December 2005 - Fractint - mailman.xmission.com

FOTD 07-12-05 (The Fractal [4])
by Jim Muth 07 Dec '05

07 Dec '05

FOTD -- December 07, 2005 (Rating 4) Fractal visionaries and enthusiasts: Today's fractal is the central part of the much larger fractal that results when 0.4 parts of Z^(-0.8) are subtracted from Z^2, and (1/C) is added. The entire bloated fractal extends far to the northeast of the small part that appears on the screen, though most of this extended part holds little of interest. The image consists of a Mandelbrot set, this much is obvious. But the set is distorted to such a degree that its various parts are hard to identify. East Valley, which lies at the bottom of the main bay, is easy to find, but there are two buds of nearly the same size, making it difficult to tell which is the large period-2 bud. A check of the filaments reveals that the large bud on the left is the actual period-2 bud, and the filament curving outward and downward from it is the main stem. We know this is the true main stem because it does not split. The broken filament extending to the northwest of the bud is a secondary one, which has become blown up beyond its normal importance. The large bud on the right of the main bay is actually the north period-3 bud. Its filament splits into two main branches, and the point of the split has 3 arms radiating from it, indicating that the bud has a periodicity of 3. This point is the lowest order true 'star'. (I do not count the 'straight' 2-armed star of the main filament.) Today's distorted M-set may be explored just like the true M-set. All the familiar features and sub-midgets are there in their proper places, with their familiar patterns mostly intact, but with the normally flat iteration bands enhanced by the pattern present at that point of the parent fractal. The true Mandelbrot set is 'connected'. All its midgets are connected to the main bay by infinitely thin filaments. But today's distorted set is obviously not connected. Parts of it are clearly separate from the main bay. I am not sure if these disconnected parts actually are connected to the main bay in the underlying four-dimensional Julibrot. My instinctive guess would be that they are connected, though I am unaware if this has ever been determined. These disconnected parts are filled with small midgets, just as the connected parts are. And as would be expected, the patterns around the disconnected midgets are also disconnected. Instead of being surrounded by the expected connected and splitting features, the midgets are surrounded by scattered bits and pieces of debris arranged in groups of 2,4,8.... These 'discon- nected' midgets are usually rather bland. I rarely find much of interest in them. The fractal is 'critical, meaning Z was automatically initial- ized by the M-Mix4 formula to a critical point of the calculated expression. Its midgets are therefore intact. But the generat- ing expression, (Z^2)-0.4(Z^-0.8), has more than one critical point. There is a second Mandeloid connected with another criti- cal point hidden almost invisibly in the image. Notice that the lower right part of the image is filled with holes, and the largest hole, located at the end of a prominent filament, has a purplish valley showing through it. This valley is the only part of the almost totally obscured second Mandeloid that is visible. A quick check will reveal that it has not been calculated at its critical point. But this 'ghost' Mandeloid is important. The midgets of the top Mandeloid will always cut through the ghost beneath, but the top midgets will be surrounded by features that mirror the Julia sets of the part of the 'ghost' Mandeloid over which they lie. It is in areas where the interesting parts of both Mandeloids overlap and mix together that the best scenes exist. In the next few FOTD's I will show several of these scenes found in the lower right part of today's image. I named today's image "The Fractal", which is stating the obvious. Unfortunately, after careful consideration, I could rate the image no higher than a sub-standard 4. The above- average images will come in the next few days. The render time of 1-1/3 minutes is fast even on slow machines. And for the convenience of those with handicapped computers, the completed GIF image has been posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds all morning and light snow in the afternoon kept the fractal cats confined to quarters all day Monday here at Fractal Central. Needless to say, they were a bit spoiled over the weekend, and sulked when they did not get all the tuna they could eat. The snow ended on Tuesday and the sky partly cleared, but with a temperature barely above freezing, and two inches (5cm) of snow on the ground, the duo never left the porch. My day was at the usual degree of activity. The next FOTD will appear in 24 hours. Until then, take care, and do your fractal shopping early. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Fractal { ; time=0:01:19.58--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=1.5457/0.342387/1.078531/1/87.5/-2.5056\ 3458870090017e-014 params=1/2/-0.4/-0.8/0/0 float=y maxiter=512 inside=0 logmap=yes periodicity=10 colors=000G00K00O00S00W02_04c06i28mEApPCs`EvkGocIh\ WKaOMVGPO9QNARNASNAUNAXNA_NAbNAeP8hR6kT4mU2or9qkGr\ dNsYUtR`uWYv_WwdTxhRylPzqMzuKzyIziMzVPzWQzXRzYSzZT\ zZUzSTzMTzFQz9MzhKziKzjKzkKzlKzlCz`CzQCzECz3Cz6Ez8\ GzAIzCJzFLzHNzJPzLQzdIzxBziKzVTzHazNXzTSzYNzcIziLz\ nOztRzyUzqXzi_zaayVcxUewTgvSjuRmnQptPqrPoqPmpQkoRj\ nSimTilUkkVmjWoiXqhYsgPufHwe9ycFzaLz_QzXMzUIzRFzPB\ zQ8zRHzPQzOYzNHzdIzYJzRQzWXz`czejzj`zeRz`HzXczVgzR\ kzNozJpzHqzFrzDszCvzBxzBzzBhzHRzMAzRIzSQzSTzxQziOz\ V5z4EzA7zsMzItzgkz`bzUUzN8zmdzw_zlVzaQzR`zATzDHzQK\ zLQzHPzGOzGNzGmzXfzS_zOTzKazrYzhUzZQzPez6`z9WzBRzE\ JzIKzHLzGHz1Jz5Kz9LzDlzHZzGPzAXztrzPizMazKUzIXzfRz\ jPz_NzQZzlSzWazaUzRgzEkzAbzCUzExz_dzQGzvJz`yzEkzIb\ zHUzGpzMhzK`zJTzHdzP_zMVzKQzI9zZEzSIzM`ztXziTz_PzQ\ 6zuCzgHzU6z6CzAHzDcz1cz9cz1Uz5Rz9OzDtzBbzEjzdazWUz\ OgzkazcXzWRzONzNrzSszLtzF } 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 06-12-05 (Berries Went Away [5])
by Jim Muth 06 Dec '05

06 Dec '05

FOTD -- December 06, 2005 (Rating 5) Fractal visionaries and enthusiasts: Let the trumpets blare, let the cats rejoice. I'm back! And I have already created another fractal. Unlike carbs and trans-fats, today's fractal is most certainly not hazardous to your health. It is a harmless Julia set of the Z^(1.3)+C Mandeloid as it appears 13 levels up the logarithmic ladder to infinity. The large inside part of the image has been activated by the 'bof60' inside fill. I named the image "Berries Went Away" because an earlier version of the image looked like a pile of blackberries, and, while trying to decide on a name, I heard a news report on the radio that, due to legal problems, electronic blackberries might soon become useless. (I couldn't be less concerned.) Mostly due to its amber coloring, the image rates a 5, which is the every-day average. The render time of just under 1-1/2 minutes will be reduced to mere seconds on the fastest machines. But some fast S.O.T.A. machines are allergic to Fractint. Those with such delicate prima-donna units can see the image by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and see the image posted there, without the chore of running the parameter file. The weekend search for the new Fractal Central went reasonably well. We checked two properties in Lewisburg, which is located in the Susquehanna Valley area of central Pennsylvania. But we have much more shopping to do before we make a final decision. Temperatures that were too chilly for comfort limited the cats' outdoor time over the past few days. But my sister, who kept the cats from becoming lonely while we were away, and also kept them overfed, reports that the duo made the most of things, taking brief advantage of the few rays of sun that managed to filter through the clouds and holly trees, while enjoying the extra-generous treats of tuna. Until the next FOTD appears in 24 hours or so, start taking care again. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Berries_Went_Away { ; time=0:01:24.92--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC center-mag=-0.135593/-0.096485\ 2/0.6666667/1/-77.5/2.583350200424661e-014 passes=1 params=1.3/0/13/0/0.168/-0.444/0/0 float=y maxiter=256 inside=bof60 logmap=yes periodicity=10 colors=000B8AEAAHCAKEANGAQIATKAWMCZOEaRGdUMgXSj_Ym\ bbpefsjkvnpzsuzvzzzzzxzzuzztzzrzzozznzzozzpzzpzzrz\ zryzsxztvztvzuuzutzvszxszxrzyph_MfTOeMOzevzVozLiz9\ bzGfzMizSkzWnzapzftzkvzoyztzzyzzzzzzzzzzzzzzzzzyzy\ bsuetrhtojukluiovervbtvZvxVyxSzyOzyLzzGzzDzzEzyEzy\ EyxEuxEsvEovEkuEhuEeuZZZpS9sZPtdavinxoyztzzyzstzjp\ zalzSixIerYepkepahyQjzSnzTpzVszWuzYxzZzz_zzazybzxd\ zxbzybzybzybzybzybzybzyazyazyazyazyazyazyazybzzbzz\ bzzbzzdzzdzzdzzdzzdzzbzzbzzbzzbzzazyazxazvaxuaut_s\ s_pr_np_ko_jnehnjfnnensdnvbnzanz_nzboudoreolfohiod\ joZkoTloPnorzzzzzzzzzzzzzzzzzzzzzzzzzzzuzykzxazvQz\ uGzJYzY_fja0je9jhIjjPjnWjpajshjvnjytjzzjzzkzzkzykz\ ulzslyplxlnxjnvhnudouaotYosVpsSprOppLppInrLlsMjtOh\ uQeuSdvTaxWZyYWzZVz_TzVTzPSzLSzESz9PzIMuOJpTGj_Dee\ 9Zj6To9YrD_sGbtJeuMixPkySnzVpzYtz_vzbyzezzhzziyziu\ zipzilziixidui_siWriQoiMl } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(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|< p4+100 } END PARAMETER FILE=========================================

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Re: another Muth zoom.
by JackOfTradeZ 05 Dec '05

05 Dec '05

Jim Muth FOTD zoom to E+58 is posted: http://www.fractal-animation.net/vid/muthzoom3_e58.zip . WMV format, 320x240 2 min. 11 sec. 7.5 MEG It is a deep zoom, but took less time to do than I would have thought, presumeably due to the low iteration count. A nice view of the period doubling phenomenon as the rays go from 2->4->8->16->32->64. JoTz

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No FOTD until December 6th
by Jim Muth 03 Dec '05

03 Dec '05

Fractal enthusiasts: Sorry for the disappointing news, but there will be no FOTD's until next Tuesday, Dec. 6. We will be out of town in central Pennsylvania on Friday and the weekend, checking for possible new locations for Fractal Central. While we are away, my sister will be looking after the fractal cats. I have decided it is definitely time to throw in the towel for Baltimore. Jim M.

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Revised par and a new one
by Lee H. Skinner 01 Dec '05

01 Dec '05

The image 60529013.gif that I posted a few days ago needs to have a mathtolerance command inserted into it to get the correct image, so I'm reposting it. 60529013 { ; ; t= 0:12:47.59 on a P4 2Gh at ; 1600x1200 Image Copyright 2005 ; by Lee H. Skinner ver=2004 ; Fractint Version 2004 Patchlevel 2 reset=2004 type=formula formulafile=fractint.frm formulaname=mandelbrotmix4 function=recip passes=1 mathtolerance=0.05/1 center-mag=-28.44386721751718000/-11.7012260054645100\ 0/6.082476e+011/0.9998/-69.9574025021650385/0.0859563\ 195570046401 params=-5.46/-1.5/-2.67/-4.5/0/200000000000000 float=y maxiter=2500 inside=bof61 outside=tdis symmetry=none periodicity=10 mathtolerance=0.05/1 colors=000flv<2>otvswwuxxwyyzzz<3>rwzovzhsw<3>Gch8_d8\ Xa<3>8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6\ >UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc\ 0ce7_<3>zb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8\ KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm\ 9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S\ <3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0\ Ul0Xq0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U\ 6X<2>F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl\ <3>S_v<3>civ } Also, here is a closer zoom into today's FOTD midget. 61201010 { ; ; t= 1:13:52.58 on a P4 2Gh at ; 1600x1200 Image Copyright 2005 ; by Lee H. Skinner ver=2004 ; Fractint Version 2004 Patchlevel 2 reset=2004 type=formula formulafile=fractint.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=+0.64171460174044760/-1.55368223772558900/\ 4.597402e+007/1/72.5000004021203495/4.145932290602893\ 92e-007 params=-2/-1.4142/-0.2/-14.142/0/0 float=y maxiter=5000 inside=255 outside=tdis symmetry=none periodicity=10 cyclerange=1/254 colors=000zzz<3>S`9<3>`jEclFeoGhrI<3>UnXRm_NlcJkgFfpA\ az<3>PJoSFlWAi_5fc0ce7_<3>zb0<2>zz1zzC<2>zzz<3>jqdfo_\ blU<3>Mb8<3>LQ8KM8KJ8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhM\ BiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<3>zm3zj4zg4zd4z`4z\ Y4<8>zM8zK9zJ9<3>zDBz00c0b<15>Q2LQ3JP3I<2>M3FL4DJ3AH2\ 9<3>S27V27Y26<2>e14zs4zY0n13<3>z00<13>U6ES6FP7G<3>F9L\ AAGAD0<4>CM5DN6DTzESzFTzFVA<3>HaEIcFJeG<2>Nb4P`0Sb5<4\ >flVjo_mqe<3>zzzxzz<3>eqsaorXlpSjnNglGch8_d<3>8MS<3>L\ IKOGISFGVEEYDCaB9<3>uB2zA0xA0<4>kA0iA0fA0<3>XA1<7>vts\ z05000 } 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 }

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FOTD 01-12-05 (Metabilis-3 [5])
by Jim Muth 01 Dec '05

01 Dec '05

FOTD -- December 01, 2005 (Rating 5) Fractal visionaries and enthusiasts: Today's image is named "Metabilis-3". The words have no meaning, they simply came to mind while I was studying the image. Most likely the words are the vaguely remembered name of an alien planet in one of those junky sci-fi movies I watch so many of. The image itself is based on whimsy -- a mixture of negative portions of Z^(-1.4142) and Z^(-14.142), with (1/C) added. The parent fractal is a grossly overblown thing in several separate pieces, with a number of open 'inside' areas scattered about. Today's scene is located in a valley of one of these open areas. Much of today's image consists of 'inside' stuff, which I have colored a dull purple. To add detail to an otherwise flat scene, the 'outside' parts were rendered with the outside=tdis option. Maybe I'm being too strict with my rating, but IMO, the image is only average, and can be rated no higher than a 5. The render time of 11-1/2 minutes borders on slowness, but relief is on hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is posted for immediate viewing. The rain moved out and the sun moved in on Wednesday here at Fractal Central. With the temperature in the middle 50's F., around 13 C., the cats had nothing to complain about as they passed the afternoon in the yard. The wind gusted at times, but they seemed not to notice. Except for a rather animated discus- sion with Fractal Lady, my day was reasonably peaceful. The next FOTD will appear on schedule in 24 hours. Until then, take a break. For just one day, stop taking so much care, and have a little fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Metabilis-3 { ; time=0:11:34.15--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.64171460189384810/-1.553682238057576\ 00/4574071/1/72.5000005174516673/1.830898137891723\ 29e-007 params=-2/-1.4142/-0.2/-14.142/0/0 float=y maxiter=1000 inside=255 outside=tdis periodicity=10 colors=000hiLjmHlqDnuAloCkiEjcGhYIgSKfNMhQQjTUlVXm\ Y`o_cqbgrdjsbcsaXs`Qs_JsZCsY6ZNxmcCfhF_mHTrJNwLOyJ\ PzHRzEa_fZRdWIbN8UYLdgYnqjxiktalqVmmNnjGogIjeKfdMb\ cNZbPV`RR_TNZUJYTSZS__Rh`QpaPybPzcdcE_eDVgCQiCLkBH\ mBBN2KPDSQN_SXgTfoVpwWzvUYvT6xdDyoKzsQnsPclO`fNEfS\ MfXUfaaffefkkfpoftsisvlrzqrteq000000000000000000Kp\ cInbHlaFjaEh`Df`YuAciBhZBHAe0cwAZtKVrTQpbMnkIloSks\ XkpZnnSqkHti7wc8rZ8mU9iO9dJA_EAWOJXYSXg`YqiYzrYwof\ ulosjxpismhnkgihfdfe_cdVadQXeOSfMNfKIgIDhG8hEKoFWv\ GgzGjqOlfVnXbpMirCprHkrMgrQcrVZr_VrcRmfRhiRclRZnRU\ qRPtRKwRGyRHkTHZUIMWI9XFEPDIHBMADJEFHIHEMJCQL9UN7Y\ L8ZK9_JA_IUzGczFUzEDbDDbBBb9Ab79b58b37b98WE8QQORab\ SmqTloSkmSjkRijRhhQgfQfeQ`dPVcOPbOJbNDaN7`M2`MEdTP\ g_QebRddRcfSbhT`kT_mUZoUYqRalOehLidJl_GpWDtSBwOIqV\ Pl`WfgbamiWtpRzqQrrPjsPcsNhrKLqNNpRQoUSnYVm`XldZkg\ ajkcinfhrhhujfviaYWdaSPKP } 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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