January 2004 - Fractint - mailman.xmission.com

FOTD 11-01-04 (Half an Elephant [6])
by Jim Muth 11 Jan '04

11 Jan '04

FOTD -- January 11, 2004 (Rating 6) Fractal visionaries and enthusiasts: In the East Valley area of the Mandelbrot set there lives a herd of elephants. Each elephant stands astride its personal bud, guarding that bud from anything that might threaten it. In the cubic M-set two elephants guard each double bud. In the quartic set, there are three elephants per triple bud. And so it contin- ues into infinity, the elephants eventually merging into a haze of undifferentiated elephant stuff. But what of the Z^(1.5)+C Mandeloid? In this set, the same trend continues. Half an elephant stands guarding each half-bud. I have no idea what happens to the ele- phants' rear ends, but the front parts are there, complete with curled trunks. It took the MandelbrotBC1 formula to show a level of the parent fractal where these half-elephants are not broken beyond recogni- tion. Luckily, that level was found only 1.5 turns up the log- arithmic hyper-spiral. I named the image "Half an Elephant", most likely because half an elephant is better than none. Of course, a half-elephant is not as good as a whole elephant, but that's another story. When the time to do the rating arrived, I pondered the image and decided on a rating of 6, which combined with the render time of 10.67 minutes gives an overall value of 56. The GIF image is available for near-instant download on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather Saturday here at Fractal Central was very cold. All day, my digital thermometer hung around 10F -12C, which kept the cat duo confined very securely to the sources of heat. They needed only one minute on the porch to convince them that the outdoors was uninhabitable. In the evening, I presented them with a treat of tuna, which lifted their sullen spirits. Today, the regular work is pretty much caught up, but the fractal lady is thinking of a trip to look at 'antiques', (IMO, discarded junk), so I guess I'll tag along. But I'll be back in plenty time to find the next FOTD fractal. Until that next fractal appears, take care, and look for the other half. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Half_an_Elephant { ; time=0:10:40.43--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor center-mag=+0.15911535849239720/-0.002404932214412\ 98/1541.738/1/22.5/4.45664338766249557e-013 params=1.5/0/1.5/0 float=y maxiter=15000 inside=255 logmap=39 periodicity=10 colors=000R9YS9YS9ZT9ZU9_V9_V9`W9`X9aY9aY9bZ9b_9c`\ 9c`9da9db9ec9ec9fd9fe9gf9gg7gg8gf9geAgdBgcBgcCgbDg\ aEg`Ff_Ff_GfZHfYIfXJfWJfVKfVLfUMeTNeSNeROeRPeQQePR\ eOReNSeMTdMUdLVdKVdJWdIXdIYdHZdGZdF_cE`cDacDbcCbcB\ ccAdc9ec9ecAdbAcbAcaAbaAa`Aa`A`_B`_B_ZBZZBZYBYYBYX\ BXXBWWCWWCVVCVVCUUCTUCTTCSTCSTDRSDQSDQRDPRDOQDOQDN\ PENPEMOELOELNEKNEKMEJMEILFILFHKFHKFGJFFJFFIFEIFEIF\ EIFEImSNoQPqNRpOQoPPnQPmROlSOkSNjTNiUMhVLgWLfWKeXK\ dYJcZJb_Ib_Ia`H`aG_bGZcFYdFXdEWeEVfDUgCThCShBRiBQj\ APkAOl9Mk7Nl8Ol9Ol9PlAQmBQmBRmCSmDSmDTnETnFUnFVnGV\ oHWoHXoIXoJYoJYpKZpL_pL_pM`pMaqNaqObqOcqPcrQdrQdrR\ erSfrSfsTgsUhsUhsVitWitWjtXktYktYluZmu_mu_nu`ovZpu\ `qtbrtcssetsfurhvriwpfxocymazlZzkWziUzhRzgOzeMzgJz\ iIzkHzmHzoGzqGzsGzuFzwFzxFzyEzzEzzDzzDzzDzzCzzCzzC\ zzBzzBzzAzzLzzMzzNzzOzzOzzPzzQzzQzzRzzSzzTzzTzzUzz\ VzzUzzVzzVzzWzzWzzXzzXPPm } 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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Re: [Fractint] FOTD 09-01-04 (Fractal Ribbons [6])
by Guy Marson 11 Jan '04

11 Jan '04

At 01:29 11/01/2004 -0700, you wrote: >On Fri, 9 Jan 2004, Jim Muth wrote: > ... >number for a constant inside or outside colour would go). > ... > Like I implied, the problem isn't as fundamental as the atan >function itself. If you're bent on identical output for the same .par >file, then you can set the default max_colors to historical values. > Hi fractinters, here are a few examples on how to find the pretty rare midgets with "inside=atan": atan-a0, b0, c0 and d0 pars are starting pics with low magnification and low maxiter (80 or 160). Zoom-in until points of intersecting colours a visible.. (atan-a1, b1, c1, d1). Then one can double the maxiter while zooming into the pic, double maxiter again, and still zooming-in onto points of intersection.. and so on.. meanwhile on can change to "logmap=yes" .. (the final midget is +/- in the centre..) have fun.. cheers, Guy ****** atan-a0 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.758205/0.076935/1 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-a1 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75820548276543810/+0.07693499922059592/100 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-a2 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75820548276543810/+0.07693499922059592/4000 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-a3 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75820548276543810/+0.07693499922059592/160000 params=0/0 float=y maxiter=160 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-a4 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75820548276543810/+0.07693499922059592/3500000 params=0/0 float=y maxiter=160 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-a5 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75820548276543810/+0.07693499922059592/7.014636e+007 params=0/0 float=y maxiter=2560 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b0 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.75122/0/0.6666667 params=0/0 float=y maxiter=100 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b1 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.74967/-9.77836e-007/10 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b2 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.74967399804496800/-0.00000097783572361/200 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b3 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.74967282502444000/-0.00000058670143418/163934.4 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b4 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.74967152290777700/+0.00000000000000000/200000 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-b5 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-1.74967152290777700/+0.00000000000000000/7.5e+010 params=0/0 float=y maxiter=2560 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c0 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=0.251563/0/0.666 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c1 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=+0.25156256516781210/+0.00000000000000000/3000 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c2 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=+0.25166857146736680/+0.00009995654063451/60000 params=0/0 float=y maxiter=80 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c3 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=+0.25166949902248790/+0.00010019991308127/60000 params=0/0 float=y maxiter=160 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c4 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=+0.25166949349197440/+0.00010020051434159/4000000 params=0/0 float=y maxiter=160 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-c5 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=+0.25166949349197440/+0.00010020051434159/2e+009 params=0/0 float=y maxiter=2560 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d0 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.750518/-0.0200659/0.66666 params=0/0 float=y maxiter=160 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d1 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75051765447904200/-0.02006592913197069/1000 params=0/0 float=y maxiter=160 inside=atan periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d2 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75051765447904200/-0.02006592913197069/1000000 params=0/0 float=y maxiter=1280 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d3 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75051765447904200/-0.02006592913197069/3e+007 params=0/0 float=y maxiter=1280 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d4 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75051765447904200/-0.02006592913197069/2.503263e+009 params=0/0 float=y maxiter=2560 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 } atan-d5 { ; Version 2002 Patchlevel 3 reset=2002 type=mandel passes=1 center-mag=-0.75051765447904200/-0.02006592913197069/2.500003e+012 params=0/0 float=y maxiter=40960 inside=atan logmap=yes periodicity=0 colors=000<58>taJubJvbK<2>ydLzeLydL<55>642531421<2>100000001<56>Q_tQ`uR`\ v<2>SbyTczSby<61>000 }

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FOTD 09-01-04 (Fractal Ribbons [6])
by Jim Muth 11 Jan '04

11 Jan '04

FOTD -- January 09, 2004 (Rating 6) Fractal visionaries and enthusiasts: With today's image we return to fractal normalcy -- a rating of 6. The illustrated scene lies in the same parent that produced yesterday's image, and once again, one of the more exotic 'outside' options was used, this time the 'atan' option. I read somewhere recently, probably in a letter on the list, that the Fractint 'atan' function has an error somewhere in it. If so, it's a bit late now to correct it, since if this were done, images such as today's, which use the incorrect version, would no longer work. Of course, we could always save the incorrect version by giving it a new name, as was done with the 'cosxx' function. Or even better, we could give the correct version a different name. Today's image reminds me of the type of image that was so popular around 10 years ago, and resembled curled satin ribbons. I named the image "Fractal Ribbons" because of this resemblance. I rated it a 6 because, at least by my standards, it is a bit above average. I cannot say why I am staying with this particular parent fractal, which is giving me such a hard time. Maybe I want to prove that potential glory lies in every fractal, even the most humble. Well, I'll stay with the same fractal another couple days. If I find nothing in it by then worth a rating of 8, I'll give it up and move on. Today's image renders in only 4 minutes, making it a reasonable value for the time spent. Hmmm, maybe I'll start giving my FOTD images a 'value' rating. I could take the present 0-to-10 rating, divide it by the minutes needed to render the image, and multiply the result by 100. This would make today's image worth 150 value points. We'll see . . . The best value of all however is still downloading the completed GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> which can be done in a minute or so. The temperature reached 34F 1C here at Fractal central on Thurs- day, but clouds moved in by midday, making things too chilly for the sensitive whiskers of the fractal cats, who passed the after- noon curled by the radiator, sleeping peacefully. A bit of tuna in the evening made their day complete. This morning is start- ing cloudy and cold again, with a few flakes of snow in the air, and even colder air due by this evening. The fractal cats will not be happy about this. For me, today will be another forgettable day -- that is unless I find a fractal that rates an honest 10. Check back here in 24 hours to see if I succeed, but don't be surprised if I fail. Fractals that rate a 10 are as rare as dodo birds. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Ribbons { ; time=0:04:07.60--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-0.61045250190546770/-0.011003094073171\ 64/2128.036/1/-142.5/-5.97177099437296022e-011 params=1.2/-2.1/-2.1/-1.2/0/50/0/0 float=y maxiter=1200 inside=255 outside=atan periodicity=10 colors=000NjAMiALhAKgAJfAKeAKdAKcALbBLaCL`DM_OMZFM\ ZGNYHNYINXJNXKOXLOWQOWQPWRPWSPWTQWUQWVQWWRWYRW_RWa\ RWcSWdSWeSWfTWgTWhTWiUWjUWkUWlVWmVWnVWnVWoWWoWWpWW\ pWWqWWrWWsWWtWWuWXsWXtWXtWXuWXvWXwWYvWYwWYwWYxWYxX\ XyWXxWXwVWvVWuUVtUUsTTrTTqSSpSRoRRnRQmQPlQOkPOjPNi\ OMhOLgOLfNKeMJdMJcLIbLGaKG`KG_JFZJEYIEXIDWHDVHCUGC\ TGBSFARF9QE9PE8OD7ND7MC6LC5KB4JB4IA3HA2G81F92EA2DB\ 2CC3BD3BE3AF3AG49H49I48J48K57L57M56N65O65P64Q64R73\ S73T72U72V81W81X80X80ZA2_B3`D4aE5bG6cH7dJ9eKAfMBgN\ ChPDiQEkSGlTHmVInWJoYKpZLq`NraOscPtdQufRvgSufRtfQt\ fQsfPrfPrfOqeNpeNpeMoeMneLneKmdKmdJldJkdIkdHjdHicG\ icGhcFgcEgcEfdDie5lf9ogDrhFrhGrhHrhHrhIrhJrgJrgKrg\ LrgLrgMrfNrfNrfOrfPrfPreQreRreRreSreSreTrdUrdUrdVr\ dWrdWrcXrcYrcYrcZrc_rb_rb`rbarbarbbv`crbbocbldbheb\ efbbgb_hbYi_WjYUkWSlUQmRPnPNoNLpLJqIHrGFsEEtCCu9Av\ 7XwKWwJVwIUwHSwGRwFQwFzzz } 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 10-01-04 (The Last Try [5])
by Jim Muth 10 Jan '04

10 Jan '04

FOTD -- January 10, 2004 (Rating 5) Fractal visionaries and enthusiasts: Against my better judgement, I tried one more time to find a quality image in the parent fractal I have been exploring for the past several days. Once again I came up short. With a rating of an average 5, today's image is not bad, but it is not good either. This will be my final venture into this particular fractal. To emphasize this point, I have named today's image "The Last Try". The image is a harlequin kind of a thing -- patches of brilliant but unorganized color and apparently random shapes surrounding the usual central midget. The image was rendered in the traditional manner, with the inside set to 'zero' and the outside set to 'iter'. Some of the other options do as good a job of rendering the scene, but I used the traditional method because I wanted to emphasize how this particular area of this particular fractal 'really' looks. Of course, when working with fractals, the word 'really' is relative. Fractals are actually nothing more than numbers -- total abstractions. It is what we do with those numbers to make them register on our senses that creates the 'reality'. The numbers can be used to create sounds as easily as images. The numbers could also be used to create tactile impressions. It is harder to imagine how one might turn a fractal formula into something that can be tasted or smelled, but stranger things have happened. Today's image renders in 26 minutes. This, combined with the rating of 5, gives a total fractal value of 19. The image may be seen by running the included parameter file or by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Those who wish to feel, taste or smell the numbers will need to invent an appropriate means of doing so. With a temperature of 28F -2C, Friday was too cold for the cats' whiskers. They seemed quite happy to spend the day sleeping by the heat. This morning the temperature is 3F -16C, and though the sun has appeared, this kind of cold is far too severe for sensitive cats to be outdoors. They will certainly be satisfied with another day by the radiator and a dab or two of tuna. I have enough work waiting to keep me busy for a good part of the day. When the work is finished, I'll have time to find a fractal in a different fractal world. In 24 hours I'll return with the fractal I find. Until then, take care, and if in the southern hemisphere, keep cool. Otherwise, keep warm. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Last_Try { ; time=0:26:04.66--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.51767124083257100/+0.951548168001671\ 90/2041548/1/-27.5/2.17169040875320185e-008 params=1.2/-2.1/-2.1/-1.2/0/525 float=y maxiter=2700 inside=0 logmap=300 periodicity=10 colors=0000J00F00F00A005005001000000100A00F00J00F0\ 0A01A0550A10A10F00J00O00U00U00Z00c00h00l00l00q00v0\ 0z00z00z00h00O001100F00O00c00q00z00zz00z00z00z00z0\ 0z00z00z00z00z10z50zA0zF0zJ0zO0zU0zZ0zc0zc0zl0zq0z\ v0zz0zz0zz5zzFzzUqzclzlhzvczzZzzOzzJzzFzzAzz1zz0zz\ 0zz0zz0zzlzzzOzz0zz0zzOzzqzzzzzzzzzzzzzzzzzzzzzzzz\ zzzqzzhzzUzzJzz5zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zq0z\ O0z10z00z00z00z00z00z00z00z00z00v00l00h00Z00U00J00\ F00500100000000100A00O00Z00l00v00z00z00z00z00z00z0\ 0z00z00z00z00z00z00z00z00z00z00z01z05z0Az0Fz0Jz0Uz\ 0Zz0cv0hv0qv0vq0zq0zq0zq0zl0zl0zl0zl0zl0zl0zl0zl0z\ F0z00q00l00zl1UlAOlJFlUAlc1ll0lv0lz0cv0Zv0Uv1Ov5Jv\ AFqFAqJ5qO1qU0qZ0lc0lh0ll0lq0lv0hz0hz0hz0hz0hz0cz0\ cz0cz0cz0cz0Zz0Zz0Zz0Zz0Zz0Zz0hz0hz0lz0qz1vzAzzJzz\ Uzzczzlzzvzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 07-01-04 (Total Failure [2])
by Jim Muth 09 Jan '04

09 Jan '04

FOTD -- January 07, 2004 (Rating 2) Fractal visionaries and enthusiasts: Today's image rates a horrendous 2. It is one of the lowest rated images ever to have made the status of FOTD. And to make things worse, it takes almost an hour to render. Normally, this image would have been an instant victim of the delete key, but I included it among the honored FOTD fractals for two reasons: first, I wanted to demonstrate what, IMO, makes a fractal image bad; second, I had a bad day at the fractal keyboard. (Those who work with fractals have bad days, just like those who work with everything else.) The image is an 'evaporated' one in the parent fractal that results when some Z^(-1.2) is subtracted from some Z^(-2.1) and (1/C) is added. This parent fractal has within it far more potential than would be guessed by glancing at today's image. To prove the point, tomorrow's image will be another scene in this same parent fractal, and I guarantee the image will have a higher rating. I will not dwell at length on the deficiencies of today's image. The image speaks, (or does not speak), for itself. The ring- like features hold some promise, but the muddy, unorganized colors spoil anything that the rings might hint at. I guess the best thing to do with today's image is to consider it a reminder that the many FOTD images which rate a 6 are indeed a little above average. I gave little thought to naming the image, finally deciding on the discouraging name "Total Failure". Few will want to devote nearly an hour of computer time to rendering the failed fractal, but Paul is one of the few, and the completed GIF image will be available for download on his web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> as soon as he can get it posted. The temperature on Tuesday here at Fractal Central reached no higher than 36F 2C, and to make things worse, a snow squall struck at 2:30 pm, just as the cats were starting to enjoy their time in the yard. The sudden snow and burst of wind sent them scurrying to be let inside. The snow moved out within 20 minutes, leaving a dusting on the grass, and the sun returned, but by then the duo were safely settled by their radiator, where they spent the rest of the afternoon sleeping. This morning is starting sunny but windy and very cold, with a temperature of 18F -8C. These are not the conditions to make sensitive cats happy, so I guess we'll have to wait and see how the day goes for them. For me it looks like a fairly routine day. Until next time and a better fractal, take care, and if the truth were known . . . Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Total_Failure { ; time=0:50:11.74--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=-1.12301102275173500/+1.063120905547293\ 00/4820.856/1/125/3.20222112715207174e-011 params=1.2/-2.1/-2.1/-1.2/0/1e+100/0/0 float=y maxiter=1500 inside=bof61 periodicity=10 colors=000kNTlMRlKQmIOmHNnXLnDKoCIoAHp8FH`fFagCciA\ ek7gm2lt5hn8eiAbdD__FXVIUPLRKNOFQLAQK0SI5UH9WFDYEH\ _CLdBPc9Tk9We8Xb7X_6YW6YT5ZQ4ZM3_J3_G2`C1`90a1n560\ aC4dH8fMBhRFkWJm`MoeQrjUtjuxoXvu8vt9ut9ttAstArtBqt\ BptCotCnsDmsDlsEksEjsFisFhsGgyDcsGfmIihKlbMoYOrSQu\ NSwPVsQYpR`lSciTfeUibVlZWoWYjXZfX`bYaZYcUZdQZfM_gI\ _n7UhE_bKdXRjRXoMbtPcsRdsUerWfrYfr`gqbhqeipgjpijpl\ konloqmnsnnxqsunnrljoiflgbjeZgbVd`RaYNZWJSY3XUF`QR\ dNahJmlGxkFvkEtkDrkCqkBojAmj9kj8jj7hj6fh3hj5ek7cl9\ amB_nDYpFWqHUrJSsLQtNOuOMvQNvSOvUPvVPvXQvZRv`SvaSv\ cTveUvgVvhVweWwbXw_YwXZwV_xS`xPaxMbxJcxHdrLemPehTf\ cKfZ`gUdgPhhKlhFpiAti8sb7sX6sQ4rK3rD2r76p69o6Dn5Gl\ 5Kk4Nj4Qi3Ug3Xf2`e2cc1gb1ja0w`0ja1mb1ec1cZ1`d2Ze2X\ f2Ug2Sh2Ph3Ni3Kj3Ik3Gk3Hf6Hb9HZCIUFIQIIMLEJLIIOMIQ\ PITTIVWIY_I_bIbfIdmIfaNhURjMVlEZnCIw6boCalI`jO_hTZ\ eZYcdXahYaiW_iUZjSXjRWkPU } 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 08-01-04 (A Little Bit More [4])
by Jim Muth 08 Jan '04

08 Jan '04

FOTD -- January 08, 2004 (Rating 4) Fractal visionaries and enthusiasts: For today, I promised a better fractal from the same formula that created yesterday's image. Well, a fractal that rates a 4 is better than one that rates a 2, but I had hoped for something a little more better. Maybe the parent fractal really is nearly worthless, or maybe I simply failed to search far enough. For today's rendering, the outside has been set to 'fmod', with a proximity value of 2. This is somewhat of a program feature, rather than a pure illustration of what exists in the formula graph at that location. The fact that I needed to resort to it is a sign that the basic fractal is not all that impressive. I named today's image "A Little Bit More" because it is a little bit better than yesterday's. Another good feature is the render time, which is only 5 minutes -- marginally worth the effort. Hopefully, tomorrow will bring a better image. I should hope for an image that rates at least a 6, my run-of-the-mill rating. The completed GIF image of today's fractal may be downloaded from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The cold kept the cats indoors here at Fractal Central on Wednesday. Not appreciating the outdoor temperature in the mid 20'sF, (around -4C), the cats barely thought of going out. They passed the day instead by catching up on their sleep. Today is starting about the same. I expect the duo will have a similar day. My day includes work, which I had best get started on. Until next FOTD, take care, and have you tried the fractal weight-loss program? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Little_Bit_More { ; time=0:05:23.84--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+0.38849806591214900/+3.327863228966088\ 00/3866.667/1/-122.5/-5.61300450563351205e-011 params=1.2/-2.1/-2.1/-1.2/0/50/0/0 float=y maxiter=1200 inside=0 proximity=2 outside=fmod logmap=yes periodicity=10 colors=000wTjuRgsPeqNcmM`iMYfMVbMSZLPWKMSJJOIGLMEO\ QDQUCSXCV`BXdBZgAak9co9er8hv8jz7lz7pz8sz9vzAyzBzzC\ zzDzzHuwLpsPkoTflXah`XddS`hNXlJUpZSenRWzQMzTNxWOuZ\ PraQodRlgSeiWcfY`c_Z`aWYcTVeRSgOPiMMkONZQOMPPNPPNP\ QOPQOORPORPOSQOSQZXQh`QsdQzhQziPzjOxjNwkMukLtlKrlJ\ qmIonHnnGloFkoEipDhpCioDjnEkmFllFmkGnjHoiIpiIqhJrg\ KsfLteLudMvcNvcNudOuePufQugRtgRthStiTtjUtkVskVslWs\ mXsnYsnYtjZtfZtbZtZZuV_uR_uN_uJ_wLaxMbzNczOezPfzQg\ qMeeJdUFcICbMD`PD_SEYWEXZFWaFUeGThGRkHQoHPrINuIMyJ\ KzJJzJIpTPbbWOlbAuiVobniWzdQz`TtXWmTZfPa_LdTHfYGdb\ GcgGalG`qF_vFYzFXzFWzHVyIVvJUtKUqLTnMTkNSiOSfPRcQR\ `RQZSQYURXVSXWTWXUVYVVZWU_XT`YTaZSb_Rc`RdaQebPfcPg\ dUzGWzIXzKYzMZzN`zPaxRbwScuUdsWfrYgpZho`imbjlckndk\ odlpelqelrfmsfmugnvgnwhnxhoyioziozisxhvugzrfzoezle\ xhbpd_haX`YUUVRaTGhR6th7zy8xs7pm7hg7`a6TW6LR6RSCXT\ IaUOgVUmW_rXexYkzZqzXnyVl } 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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Plotting the Julia set only - not the filled Julia set
by Jonathan Marshall 07 Jan '04

07 Jan '04

Hi all, I'm a mathematics PhD student whose research involves Functional Differential equations, whose solutions can be analytically continued through iterating a functional argument - thus, they obtain solutions within a component of the Fatou set. The Julia set forms a natural boundary for these solutions. For my Thesis, I am wanting to generate images of just the Julia set, without anything from the Fatou set drawn - these can be in monochrome, the Julia set in Black, and all Fatou components in white. This is fairly easily done in the case where all the Fatou components are attractive basins, and I believe that FractInt can handle this case by adding in the search for attracting orbits. The tricky cases are where neutral fixed points are involved. Siegel disks in particular. Can Fractint detect and eliminate any pixels inside a Siegel disk? If so, how? A few images from the quadratic case would probably suffice, although it would be nice if it could handle more arbitrary rational functions. Any info would be appreciated - if Fractint can't do it, then I'll code up my own routine (though it'll be specific to particular cases if I do that). Cheers, Jonathan

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FOTD 05-01-04 (Octo-Something [4])
by Jim Muth 05 Jan '04

05 Jan '04

FOTD -- January 05, 2003 (Rating 4) Fractal visionaries and enthusiasts: With today's image I make one of my rare departures from fractal purity. Instead of showing an interesting scene rendered in the normal manner, the image shows a rather ordinary scene rendered in an unusual manner. Instead of consisting of equal iteration bands, the image was created by rendering it with the outside set to 'atan'. Instead of spending my fractal time searching for a scene, I spent it in fine tuning the color palette for the smoothest possible effect. The net result rates a 4, which is somewhat below average, and shows that, at least to me, an undistorted presentation of a fractal discovery is more important than pseudo-artistic fractal 'creativity'. I named the image "Octo-Something". An early version of the image had eight 'somethings' lying somewhere in it. But whatever it was that inspired the name has long since been lost. In the image, the perennial midget is offset to the right, and has little of the usual symmetry surrounding it. The lack of symmetry is partly due to the nature of the area and partly due to the unusually low magnitude. This low magnitude has one great benefit however -- it makes the image a very fast one. The 45-second render time is a welcome relief from the 1-1/2 hour wait that was necessary to see yesterday's image. The parent fractal, which was created by combining negative portions of Z^(-1.9) and Z^(-9.1) and adding (1/C), is a shapeless thing with three large bays and many smaller coves. Today's image is located in an unlikely area that I happened to zoom into by chance. It will probably take longer to download the image than to render it from the included parameter file, but those who choose to download will not be disappointed. The completed image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Though Sunday promised to be pleasant here at Fractal Central, the promise was not fulfilled. Instead of the forecasted sun and temperature close to 70F 21C, we had heavy clouds and a temperature of 46F 8C. The cats tried the yard only a few minutes before deciding that a day indoors would be more com- fortable. The traditional tuna treat restored their spirits. Today is starting even worse -- it is raining. Check back in 24 hours to see how the cats adapt, and when you do, you might even enjoy a better fractal. Until then, take care, and keep discour- agement at bay. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Octo-Something { ; time=0:00:45.53--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.99960116589275130/-0.228694138466237\ 50/117.874/1/50/-6.99683366800485373e-012 params=-1.9/-9.1/-9.1/-1.9/0/0 float=y maxiter=1800 inside=0 outside=atan periodicity=10 colors=000Ae`9gY9iW9kU9mR9oP9qN9rL8tI8vG8xEAzBhz9m\ z7hz5cz6Cz6Ex6Gv7It7Kr7Mo7Om8Pk8Ri8Tg9Ve9Xb9Z`9`ZA\ bXAcVAeTBgQBiOBkMBmKCoICqGCrFFrEClDAfC8`C6VB4PA2JA\ 0OB5TC9XCEaDIfENjERoFWsF_rGZrGZrGZqGZqGZqGZpGYpGYp\ GYoGYoHYoHYnHXnHXnHXmHXmHXmHXlHWlHWlIWkIWkIWkIWjIV\ jIVjIViIViIViIViGWiIVhKVhMVgNVfPVeRVdTVdUVcWUbYUa_\ Ua`U`bU_dUZfUYiTZgU_fV`eVadWbcWbbXcaXd`Ye_ZfZZfY_g\ X_hW`iV`jUajTbkSblRcmQcnOdoMdpNeqOfrPgsQitRkrSmpTo\ nUqlVojWmhXkfYidZgb_e``cZaaXb_VcYTcWRbUPaSN`QL_PJY\ OHXNFWLDVKBUJASI8RG7QF5PE3NC4OD5PD5QD6RD7SE7TF8UG9\ VH9WIAXJBYKBZLC_MD`NDaOEbPFcQGdRHeSIfUJgXKhZKhaNfV\ PdURbTU`SWZRYXQ`VPbTOdQNfOMeOLdPKcQJbRKaSLaTM`UO_V\ PZWQYXRYYTXZUW_VV`XUaYUbZTc_SdaRebQfcQgePhfOigNjhM\ kjMlkLmlKnnJooIppMquIpqEpmAoi6oe2ob8mZElWKkTPjQVhN\ `gKffHkeElfGlfImfJmfLmfMnfOnfPnfRofSofUofVpfXpfYpf\ _qf`qfbujbqfcmccj`cfXccUd } 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 04-01-04 (Arachnid [6])
by Jim Muth 04 Jan '04

04 Jan '04

FOTD -- January 04, 2004 (Rating 6) Fractal visionaries and enthusiasts: Last evening I heard an item on one of the local news outlets that caused me to stop and wonder. The news item claimed that, with 500 or so homicides in 2003, Chicago had the highest murder rate in the nation, while here in Baltimore, we had only 300 or so homicides, making us only 60-percent as violent. It sounds good until one realizes that the population of Chicago is around 3,000,000, while the population of Baltimore is close to 600,000. My calculations tell me that this gives Baltimore a homicide rate 6 times that of Chicago. I wonder whether this was local Chamber of Commerce propaganda or whether the news reporters actually did not know any better. When this kind of stuff starts annoying me, I turn to fractals for distraction, and in this case, I was distracted by today's image, which like yesterday's, is an evaporated one consisting only of 'bof61' inside fill. The image is a scene in the ghost of the fractal that results when various portions of Z^(-1.8) and Z^(-8.1) are mixed and (1/C) is added, then the whole thing is evaporated by raising the escape radius to one-googol. I named the image "Arachnid". I gave it this name when the dark filaments surrounding the ever-present central midget reminded me of a spider's web in front of a carnival-like display of colors. I rated the image at a 6, since IMO it's not really that great. Another drawback is the render time, which on my machine is over 1-1/2 hours, making a download of the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> the far better choice. But before rushing for the download, give Paul an hour or so to render and post the image. Saturday was warm or chilly, depending on which side of town one was located. Here on the northeast side, the temperature reached 52F 11C, which was mild enough to keep the cats happy; but a few miles to the south, the temperature reached 70F 21C, which would have made them ecstatic. As it was, the duo spent several hours in the yard, meditating and enjoying their senior years. My day went fair enough. Hopefully, today will be just as fair. Until next FOTD, take care, and stay fairly well. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Arachnid { ; time=1:36:43.82--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+1.12455703364229600/+0.172257651110892\ 40/1.987188e+009/1/-120/-0.000760825470566633966 params=1.8/-8.1/8.1/-1.8/0/1e+100/0/0 float=y maxiter=3600 inside=bof61 periodicity=10 colors=000CaZC_YDZYDYXDWWEVWETVESUFRUFPTFOSGNSGLRG\ KQCFPGJQJNRMQSPUSSYTV`UZdVahVdkWgoXjsYpx_mvYkuWitV\ fsTdrRbpQ_oOYnNWmLTlzRjIPiGMhEKgDIfBFdADc8Bb68a56`\ 34hzFc4Qg5Wn7_k6ci5gg4jd4nb3r`2uZ2vczveCviHvlMwpRw\ sWww`wzduxcsvbquaqR0nr_lpZjnYimXgkWejVchUbfT`eSZcR\ pflYbREb1F_6GXAHVEHSJIPNJNRJKVKH_LFcMCgM9lN7pO4taP\ IO2xQCnRLeSUXUcOVlFWu6ToAQiDNdGKZJHTMEOPDPODPNCPMC\ PMCPLBPKBPKAPJAPIAPIBRHCSGDTGEUFFVFGXEHYEIZDJ_DK`C\ Gj6LaCPUHTMNXES`6XcHTfRQi`NljKotHisIdrJ_qJVqKQpKLo\ LGoLGoMGoMIkLJhLLeLMbKN_KPXKQUKRRJTOJULJVIIXFIYCIZ\ 9IWDOTGTQJZNMcKQhHTnEWsCZxJXwQVvXTvcRujPtpOtkLufJu\ aGuXEvSCvN9vI7wD4w82w40w7Ct9OrBZpDjnFulIpjKlhNggPc\ eSZdUVbXQaZM_aHZcDXe9W`BXWDYRFYMHZHJ_CK_GOZJRZMUZP\ XZT_ZWbZZfZaiZelZhoZkrZnuZkq`hnafjbcgcaddZ`eWYfUUg\ RRhPOiMKjJHkHDlEAmC7nBBjBEgBHcBK`BNXBQUBTRAWNAZKAa\ GAdDAjcAibAgaBfaBe`Bc_Cb_ } 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 02-01-04 (Just For Fun [6])
by Jim Muth 04 Jan '04

04 Jan '04

FOTD -- January 02, 2003 (Rating 6) Fractal visionaries and enthusiasts: Fractals are for fun. True, they have other uses, and perhaps deep meanings that we are yet to fathom. They might even be a mathematical manifestation of God, but above all else, fractals are fun. And today's fractal is total fun. I was in a fun mood when I found it, and with its gaudy colors, the image looks like pure fun. The image is actually a scene in the fractal that results when various portions of Z^(-1.6) and Z^(-6.1) are combined and (1/C) is added. The formula, like the last two, is whimsical. (Most likely, tomorrow's FOTD will be a play on the fractions 1.7 and 7.1.) The parent fractal of today's image is a Mandeloid with four main bays, the easternmost of which appears the most critical, with lots of Mandel-buds and filaments that terminate in rings. Several disconnected features lie a small distance to the west and north of the main Mandeloid, but these play no part in today's FOTD. The midget in today's image is located near the point where the filament of an eastern bud intersects its terminal ring. To add a bit of 'zip' to the scene, I rendered it with the outside set to 'tdis'. Then I named the whole thing "Just For Fun", which, after all, is what fractals are the best at. The rating of a 6 is boringly average, though the render time of 3 minutes is thankfully short. And the image may be seen even faster by downloading it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Once we got our act together here at Fractal Central on Thursday, the day went very well. There was lots of sun and the temperature reached 50F 10C, just mild enough to keep the cats happy during their afternoon in the holly thicket. In the evening, and against my better instincts, I went to a New Year's dinner at the home of the Fractal Lady's brother -- the second outing in 24 hours. I would rather have spent the evening in search of fractals, but all went well and now, when someone tells me to 'get a life', I can reply that I have one. But today is starting rainy, the dinners are past, and the cats already look sullen. Check back in 24 hours to see how things turn out. Until tomorrow take care, and if searching for fractals is not 'having a life', then what is? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Just_For_Fun { ; time=0:03:00.43--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.62834596524853100/+0.561897474119188\ 30/32042.8/1/-35/-1.25182780807975291e-011 params=1.6/-6.1/6.1/-1.6/0/0 float=y maxiter=1000 inside=0 outside=tdis logmap=yes periodicity=10 colors=000zzNp`QndSlhVjkYho_fsbevdcsbbqa`o`_l_YjZX\ hYVfXUcWSaVR_TPYSOVRMTQLRPJPOIMNGKMFILABLCEKEGKFJK\ HLKJOKKQKMTKOVKPYKR_KTbKVfGUeIUdKUcMUbOUaPU`RU_TUZ\ VXVOVXSUYWT__S`bRafQcjPdnOeqNguMhvLivNhvPgvRfvTeuV\ dsXcqYbp_ana`lc_keZigYghXfjWdlVbnUapT_rSYzT`vSZsRX\ pRVlQTiQRfPPbPN_OMXNKTNIQMGNMEJLCGLADK89I4AK7BL9CM\ BDOEEPGFQIGSKHTNIUPJWRKXTLYWM_YN`_OaaPcdQdfRehRfhQ\ ghPhhOgfRfaUdZWbW_`VbZSdXJfVIiTHkRGnPFqNErLEoKDkKD\ hKCdKC`KCYKBUKBQJBNJAJJAFJACJ98J94K65J96IC6IF7HH7H\ K8GN9GQ9FSAFVAEYBE_CDbCCeDChDBjEBmFApFAtGFwGKxHPyH\ TzJXzL`zNLkONjPOhPPfQQeQRcQSbRT`RUZRVYSWWSXVTYTTZS\ T_QU`OUaNUbLVcKVdIgpMVdHJUC3H87J7AL7EN7HP7LR7OT7SV\ 7VX7ZZ7a`7eb7hd7lf7oh7sj7vk7wfBwbEwZHwVLxQOxMRxIVx\ EYxA`vC_tE_rFZpHZoIZmKYkMYiNYgPXfQXdSWbTW`VWZXVYYV\ W_VU`USbURcUPfQMiMKlIHoEFrBIqCKqDMqDPpERpETpFVoGYo\ G_oHanHcnIfnJhmJjmKvQItUK } 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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