December 2003 - Fractint - mailman.xmission.com

FOTD 11-12-03 (School Days Fractal [6])
by Jim Muth 11 Dec '03

11 Dec '03

FOTD -- December 11, 2003 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal is named "School Days Fractal". I have not the slightest idea why I gave it this name, but for some strange reason, the name seems right, and therefore the image will remain so named for all eternity. The parent fractal is an irregular thing with X-axis symmetry, created when 5 parts of Z^(-1.3) are subtracted from one part of Z^(-8.6). At first glance, this parent appears to have few promising areas to investigate when the goal is to find hidden midgets. True, there are a few obvious small M-sets lying about, which give some hope, but these are little more than reflections of the M-set itself. However, notice the northernmost part of the parent fractal, where a bit of something interesting lies. Surely, no midgets will be found in this series of fragments and Julia-like spirals. That's what I thought when I first checked the area. But I was wrong. For some reason, I got the feeling that often comes over me when I am near a midget in an unlikely location. My persistence paid off, and at the end of my quest, I came upon today's scene, which BTW rates another 6. The scene is almost as interesting when an outzoom or two are done, and I did have a bit of difficulty deciding where to stop. I think I've found the best magnitude, but others might disagree. It's worth a check. As always, the render time, which today is 17 minutes, may be avoided by downloading the pre-rendered GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> In yesterday's FOTD I said that I would wax philosophical today on the philofractal list if I had the time. I did not have the time. I'll try again tomorrow. The rain moved in early Wednesday afternoon here at Fractal Central, cutting short the cats' time outside. The chilly temperature of 46F 8C only made things worse. As a result, the duo sulked admirably, and needed an extra dish of tuna to restore their spirits. This morning the rain has ended, but the wind has arisen. We'll see how the duo adjusts. I'll adjust very well as soon as the work is behind me. Until next time and next FOTD, take care, and see you in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ SchoolDays_Fractal { ; time=0:17:49.62--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+0.67507676878145810/+1.767666155180351\ 00/2.397265e+008/1/29.9999671749570034/1.754618232\ 14984e-005 params=-5/-1.3/1/-8.6/0/525/0/0 float=y maxiter=1800 inside=0 logmap=315 periodicity=10 colors=000anx_ozVozPnzLnzNozNqzNszNuzPvzPxzPxzPzzP\ zzRzzRzzRzzRzzRzzTzzTzzTzzTzzTzzNzjHzGCz0Az0Az0Az0\ Az08z08z08z08z08z06z06z16z16z36z63z83z83zA3zC3zC6z\ E6zE8zE8zEAzEAvECsECnEEhGEeGG_GGXGHRGHNGJHGJEGPGLV\ HP_JVeJY0Pz6TxCVsJXnP_hXacacYhgTnhNsjJocGnYEjRAhL8\ eE6c81_00Y00V00T00L0HE0eC3gC8hCCjCGlCJnCNnCRoCVqAY\ sAauAevAhvAlxAozAszAvz8zz8zz8zz8zz8zz8zz8zz8zz3zz0\ zz0oz0ez0Vz0Hz06z00z00z03z18z8EvGHqLLlTRhmccrdYzhV\ wnPvwJzxGzzAzz3zz0zu0zs0zq0zp0zo0zn0zm0zl0zk0zj1zi\ 3zh6zg8zfAzeCzdExcGvbHsaJo`Ll_NjaPgeRchTalVYoXVzYT\ x_PzaLzcJzcJzaLz_LzXNzVNzTPzRPzNPxLRvJRuHTuETsCVqA\ Vo8Vo3Xn1Xl0Yj0Yj0_h0_g0_g0Xc0V_0TY3RVAPRGNPJLLPJH\ VHGYGCcE8hC6lA1q80v60z30z10z00z00z00z00z00z00z00z0\ 0v03s08n0Ch0Gc0JY0NT0RP0VJ0YE0a80e10h00l0Co1NsCYvJ\ azNczRgzThzXlzYnzaqzcszgvzhxzlzznzzqzzsvzunzuezuXz\ uPzuGzuzzNzzVxz_zzgzzlzzs } frm:MandelbrotMix2 {; 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)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 10-12-03 (Your Highness [7])
by Jim Muth 10 Dec '03

10 Dec '03

FOTD -- December 10, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's venture into Fractal Land takes us to the fractal created when one-half part of Z^(-7.5) is added to 5 parts of Z^(-1.5) before (1/C) is added. The resulting fractal consists of two separate parts -- a main part with several large bays and a smaller area of non-critical stuff located some distance to the southwest of the main part. I have examined this cut-off area for over an hour without finding signs that midgets might lie there. It does have some striking tree-like elements however, which I might use in some future FOTD. Today's scene is located rather deep in the southern branch of the valley that cuts off the prominent bud at the eastern end of the string of bays comprising the main part of the parent fractal. The image is named "Your Highness", which is a term used when addressing a person of very high rank, such as a king. The name was inspired by the royal blue color of the midget at the center. This color extends to the arms radiating from the midget, giving them an unusually sharp, royal definition. Before deciding on the standard 'equal-iteration-band' version of today's scene, I tried the other outside options, and also the various 'evaporated' inside options. The other outside options create an image that is too busy. The inside options applied to the 'evaporated' version are either too busy or too simple, the lone exception being the bof61 option, which creates an exaggerated, rather hectic variation of the standard version. If I had been in a different mood, I might have chosen this variation. I rated today's picture an above-average 7, a rating that might be a bit more than it deserves. But I do like the deep-blue color of the midget and its arms, and I decided to reward myself. The render time of 11 minutes is getting to be a habit. Relief is at hand however on the FOTD web sites, where the GIF image may be found, already rendered. Those sites are at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> I am currently reading the NovDec issue of 'Skeptical Inquirer' magazine, a publication of CSICOP that I have been reading for many years. Ever since I came to realize that its main agenda is to promote the materialistic philosophies, and that it uses science chiefly to add validity to its claims, I no longer take it as seriously as I once did, but I still find it quite entertaining and informative, often containing much to ponder. If I have time, I'll do some public pondering in the philo- fractal version of tomorrow's FOTD, when, depending on one's point of view, I will spread either wisdom or superstition. Tuesday brought partly cloudy skies and a temperature of 43F 6C to Fractal Central. The fractal cats were neutral about the conditions, and did little of note while they were outside. When they came in, they asked for tuna, but when they got none, they settled for their regular food, Today, I fear the next rain area is moving in. Hopefully, the cats' indifferent mood will continue through the rain. As for me, I'm about 1/3 of the way through the day's work. If I'm lucky, I'll finish before the rain arrives. Until next time, take extra care and then a bit more care. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Your_Highness { ; time=0:11:24.43--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.12998426754146700/-0.194913908321507\ 00/4.144484e+008/1/59.999963718102002/3.7033972414\ 5712923e-005 params=5/-1.5/0.5/-7.5/0/525 float=y maxiter=1500 inside=0 logmap=238 periodicity=10 colors=000FDAHEAHFAKGAKHANIANJAQKAQLATMBTNCWQCWTCY\ WCYZCabCaeCegCehCiiCijCmkDmlCqmCqoCtqBtsBwuBwwAzyA\ zzAzy9zx9zw9zu8zs8zq8xoNwmQukTsjWqiVohUmgWkfYie_gd\ afecededcgcbibaka`m``o_aqZ`sYcuX`wWexV`zUgzT`zSXzJ\ ZzIUzGXzFUzDVzCUzBSzARrAQw9Ph8Ns8Mc7Li7KX6Ic5HT5GY\ 4FQ3DO3CM2BK2AJ2AJ2AI19H19H18G18F18F17E17D17D16C16\ B15A15A159100048048047036036025024024013012F12P01U\ 00UK9UK8UK8UK8UK8UK7UK7UK7UK7UK6TJ6SI6RH6PG5OF5NE5\ ME5LD4KC4JC4IB4HA3GA3F93E83C82B72A6296285174164153\ 1420m20m10m00hUzhUzhUzhUzhUzhUzhUzhUzLBgKAeJAcJ9aI\ 9_H8ZG8XF7VE7TD7RC6PB6NA5M95K94I84G73E63C52B429317\ 215103001PcnOamOalN`kN_kNWjM_iMZhMZhLYgLYfLXeKXeKW\ dJVcJTbJTbIRaIR`IQ_HQ_HOZHOYGNYGMXFLWFLVFKVEKUEJTE\ JSDISDIRDHQCHPCGPBKOBPNBUMAZMAcLKhKUmJcrJmwIuzHzzH\ zzGzzFzzEzzEzzDzzCzzBzzBzzAzzWzzUzzTzzSzzRzzPzzOzz\ NzzMzzKzzJzzIzzHzzMzzRzzW } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 09-12-03 (Minus-Minus Midget [6])
by Jim Muth 09 Dec '03

09 Dec '03

FOTD -- December 09, 2003 (Rating 6) Fractal visionaries and enthusiasts: The following paragraph is about a spam e-mail scam. Those who would rather not read about spam e-mail should skip to the third paragraph. ;-) Among the 150 or so pieces of junk mail that I found in my e-mail box this morning was an 'official' notice, claiming to be from my Earthlink ISP, informing me that they needed to confirm my billing information. The link led me to a web site where I was to enter my credit-card number, etc. (No personal informa- tion is in the fractal-dedicated machine that I used.) My opinion (actually I'm almost certain) is that the letter is a scam, intended to fraudulently acquire credit-card numbers, and even if it is serious, which I doubt, then Earthlink is so inept that I would rather not be connected with them. Who wants an ISP that can't even keep track of the billing information of its own customers. ;-) I guess I should not be too hard on them, after all, I sometimes lose track of my own fractals. But today's image is one I most definitely have not lost track of -- not yet, at least. It is a scene in the fractal that appears when 24 parts of Z^(-1.1) are combined with 26.4 parts of Z^(-11) and (1/C) is added. The 8 loop-like elements surrounding the midget are typical of fractals that have been created by combining negative powers of Z and adding 1/C. I have never seen these loops in fractals that contain a positive power of Z, though most likely, if I tried hard enough, I could find some. In the parent fractal of today's image, the filaments extending from the buds terminate in rings, kind of like the finger-ring on the end of a window-shade string. This ring-like nature is reflected in the midgets lying in the area, as today's midget, where the rings are stretched into eggs, demonstrates. I named today's image "Minus-Minus Midget" because of the two negative exponents of Z that were involved in its creation. My first impression was to rate it at a 7, but then I thought I saw a trace of muddiness, and reduced the rating to a 6, which is still a bit above average, though a boringly common rating. The render time of 11 minutes borders on slow, especially for those with other tasks for their machines. But the 11-minute wait can be cut to a minute or so by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A sunny but chilly late autumn day passed uneventfully here at Fractal Central on Monday. The cats thought that the tempera- ture of 37F 3C was a bit chilly and the snow was still a bit too deep, but they did venture onto the path in the yard, which had been cleared but was still wet. After an hour or so, they came indoors to pass the rest of the day sleeping. Today appears to be a slightly-warmer repeat. The work is about average; the cats' mood is average; all else is about average. Most likely, except for the fractal I will find when the work is finished, the day will be forgettable. And never forget that the next FOTD will appear in 24 hours. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Minus-Minus_Midget { ; time=0:11:36.73--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-4.19038823132904300/+9.692158006020868\ 00/6.749878e+007/1/62.5/0.000196657495929342119 params=24/-1.1/26.4/-11/0/525 float=y maxiter=1700 inside=0 logmap=243 periodicity=10 colors=000930600930B40C80E90HC0JE0KG0MJ0PK0QN0SP0T\ Q0`Y0hc8pkGxqPzyXzzczzkzzqs8xm0zp3ssHhvh_ylPzuEzz4\ yz8uz9pzBkzCfzEczG`yC_sBYm8Xf6T_4ST1QN0PH0M90K30J0\ 0H00G00K00N00Q01T04X09`0Ec1Jf4Mi6Qm9VpBYsJYvQYyXYz\ cYziYzzYzzY0QT0PT0PT8PTGN`NN`VNebNciMbqMbyM`zM`nQY\ XVVE_S0cQ0`V0YY0Vb0Se0Pi0Nm8XcJeVTnNexEpz4zz0zz0zz\ 0zz1zz3zz4zz4Kz6Ez88z91zB0zC0zC0zH0zM0zP0zT0xY0u`0\ qe0mi0im0fq0cv1_y1Xz3Tz3QzBVyJYmPb`XePbiCim0pp0nm0\ nk0ni1nh4me8mcCmbGm`JnYKnVKnTKnQKnNKnMKnJKnHKnEMnB\ Mn9Mn6Mn3Mn1Mn0Mn0Mk0Qi3Vf4_e8cb9h`CmYGqXHvTKzSMzP\ PzNTzQYzTbyXfsYkm`pecu_eyThzNkzGmz9pz3sz0uz0pz0mz3\ hz9ezG`zMYcQTYXQSbMNhJHnEBuB6y89u6Bp4Ek3Mf1Nb0PY0Q\ T0SP0TK0VG0XB0Y60_10`00b03c3KeB`fKqhSzi_zk_zm_vn_s\ p_nq_ms_puXuvTyxSzzPzzNzzKzzHzzGzzCzzBzz8zz4zz3zz0\ zz0zz6zzEzzMzzKzzJzzHzzGzzEzzCzzBzzBzz9zz8zz6zz4zz\ 3zz1zzBzz9zz6zz4zz1zz0zz0 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 08-12-03 (The Second Scorpion [5])
by Jim Muth 08 Dec '03

08 Dec '03

FOTD -- December 08, 2003 (Rating 5) Fractal visionaries and enthusiasts: It's a busy Monday here at Fractal Central, so the discussion will be correspondingly short. In yesterday's discussion, I mentioned an element in the image that reminds me of a scorpion and inspired the name. Today's image is a close-up of that scorpion, which fills the center of the screen and faces the upper-right corner of the frame. (Perhaps I should have called it a lobster.) The curled-up tail of the scorpion is clearly visible, though a bit of imagination is needed to see the claws. The background has a theme of square rather than smoothly curving spirals, one of the more unusual types of spiral. Since I spent almost no time finding the image, and only a few minutes writing this discussion, I can rate the image no higher than an average 5. The 11-minute render time can be cut significantly by download- ing the completed GIF file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> A cold, windy Sunday here at Fractal Central produced moody cats who sulked around the house most of the afternoon. Two treats of tuna were needed to restore their spirits. I'm beginning to wonder how much tuna is too much. If we need to continue giving them so many tuna treats, the duo might grow bored with tuna and demand something like lobster. Well, I've got that work to finish, so I'd best start moving. Until next FOTD, take care, and keep those iterations coming. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ TheSecondScorpion { ; time=0:10:58.28--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.38011718899537150/-2.001815087683078\ 00/1599.36/1/-52.5000000000051159/8.14260464609972\ 701e-012 params=1.096/0/96/1000 float=y maxiter=10000 inside=255 logmap=176 periodicity=10 colors=000dKUeKUfKUgKUhKUhKUhKUhKUhKUhKUhKUhKUhKUh\ KUhKUhKUhLUhMUhNVhOWhPXhQYhRZhS_hT`hUaiVbjWckXdlYe\ mZfoYfoWfoUfoTfoRfoPeoOeoMeoKeoJdoHdoFdoEdoCcoAco9\ co7co6cn7bn7am7am7`m7`l7_l7Zl7Zk7Yk7Yj7Xj7Wj7Wi7Vi\ 7Vi8Uh8Uh8Tg8Sg8Sg8Rf8Rf8Qf8Pe8Pe8Oe8Od8Nd8Mc8Mc9L\ c9Lb9Kb9Kb9Ja9Ia9I`9H`9H`9G_9F_9F_9EZ9EZ9DaA8_9BZ9\ DX8FW8HV8JT7MS7OR7QP6SO6UN6WL5ZK5aI4cH4fG4hE3zD3zC\ 3zA2z92z71z82z93zA4zB5zC6zD7zE8zF9zG9zHAzIBzJCzKDz\ LEzMFzNGzOHzPHzQIzRJzSKzSLzTMzUNzVOzWPzXPzYQzZRz_S\ z`TzaUzbVzcWzdXzeXzfYzgZzh_zi`zjazkbzlczrezodzlczj\ czgbzdazbaz_`zX_zVazSczQezNgzKizIkzFmzCozAqz7sz3uz\ 5wz6zz7zz8zzAzzBzzCzzDzzFzzGzzHzzIzzJzzLzzMzzNzzOz\ zQzzRzzSzzTzzVzzWzzXzzYzz`zz_zzZzzYzzXzzWzzVzzVzzU\ zzTzzSzzRzzQzzPzzPzzOzzNzzMzzLyzKyzKyzIxzGxzExzCxz\ Awz8wz6wz4xz5wz6wz7wz8wz9wzAwzBwzCwzDvzEvzFvzGvzHv\ zIvzJvzKvzLuzMuzNuzNuzOuz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================

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FOTD 06-12-03 (Fractal farworks [5])
by Jim Muth 06 Dec '03

06 Dec '03

FOTD -- December 06, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a kind of freak. To begin, it is an 'evaporated' scene in a fractal created by a formula that I invented at random, using nothing but alternating 1's and 4's. In addition, the 'all-inside' picture has been rendered with the inside=fmod option, with the proximity set to 0.24177, a setting that is rather critical. The resulting image consists of dark zig-zagging arms highlighted by points of fiery brilliance. But strangely, the brilliant points exist only in the upper two-thirds of the image. The lower third is a dull black and blue. Near the center lies the ubiquitous midget, appearing much like an exploding skyrocket. This fireworks effect inspired the name "Fractal Farworks". The mis-spelling is intentional, representing both the infinitude of the universe of fractals and the way the word is pronounced here in the local area. After meditating on the image for several minutes, I could find no reason for rating it higher than the 5 which I assigned it. The render time of the parameter file is a moderate 6 minutes, which can be cut significantly by downloading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With snow and sleet falling all day Friday and the temperature hovering around freezing, the fractal cats had as pleasant a day as possible, sitting on their shelves by the windows, watching the birds outside scrounging for food. Their day ended with a treat of tuna. Snow is still falling this morning, with around 1 foot 30cm on the ground. I guess the cats will have a repeat day. As for me, I'm simply going to relax and watch the snow. In between snowflakes I might find a fractal. And if I do, which is a near certainty, the fractal will appear as tomorrow's FOTD. Until then, take care, and then take more care. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Farworks { ; time=0:06:10:15--SF5 0n a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotmix4 function=recip passes=1 center-mag=+2.03354144153070000/-0.028206890074231\ 47/30377.39/1/-89/1.78200502964909191e-010 params=14/-1.414/1/-14.14/-1.4/1e+100 float=y maxiter=1800 bailout=9 inside=fmod proximity=0.24177 logmap=yes periodicity=10 colors=0000UzzS`zMgzFoz9vzGozMizSbzYXzcQziKzjLzjMz\ kNzkOzlPzlPzmQzmRzmSznTznTzoUzoVzpWzpXzpXznWzmVzlU\ zkTzjSziRzgQzfPzeOzdNzcMzbLzaLzcNzdOzeQzfRzhSziUzj\ VzkXzmYznZzo`zpazqbzr_zrYzrWzsTzsRzsPztMztKztIzuFz\ uDzuBzu9zvZzvwzwrzwnzxizxezyazyXzzTzzOzzKzzGzzJzzM\ zzPzzSzzVzzYzz`zzczzfzzizzlzzozzrzznzzkzzhzzezzbzz\ _zzWzzTzzQzzNzzKzzHzzHzzHzzHzzHzz`zzbzzczzezzgzzhz\ zizzjzzkzzlzzmzznzzozzozzpzzqzzrzzszztzzuzzuzznzzh\ zzazzWzzSzzPzzMzzJzzFzzCzz9zz6zz3zz2zz2zz2zz1zz1zz\ 1zz1zz2zz3zz4zz4zz5zz6zz7zz7zz8zz9zzAzwAyrFxnKwjPu\ fUsaZqYcoUhmQmkMriOpgPneQlcRkaSi_TgYUeWVdUWbPX`KYZ\ GZYE_WC`UBaTCU`DMgDFnBEj00K9Cc8B_7AX69T58Q89PB9OD9\ NGAMJALLAKOAJRBITBHWBGZCF`CEcCDeCCdGDcKEcOFbSGaVHa\ ZI`bJ_fK_iLaeJcbHe_FgXEiUCkQAmN8oK7qH5sE3tB2uEAuHI\ vKQvNXwQdwTlwWstVqqUonUmkTkhSieSgbRe`Rd_Qf_PgZOiZN\ jYMlYLmXKnXJpWIqWHsVGtaZT } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 05-12-03 (Austral Astrals [7])
by Jim Muth 05 Dec '03

05 Dec '03

FOTD -- December 05, 2003 (Rating 7) Fractal visionaries and enthusiasts: To create today's image I added a tiny bit of Z^i to the Mandel- brot set and examined the East Valley area of the resulting fractal, which on the large scale is indistinguishable from the M-set itself. But though that tiny imaginary part makes no difference on the large scale, it does make changes on the smaller scale, especially in the area near the real axis. Today's image is one of a midget in the East Valley area of the M-set. The midget has been shifted and changed somewhat by the addition of the tiny imaginary part to the formula. But by far the greatest part of the effect of the image is a result of rendering the outside with the 'fmod' option. The blue background appears to be blended unusually smoothly for a 256-color GIF image, but a close examination will still reveal traces of color bands. Because of the extra effort I put into smoothing the background, I have decided to again reward myself with a rating of 7. After a few moments study, I named the image "Austral Astrals", which might be roughly translated as 'southern stars'. I had no good reason for choosing such a name. The words simply sounded good to me. Those who plan to run the included parameter file will find them- selves facing an 11-minute wait to see the image. Those who decide to download the completed image will see it faster. The GIF file of the image may be downloaded from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Thursday was cloudy and chilly here at Fractal Central. The cats managed about 30 minutes in the yard before the temperature of 36F 2C chilled their ears and brought them indoors to their window shelves. The traditional evening treat of tuna eased their chagrin. But this morning we have around 6 inches, 15cm of snow on the ground, and it is still snowing heavily in big fat 'quarter-pounder' flakes. The local weather experts are forecasting up to 16 inches 40cm by the time it ends later Saturday. The cats will not be happy about this. I'll be happy however, for despite my advancing age, I still enjoy watching the snow fall. And for some reason, fractals appear to look better in snowy weather. Until next time, take care, and I guess I'll be shoveling off. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Austral_Astrals { ; time=0:11:41.73--SF5 on a p200 reset=2002 type=manzpower passes=1 center-mag=+0.26761112108950750/-0.003830805561863\ 68/1.094852e+010/1/-5/0.00133 params=0/0/2/4.4e-006 float=y maxiter=2500 bailout=9 inside=0 proximity=0.04 outside=fmod periodicity=10 colors=000AVzAUzAUzAUyAUxAUwATwATuASuASsARrARpAQoA\ QmAPlAPkAOjAOi9Nh9Ng8Mf8Le8Kd7Jc7Ib7Ha6G`6F_5EZ5DY\ 5CX4BW4AV29U4AT5BS6BR7CQ8CP9DOAENBEMCFLDFKEGKFHKGH\ KHILIIMJJNKKOLKPMLQNLQOMQPNQQNQROQSOQTPQUQQVQQWRQW\ SPXRQXRQXRQXQQXQQXQQXPQXPQXPQXOQYOQYOQYNQYNRYNRYMR\ YMRYMRYLRYLRZLRZKRZKRZKRZJRZJRZJSZISZISZIS_HS_HS_H\ S_GS_GS_GS_FS_FS_FS`DT_FS_GS_HR_IR_KQ_LQ_MP_NP_PO_\ QO_RN_SNZUMZVMZWLZXLZZKZ_KZ`JZaJZcIZdIZeH_fH`gHehJ\ khKoiLuiMzkMyiNxhNtgOvfOueOtdPscPrbQqaQp`QpZRoYRoX\ SnWSnVSmUTmTTlSTlRUkQUkOVjNVjMViLWiKWhJXhIXgHXgGYf\ FYfEYbJV_NTWSRTWOQ_MMdKJhHFmFCqD9uBHoHOjNVeTa`ZeZ`\ hWciPbfQadRabSa`TaZU`XU`VV`TW`QX_OY_MY_KZ_I_ZG`ZEa\ ZAdXCaZE__FY`HWaIUcKRdMPeNNfPLhQJiSHjUEkVCmXAnY8o_\ 6p`4qY4nW4lU4iR4gP4dN4bL4_I4YG4VE4TA2RC4RD5RF6RG8R\ H9RJARKCRLDRNEROGRPHRRIRSKRTLRVMRWORXPRZQR_SRaTRbU\ RcWReXRfYRg_REYdEYdEYcFYc } END PARAMETER FILE=========================================

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FOTD 04-12-03 (Silver Journey [7])
by Jim Muth 04 Dec '03

04 Dec '03

FOTD -- December 04, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's discussion will be short, as I must get things wrapped up before the fifth storm of the century to appear this century arrives. At least that's the way the local media is presenting the coming period of unpleasant winter weather. Today's silvery image lies in the fractal that results when 0.39 parts of Z^5 are subtracted from 1.3 parts of Z^3. The 'tdis' outside coloring option created most of the sinuous silvery effect. The name "Silver Journey" was the first thing that came into my mind while I was contemplating the image. I will not concern myself with the question of where the name was located before I thought of it. When rating the image I was undecided between a 6 or a 7, and to do myself a favor, finally decided on a 7. The waiting time of 5 minutes to run the parameter file can be eliminated by down- loading the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday here at Fractal Central was mostly sunny but quite cold and blustery, with a temperature that barely reached freezing, and a wind that let no one forget the arrival of winter. The once-dynamic cats tested the outdoors only a few minutes before deciding that such conditions are best appreciated from their window shelves inside the house. In the evening we gave them a treat of tuna to ease their frustrations. Today is starting cloudy and just as cold, though the wind is gone. Snow and sleet are due later today. We'll see how the dynamic cats adjust. I'm going to adjust by finishing the small amount of work now on the shelf and getting any chores done before the predicted bad weather appears. If I finish early enough, I'll check the latest issue of "Skeptical Inquirer", which has sat unread on my shelf for several weeks. When tomorrow arrives, the next FOTD will appear regardless of the weather. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Silver_Journey { ; time=0:05:20.98--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=mandelbrotmix4 function=ident passes=1 center-mag=+0.36324468569947000/+0.001674684322820\ 00/2.470857e+008/1/115.00000007684983/1.2494980819\ 9409373e-006 params=1.3/3/-0.39/5/0/0 float=y maxiter=700 inside=0 outside=tdis periodicity=10 colors=000N3SL6VJ8XIAZGC`FEbDGdBJgALi8Nk7Pm5Ro4Tq7\ DW92AF6ILDPRLWXScb_jhfqmmxdbwWSwNHvE6v52v42m32e22X\ 14P06H5BL9GODKSHPVMUYSYaXbeagifknkprptvlothjscer_`\ qYXqXTqWPqVLrVHrUErUArU6sU2sU2sU2sW2tX7tYDuZJu_OuX\ ViV`YSgMQmAPpGOqMNsRMuXLwaKxgKzlLzkMOiNMgOKePIdQGb\ RE`RD_RJYROXRUVRZURcTRiRRnQRsPJiLC_I5RFBPJGONMNRRL\ VXKZaJbfIeeLgdOhcRibUjaXka_l`bn_eoZhpYkqXnrXpsVmqU\ jpTgnSemRblP_jOYiNVhbg8`h9YiBWjCUkDRlFPmGNnHKoJIpK\ GqLJoNLmONkQPiRSgTUeUWcWYbX_XU`SSaMQbHOcBMd6KbAJaE\ J`HJZLJYPJXSJVWJU_JTbJUaKU`LU`LU_MU_MVZNVYOVYOVXPV\ XPWWQWVRWVRWUSWUSXWYXYcX_hXanXcsZ`t_Yt`VtaStbPtcMt\ eJufGugDuhAui7uj5ukGokQjk`dkj_ktVjtTjtRitQitOitNht\ LhtKgtIgtHgtFftEftCetBet9et8cpAblCaiE`eF_bHZZJYWKX\ SMWOOVLQUHRTETSAVR7WQEYPKZPQ_OW`NaaNgbOceO`hOYkOVn\ OSqOPtPTrQWqRZpSboTenUhmVllWokXrjXuiSuhOufKXdGUbCS\ `8Q_ANZCKYEHXGEWIBVK8UM5T } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 03-12-03 (Basic Superstrings [6])
by Jim Muth 03 Dec '03

03 Dec '03

FOTD -- December 03, 2003 (Rating 6) Fractal visionaries and enthusiasts: One of the latest fads in physics is the theory of superstrings, or more recently, super multi-dimensional membranes, which twist and turn in an 11-dimensional spacetime, and somehow manifest in our everyday 4-dimensional spacetime as the various sub-atomic particles. This is supposed, or hoped, to be the beginning of the big breakthrough (yet another breakthrough) that will eventually lead to the holy grail -- a theory of everything that makes mathematical sense. Whether such a theory would make common sense is another story. It should be apparent that I hold little hope of this theory being the big one that would explain even physical, much less conscious, existence. I have seen too many breakthroughs come and go during the 40 or so odd years I have been following the latest trends in science. But breakthrough or not, superstrings are real. Today's image has captured a number of them encirc- ling a midget in a different part of the same fractal that held yesterday's image. I named the image "Basic Superstrings" because superstrings and supermembranes are currently looked upon as the most basic sub- atomic entities. The rating of a 6 is becoming boringly common, but it is the fairest rating I could give today's image. The render time of under 2 minutes is about equal to the time required to go on-line and download the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The temperature on Tuesday here at Fractal Central barely reached 40F 4C, while the winds continued unabated. Even the occasional burst of warm sun was not enough to lure the fractal cats outdoors. They spent another day indoors by their windows, watching the world go by. In the evening, I gave them a treat of tuna to ease their frustration. Now I must shift from fractal mode to work mode. But when the work is finished, I'll shift back into fractal mode. The results of that shift will appear as tomorrow's FOTD. Until then, take care, and stay fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Basic_Superstrings { ; time=0:01:50.45--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.78010197328101300/-0.143377273422810\ 70/2.749007e+011/1/14.9822749561698103/-0.145702029 params=7.5/-1.75/0.7/-7.5/0/525 float=y maxiter=300 bailout=9 inside=0 logmap=33 periodicity=10 colors=000J0YL3aN7cN9fPDhSFjSJlULqUPsWSuYWxYYz_az_\ czjjzsqzzxzzzzzzzzzzzzzchzFSz0Bz00u01s03q05n07l0Bj\ 0Dh0Ff0Hc0Ja0N_0PY0SW0UU0WS0YD0_00a05U0DN0NF0Y70fB\ 0qL0zW0zf0zm0zm0zm0zm1zm3zm5zm7zm9zmBzmDzmFzmHzmJw\ zLuzNszPqzSozNmzJmzFmzBmz7mzAmzKLzULzcLzmNzmNzmPzm\ PzmPzoLzqHzsDzuLzwUzxazyjzzszzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzqzzhzza\ zzfzzjzznzzjzzfzzazzYzzUzzPzzLzzHzzDzz9zz5zz1zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\ 0zz0zz0zz0zz0zz0zz0zz1zz3zz5zz7zz9zzBzzDzzFzzHzz7z\ z0zz0zz0zz0zz0zz0zz0zz0zz1zz7zzDzzLzzSzzYzzfzzlzzs\ zzzzzazzFzz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz9zz\ JzzWzzfzzszzzzuzzszznzzlzzzzzzzzzzzzzzzzzzzzzzzzuz\ zszznzzjzzfzzazz_zzPzzLzz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 02-12-03 (Harmonic Voltage [8])
by Jim Muth 02 Dec '03

02 Dec '03

FOTD -- December 02, 2003 (Rating 8) Fractal visionaries and enthusiasts: I have never learned to appreciate 'New Age' music. With a few exceptions, the genre seems to be 'over my head' (or maybe beneath me). And this is strange, because I most certainly do appreciate the traditional 'classical' music, which is approach- ing the verge of extinction, at least here in the USA. When hearing New Age music, I am inevitably struck by the way it appears to drone on and on in abject monotony. It sounds good for a minute or two but nothing interesting ever develops. Yet some people I speak to are enthralled by this music. They tell me it is the best thing to come along since music was invented. New Age music concerts are very well attended. Why then do I get nothing from it? Either the music is empty of meaning or it is filled with meaning which I cannot recognize. Most likely the truth, if an absolute truth exists, lies somewhere between these extremes. The experience of appreciating music is a co-operative effort shared by composer and listener. The composer places the seeds of enjoyment in his work, but it is up to the listener to supply the environment in which these might germinate into enjoyment. If a work lacks the seeds, it will quickly be forgotten. If a listener lacks the fertile soil in which a particular type of seeds might grow, the work will have no effect on him. I guess I'm in the latter class as far as 'New Age' music goes. Now what does this venture into music appreciation have to do with fractals? Well, the name of today's striking image from the M-Mix4 formula is "Harmonic Voltage", a title I borrowed from a computer-animation music video I saw recently on local TV. The visual part of the video was IMO spectacular, but the music that accompanied the animation was IMO bland to say the least. Surely, I thought, such spectacular images must inspire or be inspired by better music than this. Curiously enough, the fractal lady enjoyed the music but said 'ho-hum' to the visuals. I guess it's all in the mind of the beholder, much as some phil- osophers claim the entire real world is. Oh by the way, I really like today's image, which I have rated at an exceptional 8. The sinuous flames radiating from the central midget were produced by rendering the formula with the outside set to the 'tdis' option. One final note -- I wonder what today's scene would look like if it were 'evaporated'. To enjoy the image, run the included parameter file or download the image from one of the two FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Monday was partly cloudy and chilly, with a temperature of 50F 10C and the strong winds that the cats dislike. The duo spent most of the afternoon sitting by the window, watching the wind in the trees and the birds soaring by. They ventured outside for only a few minutes. Their moods were unusually bright for a day of confinement however, and no tuna was needed. Today promises to be similar, but even colder. It remains to be seen how the duo will react. My reaction will be satisfaction when the bit of work now on the shelf is finished. Until next FOTD, take care, and enjoy yourself. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Harmonic_Voltage { ; time=0:02:43.23--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.636639299894244/-0.4107349017976644/\ 8.656232e+010/1/-177.5/-0.000331809106303253276 params=7.5/-1.75/0.7/-7.5/0/525 float=y maxiter=1250 inside=0 outside=tdis periodicity=10 colors=000IDOFBNDBMBBMDAKDAJDAJD8ID8ID8HD7HD7FD7FD\ 7EE6DE6DE6BE4BE4AE4AE48E38E37E37F26F24F24F23F03F02\ F02F00F00F00D00F00I20K30M60O70RA2UB2VE2YF3_I3bJ3cM\ 4fN4iQ4kS6nU6qX6sY7v_7ya7zc8ze8zg8ziAzkAzoBzmAzkAz\ iAzgAzfAzc8zb8z_8zZ8zY8zV7zU7zR7zQ7yO7wM6wK6vI6vH6\ uF6uD4sB4r84r74q64q33o23o03n03m00n03n06o07o0Ao0Bq0\ Eq0Fr0Ir0Jr0Ms0Ns0Qs0Ru0Uu0Vv0Yv0Zv0aw0bw0ew0fy0iy\ 0jz0mz0nz0qz0rz0uz0vv2sq7rkDqfHoaMnXRmRVkM_jHeiBjg\ 6nf0se0yc0zb0wc0se0oe4jf7ffBbgEYgIUiMQjOKjSHkVDkZ7\ ma3me0ng0naFcXYVQoMKzDIz8Fz4Dz0Az07z06z04z04z04z03\ z03z03z02y02w02u00s00r00q00o00m00k00j00i00f00e00c0\ 0b00_00Z00Y00X00V00Y06Z0A_0Fa0Kb0Oe0Uf0Zg0bi0gj0mm\ 0qn0vo0zq0zu0zr0zq2zo3zn4ym7vk8ujAsiBqgDofFneHkcIH\ NcHOeHMYHSOcYQaXR_VUZTVXRXVQYUP_TOaRNbOMcMKeKJgJIi\ HHjFFkFDnEEmEEkDEjDEiDFiBFgBFfBFeAHcAHc8Hb8Ha8I_aI\ XZIVXHVVHUSFSQFRZEHZEHJDO } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 01-12-03 (Seasonal Wreath [8])
by Jim Muth 01 Dec '03

01 Dec '03

FOTD -- December 01, 2003 (Rating 8) Fractal visionaries and enthusiasts: Like so much of our current view of reality, fractals are non- intuitive. Before the theory of relativity, who could have thought that matter is a different form of energy, that electro- magnetic waves are transmitted by nothing, or that the present moment of time is not universal but unique to the individual observer? Before the quantum theory, who could have guessed that photons and electrons are incomprehensible things that can be seen as either waves or particles; or that, with a proper experimental set-up, it is apparently possible to change the past; or that the closest we can come to reality at the quantum level is the mathematical equations which describe it? Before fractals were discovered, who could have guessed that an expres- sion as simple as Z^2+C could lead to infinity? The world extends far beyond the part of it comprehended by an ant. It extends far beyond the part of it comprehended by the fractal cats. These lower forms of life (the cats would dis- agree here) lack the intelligence to grasp the vastness of exis- tence. But then there is man. Is our intelligence the highest form of intelligence possible? Is it sufficient to grasp the totality of existence? Apparently not. One-hundred years ago, we assumed that our local galaxy com- prised the entire universe. Then the telescope at the Mount Wilson observatory showed that we were hugely underestimating the vastness of the universe. In recent years we have been pon- dering an infinity of parallel universes combined into an infi- nitely more vast multiverse. Next, we might be thinking of an infinity of multiverses. And there are those 11 dimensions (up from 10) required for M-theory to make sense. How can we find a 'theory of everything' when our concept of 'everything' keeps growing? I sometimes feel that, due to the limitations of out intellectual apparatus, we are even today unaware of as much of existence as an ant going mechanically about its programmed chores. And artificial intelligence can be of little help, for we will design our computers to 'think' as much like ourselves as possible. If a computer actually were to start thinking in a truly new and original manner, we would likely fail to comprehend its unfamiliar logic, and assume it was malfunctioning. We would re-program it to 'think' more like ourselves. It is kind of discouraging. We are nearing the limits, and the limits are ourselves. 120 years ago, we thought we had discov- ered almost all there was to know; today it looks like we don't even know what we don't know, and even worse, because of our limited minds, we never will know. Oh, before I forget -- we have a fractal today. It is an 'evap- orated' scene in the fractal created by a whimsical formula of 1's and 4's based on the square root of 2. I named it "Seasonal Wreath" because it reminds me of the wreaths that decorate so many doors and windows at this time of year. I rated the image at an exceptional 8, which might be a bit liberal. But after almost three weeks of Mandelbrot images, it seems like a refreshing change. The render time of two minutes is well within reason, even though a download of the completed image might be a bit faster. That download may be found on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday turned out to be another near-average day here at Fractal Central, a bland day, slightly chilly, with little to tell about. The partly cloudy skies and temperature of 48F 14C were barely acceptable to the cats, who were outdoors only an hour. Their spirits were lightened, however, by the last of the left- over turkey. This morning is starting mild with promises of a pleasant day. But a cold front with high winds is due around midday. The cats dislike wind and cold, so we'll have to hope for the best for them. Until tomorrow, take care, and take life one fractal at a time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Seasonal_Wreath { ; time=0:02:17.81--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.32911156705464600/-0.065564664774447\ 56/15547.06/1/-67.5/1.6424422933e-010 params=14/-1\ .414/1/-14.14/-1.4/1e+100 float=y maxiter=1800 inside=bof61 periodicity=10 colors=000ZO`SUbL`dFffMd`TbV_aPf_JlZEmcDnhCnmBorAo\ w9r`VuEoqFlnFjkFghFedFbaF`ZFYWFWSFUPFRMFPJFMAAACFH\ 9FF6FD9JFBMGEQIGTJJWLL_MObOQfPTjRcnSmsUrwVzzWrxYhv\ Zbt_bsabrbbrcbqecpfcpgcoicnjcnkcmmclncloeinfgngenh\ cnianj_mkYmlWmnTmoRmpPlqNlrLlsJltHluFlrEfoEalEXiER\ fEMcEH`EBYE6VE1UI3TM4SQ5RT6QX8P`9OcANgBMkDLnEKrFJv\ GIyHJtNKpTLlYMhcNdhO`nPXs72lB3jF3iJ3hN3gQ4eU4dY4ca\ 4be4ah5_l5Zp5Yt5Xw5Wu6Vt6Ur6Uq7To7Tn7Sl8Sk8Rj8Qh9Q\ g9Pe9PdAObAOaAN`ANcEMeIMgLMiPLkSLnWLpZLrbKteKviKxl\ KZ4fa7dc9beB`gDZiFXkHWmKUoMSqOQsQOuSMwULrSKnRJjQIf\ PIkHaeFU_DMVBETCHSCKRCNQCQPCTOCWNCYMD`LDcKDfJDiIDl\ HDoGDqMLnRSkW_h`feenbju`etW`sSWrNSqJNpEIoAEn6Hl8Jj\ 9MhAOgBReCTcDWbEY`F`ZGbXHeWIgUJjSKlRLiPMgNNeLOcJP`\ HQZFRXDSVBTS9UQ7VO5WM3XK2XI3VH3TG4RF4QE5OD5MC6KB6J\ A7H97F88D78C87E87F87G96H96I96JA5KA5LA5MB4NB4OB4PA4\ QA4RA4SA4TA4TmCPs4UlBXeHZ } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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