d*10000000000 > d=d-5*bt2 > dt2=d>1 > iv2=d==3 > fac2=trunc(da/100000) > da=da-fac2*100000 > bo2=(da/100000)/10 > ; > if (mi3==1) > d=(ba-mi3)*1000000 > fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet > d=d-fr*1000 > lv=(trunc(d/100))/100 > d=d-lv*10000 > am=d/100 > u=real(rotskew*pi/180) > t=exp(-flip(u)) > bo=1/real(magxmag) > q=bo/0.75*imag(magxmag) > dd=tan(imag(rotskew*pi/180)) > da=2*q*t > rs=2*bo*(dd+flip(1))*t > zz=center+(-q-bo*dd-flip(bo))*t > z=z-zz > d=imag(conj(da)*z)/imag(conj(da)*rs) > le=d<=lv > if (le) > dd=lv-d > z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs > endif > z=z+zz > else > da=(ba-mi3)*100000000000 > d=trunc(da/10000000000) > bt3=d>6 > da=da-d*10000000000 > d=d-5*bt3 > dt3=d>1 > iv3=d==3 > fac3=trunc(da/100000) > da=da-fac3*100000 > bo3=(da/100000)/10 > endif > ; > if (vb) > if (d3) > if (ab) > z=z*le+pixel*(le==0) ;Spider > c=p1 > else > z=z*le+pixel*(le==0) > c=p1 ;newton > endif > elseif (ab) > c=z ;Phoenix > z=z*le+pixel*(le==0) > else > c=0.4*log(sqr(z^mm)) ;many mods > z=0 > endif > elseif (d3) > if (ab) > c=p1 ;Julia > z=z*le+pixel*(le==0) > else ;bees > c=p1 > z=z*le+pixel*(le==0) > endif > elseif (ab) > c=z ;Mandel > z=0 > else > c=z ;Secant > z=z*le+pixel*(le==0) > endif > t=0 > bo=|z| > p=pp > z0=p7 > zold=(0.0,0.0) > cb=p9 > ba=bb0 > : > if (tt) > t=t+1 > if (ex0) > ex0=t<mi1 > if (bo>bs) > u=2*(fn1(t/sfac)) > ex0=0 > if (ir0) > t=0 > endif > if (d4) > z=z*u > if (mo) > c=0.4*log(sqr(z^mm)) > else > c=pixel > endif > else > z=z*le+pixel*(le==0) > cb=p9*u > c=p1*u > p=pp*u > endif > tt=tt-1+ex0 > endif > elseif ((ex1)&&bo>bl) > if (bo<bh) > d3=dd1 > ba=bb1 > ab=ab1 > ex1=0 > tt=tt-1 > if (w1) > u=2*(fn2(t/ofac)) > else > u=1,0 > endif > if (ir1) > t=0 > endif > if (d3) > vb=v1j > if (rs1) > z=pixel > cb=p9*u > c=p1*u > p=pp*u > else > c=p1 > z=z*u > cb=p9 > endif > else > vb=v1m > if (rs1) > c=z*u > z=pixel*(sc1+px1) > z0=p7*u > ph=ph*u > else > c=z > z=z*u > endif > if (mo1) > c=0.4*log(sqr(z^mm)) > endif > endif > endif > elseif (ex2) > if (dt1) > if (iv1) > d=bo>bo1 > else > d=bo<bo1 > endif > if (bt1) > d=d+(t>mi1) > endif > else > d=t>mi1 > endif > if (d) > ab=ab2 > d3=dd2 > ba=bb2 > ex2=0 > tt=tt-1 > if (w2) > u=2*(fn2(t/fac1)) > else > u=1,0 > endif > if (ir2) > t=0 > endif > if (d3) > vb=v2j > if (rs2) > z=pixel > cb=p9*u > c=p1*u > p=pp*u > else > cb=p9 > c=p1 > z=z*u > endif > else > vb=v2m > if (rs2) > c=z*u > z=pixel*(sc2+px2) > z0=p7*u > ph=ph*u > else > c=z > z=z*u > endif > if (mo2) > c=0.4*log(sqr(z^mm)) > endif > endif > endif > elseif (ex3) > if (dt2) > if (iv2) > d=bo>bo2 > else > d=bo<bo2 > endif > if (bt2) > d=d+(t>mi2) > endif > else > d=t>mi2 > endif > if (d) > ab=ab3 > d3=dd3 > ba=bb3 > ex3=0 > tt=tt-1 > if (w3) > u=2*(fn3(t/fac2)) > else > u=1,0 > endif > if (ir3) > t=0 > endif > if (d3) > vb=v3j > if (rs3) > z=pixel > cb=p9*u > c=p1*u > p=pp*u > else > cb=p9 > c=p1 > z=z*u > endif > else > vb=v3m > if (rs3) > c=z*u > z=pixel*(sc3+px3) > z0=p7*u > ph=ph*u > else > c=z > z=z*u > endif > vb=v3m > if (mo3) > c=0.4*log(sqr(z^mm)) > endif > endif > endif > elseif (ex4) > if (dt3) > if (iv3) > d=bo>bo3 > else > d=bo<bo3 > endif > if (bt3) > d=d+(t>mi3) > endif > else > d=t>mi3 > endif > if (d) > ab=ab4 > d3=dd4 > ba=bb4 > ex4=0 > tt=0 > if (w4) > u=2*(fn4(t/fac3)) > else > u=1,0 > endif > if (d3) > vb=v4j > if (rs4) > z=pixel > cb=p9*u > c=p1*u > p=pp*u > else > cb=p9 > c=p1 > z=z*u > endif > else > vb=v4m > if (rs4) > c=z*u > z=pixel*(sc4+px4) > z0=p7*u > ph=ph*u > else > c=z > z=z*u > endif > if (mo4) > c=0.4*log(sqr(z^mm)) > endif > endif > endif > endif > endif > if (vb) > if (d3) > if (ab) > z=z*z+c ;Spiderjul John Horner > c=c*sp+z > else > z1=z^p-1 ;Qusinewton Pusk s Istv n > z2=p*z*z > z=z-z1/z2 > endif > elseif (ab) > z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike > Wareman > zold=z > z=z1 > else > z2=fn1(z)+c ;Many_mods Linda Allison > z1=cos(z2) > z=c*(1-z1)/(1+z1) > endif > elseif (d3) > if (ab) > z2=z*z ;Julia Pusk s Istv n > z=z2*z2+p6*z2+c-p0 > else > z1=fn1(z)-cb ;Bees Ray Girvan > z2=z1^p8-1 > z3=p8*(z1^(p8-1)) > z=z-(z2/z3) > endif > elseif (ab) > if (dm) > z=z*z+c+c*c-dp ;Double Mandel > else > z2=z*z ;Mandel Pusk s Istv n > z=z2*z2+p6*z2+c-p0 > endif > else > z3=z ;Secant Mike Wareman > z1=z0*z0*z0*z0-1 > z2=z*z*z*z-1 > z=z-z2*(z-z0)/(z2-z1) > z0=z3 > endif > bo=|z| > bo<ba > } > -----------------------------------------------end-frm---------------------- > - > > > > > ------------------------------ > > Message: 2 > Date: Wed, 02 Feb 2005 09:52:53 -0500 > From: Jim Muth <jamth(a)mindspring.com> > Subject: [Fractint] FOTD 02-02-05 (Triple Beast [5]) > To: fractint(a)mailman.xmission.com > Cc: philofractal(a)lists.fractalus.com > Message-ID: <1.5.4.16.20050202095518.2ac7fde6(a)pop.mindspring.com> > Content-Type: text/plain; charset="us-ascii" > > > FOTD -- February 02, 2005 (Rating 5) > > Fractal visionaries and enthusiasts: > > Today is the next to last time we will meet the fractal beast > that has been prowling the neighborhood for the past two days. > The beast is actually a four-dimensional thing with more aspects > than it has fleas. I named today's view of the critter "Triple > Beast" because the beast appears to have been stretched in three > different directions. > > Most of the features that appear in the Mandelbrot aspect of the > scene are still recognizable, though some have been stretched > almost beyond recognition. And one of the green inner spirals > has apparently split into a double spiral. > > The double spiral is only an accidental effect. It appears > because the calculated slice of the Julibrot that we see on the > screen cuts twice through a curved four-dimensional tube-like > feature something like a rolled-up scroll that has been bent in > the middle. > > Since the beast is starting to become boring, and we have seen > such distorted Mandelbrot features quite a few times before, I > could rate the image no higher than a 5, which is average. But > the beast is near the end of its life, and will make only one > more appearance before being sent to the oblivion where all the > undiscovered fractals are awaiting it. > > The beastly fractal may be glimpsed by running the included > parameter file, or by downloading the finished image from the > FOTD web site at: > > <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> > > The next installment of philosophy is but two days off. So be > patient. Enlightenment is nigh. > > Tuesday was another perfect day for this time of year here at > Fractal Central. Warm sun and a temperature of 39F 3C made > conditions near ideal, at least in the places where the snow had > melted and the ground was bare. The fractal cats enjoyed > conditions to the best of their ability, and when they finally > came indoors, were ready to curl up and sleep. Today is > starting the same. Another good day would appear to be in store > for the duo. > > For me, the work is normal. It looks like the day will be > neutral. This means ample time for the last of the beastly > images. Until the final beast appears in 24 hours, take care, > and be ready for new ideas. > > > Jim Muth > jamth(a)mindspring.com > jimmuth(a)aol.com > > > START PARAMETER FILE======================================= > > Triple_Beast { ; time=0:02:41.04--SF5 on a P200 > reset=2004 type=formula formulafile=allinone.frm > formulaname=SliceJulibrot2 center-mag=-0.000003485\ > 49440916/-0.00000142882743436/518039.3/0.05033/\ > 156.558086503412028/-40.9116101381892818 > params=55/-157/-81/166/0.288136932805/0.4826454054\ > 09/0.288136932805/0.482645405409 float=y > maxiter=5000 inside=0 logmap=288 periodicity=10 > colors=000SYsSXrSWqSVpSUoSTnSSmSQlTOkUMjVKiWIhXGgY\ > Ef_CeaAdcAceAbgAaiA`kC_mEZoGYqIXrKWsMTrOSqQRpSQpUP\ > oWOnXNnYMmZLl_KlaJkcIjeHjgHkhGkgFlfEldDmbCm`BnZAnX\ > 9kV8hT8eR8bP7_N7XL7UJ6RH6OF6LD5IB5FC5CC49D46D43D45\ > E57F59G6AH6CI6EJ7FK7HL8JM8KN8MO9OP9QQARRATSAVTBWUB\ > YVC_WC`XCaYEbZGbZHc_Jd`Kd`MeaNebPfbQgcSgdThdVheWif\ > YjgZjh`kiakjclkdmlfmlgmmimminmjomjpmjqnjrojtpjuqjv\ > rjwsjxtlxujwtivshurgtqftpdsocrmbqlapk`oj_oiYnhXmgW\ > lfVkdUjcTjbRiaQh`Pg_OfZNfYMgXKgVJgUHhTGhREhQDiPBiN\ > AiM8jK7jJ5jI4kG2kF1kE0gH1dJ1aM2ZO2WR3TT3QY4Na4Kf5U\ > o5cs2mz5mz8mzBhtEcrHZqKUoNPnQLmTMkWNjZOiaPidQhgRhj\ > SgmTgpShsTgrTfrTfqTeqUepUbpU_pUZoUUoVTnVTnVSnVSmVR\ > mWRnWQoWQpWPqWPsXOuXOwXNxXNzXMzYMzYLzYLzYKzYKzVOzS\ > SzQWzN_zLczPgzUkzZozcszhvzmuzmwzmvzmvzmuzmuzmtzmtz\ > mszmszmrzmrzmrzmqzmqzmpzmpzmozmozmnzmnzmmzmmzmmzml\ > zmlzmkzmkzmjzmjzmizmizmiz } > > frm:SliceJulibrot2 {; draws most slices of Julibrot > pix=pixel, u=real(pix), v=imag(pix), > a=pi*real(p1*0.0055555555555556), > b=pi*imag(p1*0.0055555555555556), > g=pi*real(p2*0.0055555555555556), > d=pi*imag(p2*0.0055555555555556), > ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), > sg=sin(g), cd=cos(d), sd=sin(d), > p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), > q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), > r=u*sg+v*ca*sb*cg, s=v*sin(a), > c=p+flip(q)+p3, z=r+flip(s)+p4: > z=sqr(z)+c > |z|<=9 } > > END PARAMETER FILE========================================= > > > > > ------------------------------ > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > > > End of Fractint Digest, Vol 24, Issue 2 > *************************************** >

1 0

FOTD 02-02-05 (Triple Beast [5])
by Jim Muth 02 Feb '05

02 Feb '05

FOTD -- February 02, 2005 (Rating 5) Fractal visionaries and enthusiasts: Today is the next to last time we will meet the fractal beast that has been prowling the neighborhood for the past two days. The beast is actually a four-dimensional thing with more aspects than it has fleas. I named today's view of the critter "Triple Beast" because the beast appears to have been stretched in three different directions. Most of the features that appear in the Mandelbrot aspect of the scene are still recognizable, though some have been stretched almost beyond recognition. And one of the green inner spirals has apparently split into a double spiral. The double spiral is only an accidental effect. It appears because the calculated slice of the Julibrot that we see on the screen cuts twice through a curved four-dimensional tube-like feature something like a rolled-up scroll that has been bent in the middle. Since the beast is starting to become boring, and we have seen such distorted Mandelbrot features quite a few times before, I could rate the image no higher than a 5, which is average. But the beast is near the end of its life, and will make only one more appearance before being sent to the oblivion where all the undiscovered fractals are awaiting it. The beastly fractal may be glimpsed by running the included parameter file, or by downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The next installment of philosophy is but two days off. So be patient. Enlightenment is nigh. Tuesday was another perfect day for this time of year here at Fractal Central. Warm sun and a temperature of 39F 3C made conditions near ideal, at least in the places where the snow had melted and the ground was bare. The fractal cats enjoyed conditions to the best of their ability, and when they finally came indoors, were ready to curl up and sleep. Today is starting the same. Another good day would appear to be in store for the duo. For me, the work is normal. It looks like the day will be neutral. This means ample time for the last of the beastly images. Until the final beast appears in 24 hours, take care, and be ready for new ideas. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Triple_Beast { ; time=0:02:41.04--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 center-mag=-0.000003485\ 49440916/-0.00000142882743436/518039.3/0.05033/\ 156.558086503412028/-40.9116101381892818 params=55/-157/-81/166/0.288136932805/0.4826454054\ 09/0.288136932805/0.482645405409 float=y maxiter=5000 inside=0 logmap=288 periodicity=10 colors=000SYsSXrSWqSVpSUoSTnSSmSQlTOkUMjVKiWIhXGgY\ Ef_CeaAdcAceAbgAaiA`kC_mEZoGYqIXrKWsMTrOSqQRpSQpUP\ oWOnXNnYMmZLl_KlaJkcIjeHjgHkhGkgFlfEldDmbCm`BnZAnX\ 9kV8hT8eR8bP7_N7XL7UJ6RH6OF6LD5IB5FC5CC49D46D43D45\ E57F59G6AH6CI6EJ7FK7HL8JM8KN8MO9OP9QQARRATSAVTBWUB\ YVC_WC`XCaYEbZGbZHc_Jd`Kd`MeaNebPfbQgcSgdThdVheWif\ YjgZjh`kiakjclkdmlfmlgmmimminmjomjpmjqnjrojtpjuqjv\ rjwsjxtlxujwtivshurgtqftpdsocrmbqlapk`oj_oiYnhXmgW\ lfVkdUjcTjbRiaQh`Pg_OfZNfYMgXKgVJgUHhTGhREhQDiPBiN\ AiM8jK7jJ5jI4kG2kF1kE0gH1dJ1aM2ZO2WR3TT3QY4Na4Kf5U\ o5cs2mz5mz8mzBhtEcrHZqKUoNPnQLmTMkWNjZOiaPidQhgRhj\ SgmTgpShsTgrTfrTfqTeqUepUbpU_pUZoUUoVTnVTnVSnVSmVR\ mWRnWQoWQpWPqWPsXOuXOwXNxXNzXMzYMzYLzYLzYKzYKzVOzS\ SzQWzN_zLczPgzUkzZozcszhvzmuzmwzmvzmvzmuzmuzmtzmtz\ mszmszmrzmrzmrzmqzmqzmpzmpzmozmozmnzmnzmmzmmzmmzml\ zmlzmkzmkzmjzmjzmizmizmiz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

1 0

Fractint_Multifractal
by Albrecht.Niekamp＠t-online.de 02 Feb '05

02 Feb '05

Hi, IÂ´m back again. There are several reasons. The first one is that I managed to boot Windoze98 as additional OS. As you know this OS has a perfect DOS support and allows switching between DOS and windows vv. Also I like it because it is compact and easy to handle. All the hardware, AGP, USB, DVD, Firewire etc is there. For Fractint I use an ancient Nvidia G-force 4 video card which has full Vesa support, also 1600/1200. The second reason is that I have some ideas how to improve and complete my multifractal formula. There is another one not mentioned today. In my email archive dated July19 I found a request by David Lowenstein asking for multifractals composed of different fractals at the same time. Maybe this is an answer, although possibly not the one you expected. Multifractal_10 composes images using max 5 different formulas simultaneously. There are 9 frms to choose from. There are five "channels": basic shape, outside and inside 1-3.The transitions are controlled by an iteration counter or by border (z) values, in and out (bigger or smaller), or iteration and border simultaneously. At the transition points optional resets are provided, either of the iteration counter or the z-value (or both), which affect the coloring and further iteration. Five different bailout values can be applied, ranging from 1 to one million. The effect is compression or expansion of the colours. A unique programmable "warp-effect" can be applied to each channel. It changes the behaviour and looks of the channels, pending on previous iterations, a choosable function and a "warp" factor. Maybe this just means a distortion, maybe a 3d effect. Sylvie GalletÂ´s lake effect is optional, fully integrated and works with all formulas, inside3 is shut off if activated. There now is a second basic "Double mandel" which allows the creation of "mandscapes", 2 samples with different insides, symmetric or asymmetric are provided. The par-files are demos for the contributing formulas to give you an impression about their looks, mostly with activated lake effect. "Pandemonium" is a basic image with lots of zooming spots. I gave it that name because so many different structures are hidden somewhere. "Debugflag=322" must be deactivated. Please check your SS-tools.ini. Any questions are welcome, of course. Attached is a printable wordpad file which is handy if you should want to compose your own image. If it does not get through, please paste the following part to an editor, using size9 to make it small enough for one sheet of paper. Sincerely, Al. ---------------------------------------------------------------------------- - Multifractal_10 Inputs Real P2 First Input (before the dot) 5 Digits : Channels : 1_Basic Shape 2_Outside 3_Inside1 4_Inside2 Inside3 Frms: 1_Secant 2_Mandel(2) 3_Bees 4_Julia 5_Many Mods 6_Phoenix 7_Newton 8_Spider Second Input (after the dot) 2 Digits_Many Mods_Number of sides 2 Digits_Phoenix 2 Digits_Spider 1 Digit_Reset on Transitions (Shape) 0_no 1_Dble Mandel 2_Iter-reset 3_both +5_warp 4 Digits_Reset Channels 2-5 0_no 1_z-reset 2_Iter-reset 3_both +5_warp Imag P2 First Input 5 Digits_Colour (Bailout) Number for each channel (5 available) Second Input Variables : 4 Digits_Mand/Jul (2 var) 2 Digits_Secant 4 Digits_Bees Real P3 First Input 2 Digits_Newtonvariable 4 Digits_Colour1 Second Input 5 Digits_Colour2 5 Digits_Colour3 Imag P3 First Input Basic Shape : Warp-factor (fn1 is used) Second Input 5 Digits_Colour4 6 Digits_Colour5 Real P4 First Input Outside : Warp-factor (fn2 is used) Second Input Outside : 4 Digits+1fractal digit_Border-out 4 Digits+1 fractaldigit_Border-in Imag P4 First Input Inside1_Maxiter Second Input Inside1 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border 5 Digits_warp factor (fn2 is used) 4 Digits+1 fractaldigit_border1 Real P5 First Input Inside2_Maxiter Second Input Inside2 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border 5 Digits_warp factor (fn3 is used) 4 Digits+1 fractaldigit_border2 Imag P5 First Input Inside3_Maxiter Second Input Inside3 : 1 Digit_Transition: 1_maxiter 2_borderout 3_borderin +5_maxiter+border 5 Digits_Warp factor (fn4 is used) 4 Digits+1 fractal digit_border3 Alternate Input Imag P5 First Input : 1_Lake effect enabled (Inside3 disabled) Second Input : 2 Digits_Frequency 2 Digits_Waterlevel 2 Digits_Amplitude ------------------------start-pars----------------------------------------- Secant_basic { ; Lake effect active ; Time 0.42.00.86 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/sin/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/10000.32595700022/55234.0\ 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200A85<17>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ 0s00<3>z00<25>C00A00800<3>000<12>NNNPPPQQQ<8>fffgggiiijjjlll<3>sss<25>BB\ B999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<2>864 } Bees_Basic { ; Lake effect active ; Time 0.09.10.85 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/sin/exp/sin passes=t center-mag=1.00827/0.00308737/0.6630435/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/30000.32595700022/35234.0\ 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200A85<17>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ 0s00<3>z00<25>C00A00800<3>000<23>fffgggiiijjjlll<3>sss<25>BBB999777<2>22\ 2000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<2>864 } Julia_Basic { ; Lake effect active ; Time 0.31.26.42 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/sin/exp/sin passes=t center-mag=0.0659115/0.0324086/1.087898/1.0222/90/3.88578058618804789e-0\ 16 params=-0.05825983458967864/0.3785210730307932/40000.32595700022/25234.0\ 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000047049<5>0BL0DN0DP<4>0KZ0L`0Mb0Nd0Of0Qh<3>0Up4Yr8atCgvGkxKqz<3\ >4_s0Vq0Uo<12>0FQ0DO0DM<3>08E06C06A048046024012000100<12>R0LT0NV0PX0P<3>\ d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_e0Z<3>Y0SW0RU0O<5>I0F\ G0EE0CC0A<3>304102010<4>0B10D10F10H20J20L20N2<2>0T40V40X3<3>0d40f50h5<3>\ 0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>0I20G20E20C20A1081<3>\ 0000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM<3>DdTDfVEhWFjYFlYGn_\ Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK<4>6IC5GB5DA<5>121000\ 001023025 } Phoenix_basic { ; Lake effect enabled ; Time 0.19.25.24 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=exp/sin/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/60000.32565700023/25234.0\ 506030602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter logmap=5 periodicity=0 rseed=-2436 colors=200432<20>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ 0s00<3>z00<25>C00A00800<3>000<7>FFFHHHJJJ<9>___aaaccc<3>iiijjjlll<3>sss<\ 25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211 } Newton_Basic { ; Lake effect active reset=2004 type=formula formulafile=mfr9n.frm formulaname=multifractal_10 function=exp/sin/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/70000.32595700023/55234.0\ 506030602/152048.0404808048/384.1604894048/384.00482000595/256.1007683/5\ 12.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=2 periodicity=0 rseed=-2436 colors=200432<20>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ 0s00<3>z00<25>C00A00800<3>000<9>IIIKKKLLL<9>bbbdddfffgggiiijjj<3>qqqsssq\ qq<24>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211 } Spider_Basic { ; Lake effect active ; Time 0.09.42.76 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=exp/sin/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/80000.32595700023/25234.0\ 506030602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=2000NU<8>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7\ A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<11>LLLNNNPPPQQQSSS\ UUU<6>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<\ 15>0OW } Many_mods_basic { ; Lake effect active reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/sin/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/50000.16595700022/55234.0\ 506020602/151024.0204808192/384.32768524288/384.00482000595/256.1007683/\ 512.1007683001/1.244062 float=y maxiter=1024 inside=maxiter outside=tdis logmap=yes periodicity=0 rseed=-2436 colors=20009C<19>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3\ >unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<23>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<3>07A } Pandemonium { ; Time 0.21.15.48 ; reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-0.489028/0/0.6666667 params=-0.05825983458967864/0.3785210730307932/21225.64595718025/21235.0\ 311030602/150056.0204808192/384.32768524288/384.00482000595/256.10076830\ 01/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000gt<22>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB\ 7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<23>fffgggiiijjjll\ l<3>sss<25>BBB999777<2>222000012<22>0_k0am0bo0cq<4>0kz0jx0hv } Mandscape2 { ; asymmetrical inside ; Time 0.14.07.06 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=exp/exp/exp/sin passes=t center-mag=-0.504822/4.44089e-016/0.9463538 params=-0.05825983458967864/0.3785210730307932/20227.32595710661/25255.1\ 111020602/151024.0204808192/384.32768524288/384.00482000595/128.10076800\ 01/512.10076800005/768.10076800002 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=000376<2>121000001023025047049<5>0BL0DN0DP<4>0KZ0L`0Mb0Nd0Of0Qh<3\ >0Up4Yr8atCgvGkxKqz<3>4_s0Vq0Uo<12>0FQ0DO0DM<3>08E06C06A0480460240120001\ 00<12>R0LT0NV0PX0P<3>d0Wf0Yh0Z<3>p0e<3>xOtzUxyOuwIquCns6iq0g<2>k0bi0`g0_\ e0Z<3>Y0SW0RU0O<5>I0FG0EE0CC0A<3>304102010<4>0B10D10F10H20J20L20N2<2>0T4\ 0V40X3<3>0d40f50h5<3>0p6<3>WxZczeUyY<2>0s8<4>0i60g60e60c4<2>0Y40W30U4<5>\ 0I20G20E20C20A1081<3>0000101221532653863A84DA5EB5HB<2>7NG8PI8RJ9TKAVNAXM\ <3>DdTDfVEhWFjYFlYGn_Gp`Prd<3>zzz<2>_ulRsgHqaHo`GmZFkXFiX<5>BYOAWMAUL9SK\ <3>7KE6IC5GB5DA4B9497 } Mandscape1 { ; symmetrical inside ; Time 0.14.02.12 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=exp/exp/exp/exp passes=t center-mag=-0.504822/-3.9968e-015/1.1027/0.8582 params=-0.05825983458967864/0.3785210730307932/20222.32595710666/25234.1\ 111020602/151024.0204808192/384.32768524288/384.00482000595/128.10076800\ 01/384.10076800005/512.10076800002 float=y maxiter=1024 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200A85<17>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q0\ 0s00<3>z00<25>C00A00800<3>000<23>fffgggiiijjjlll<3>sss<25>BBB999777<2>22\ 2000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<2>864 } Lite_Zoom { ; Different outside ; Time 1.51.37.67 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50466/1.66533e-016/4.219409/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21225.64595767025/13234.0\ 311030602/151024.0204808192/384.32768524288/384.00482000595/256.10076830\ 01/512.1007683001/768.1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000LS<11>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3\ >unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>00\ 0<11>LLLNNNPPPQQQSSSUUU<6>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012\ <11>0JQ } Multimix { ; Lite zoom ; Time 3.23.44.07 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_9 function=sin/exp/exp/sin passes=t center-mag=-1.22699/8.32667e-017/13.33333/1/90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21225.64595718025/23434.4\ 911030602/152048.0409608192/384.3276898304/384.00482000595/256.100768300\ 1/512.1007683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=2000KQ<6>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7\ A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<9>IIIKKKLLL<9>bbbd\ ddfffgggiiijjj<3>qqqsssqqq<24>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<1\ 7>0LS } Hades { ; The gate to the underworld ; Time 2.09.12.02 reset=2004 type=formula formulafile=mfr10.frm formulaname=multifractal_10 function=cos/sin/sin/sin passes=t center-mag=-0.188053/0.00113846/24.61324/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21222.32595700021/22222.0\ 506020602/551024.0204808192/384.32768524288/384.0048000545/256.100768555\ 55/512.10076855555/768.10076855555 float=y maxiter=3072 inside=maxiter outside=tdis logmap=3 periodicity=0 rseed=-2436 colors=200222<24>iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3\ >0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3\ >000400<23>o00q00s00<3>z00<31>000 } -----------------------------------------start frm--------------------------- FRM:Multifractal_10 { ; Albrecht Niekamp Jan2005 ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ;0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2: 2digits_many-mods 2digits_phoenix 2digits_spider ; 1digit_shapereset:0_no 1_dblmandel 2_iter-reset 3_both +5_warp ; 4digits reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 6digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ; optional: 1_lake effect, 2digits_frquency 2digits_level 2digits_ampl ;fn(1) shared by many-mods+bees ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Qusinewton Pusk s Istv n z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba } -----------------------------------------------end-frm---------------------- -

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FOTD 01-02-05 (The True Beast [6])
by Jim Muth 01 Feb '05

01 Feb '05

FOTD -- February 01, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's image bears the name "The True Beast". I gave it this name because it brings out the full beastly nature that was partly hidden in yesterday's image. Today's image shows the same midget that appeared yesterday, but the midget has been sliced in a different direction, one that is totally oblique to all six perpendicular planes of the four-dimensional Julibrot. In yesterday's image the spiral arms could be seen and followed as they multiplied and converged onto the midget. In today's image the arms are still there, but they are of a different number, and they no longer converge on the midget. Some arms have vanished entirely, leaving only traces where they almost appear. Others have morphed into horseshoe-like shapes, while still others have become concentric closed rings. I have kept the color palette and logmap from yesterday's image so that the corresponding parts can be more readily identified, but considerable stretching and skewing was necessary to restore the image to the same proportions. To see the area when it is unstretched, go the the 'z' screen, then the 'f6' screen and reset the 'x' mag factor to 1. Due to the skewing, the midget is some distance off the screen to the right, but it can easily be seen why stretching was necessary. The rating of a 6 might be a bit overdone, but today's image is still curious, amd well worth a look. The image may be viewed by running the attached parameter file or by downloading it, already rendered, from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The philosophy, entertaining if not enlightening, is included in the philofractal version of today's FOTD. With warm sun and a temperature of 39F 3C, Monday was marred only by the soggy melting snow still covering the yard. The cats managed over an hour on the porch and even enjoyed a short trek to the holly thicket. When the day ended, they were happy enough so that no special treat was needed. This morning is starting the same as Monday. I assume the duo will have a similar day. For me the work is about average, which means that the next FOTD will appear in 24 hours as scheduled. Until then, take care, and be open minded but not too credulous. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_True_Beast { ; time=0:02:44.06--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=Slicejulibrot2 center-mag=+0.000005602\ 47472017/+0.00000088644054031/846681.8/0.02445/\ 171.009021891882384/-58.4065041085181846 params=195/2.76/81.96/-30.91/0.288136932805/0.4826\ 45405409/0.288136932805/0.482645405409 float=y maxiter=5000 inside=0 logmap=288 periodicity=10 colors=000SYsSXrSWqSVpSUoSTnSSmSQlTOkUMjVKiWIhXGgY\ Ef_CeaAdcAceAbgAaiA`kC_mEZoGYqIXrKWsMTrOSqQRpSQpUP\ oWOnXNnYMmZLl_KlaJkcIjeHjgHkhGkgFlfEldDmbCm`BnZAnX\ 9kV8hT8eR8bP7_N7XL7UJ6RH6OF6LD5IB5FC5CC49D46D43D45\ E57F59G6AH6CI6EJ7FK7HL8JM8KN8MO9OP9QQARRATSAVTBWUB\ YVC_WC`XCaYEbZGbZHc_Jd`Kd`MeaNebPfbQgcSgdThdVheWif\ YjgZjh`kiakjclkdmlfmlgmmimminmjomjpmjqnjrojtpjuqjv\ rjwsjxtlxujwtivshurgtqftpdsocrmbqlapk`oj_oiYnhXmgW\ lfVkdUjcTjbRiaQh`Pg_OfZNfYMgXKgVJgUHhTGhREhQDiPBiN\ AiM8jK7jJ5jI4kG2kF1kE0gH1dJ1aM2ZO2WR3TT3QY4Na4Kf5U\ o5cs2mz5mz8mzBhtEcrHZqKUoNPnQLmTMkWNjZOiaPidQhgRhj\ SgmTgpShsTgrTfrTfqTeqUepUbpU_pUZoUUoVTnVTnVSnVSmVR\ mWRnWQoWQpWPqWPsXOuXOwXNxXNzXMzYMzYLzYLzYKzYKzVOzS\ SzQWzN_zLczPgzUkzZozcszhvzmuzmwzmvzmvzmuzmuzmtzmtz\ mszmszmrzmrzmrzmqzmqzmpzmpzmozmozmnzmnzmmzmmzmmzml\ zmlzmkzmkzmjzmjzmizmizmiz } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END PARAMETER FILE=========================================

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