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FOTD 13-04-11 (Patterns in Space [8])
by Jim Muth 12 Apr '11

12 Apr '11

FOTD -- April 13, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a departure from my usual fare of escape-time images. It was created by the type=dynamic formula of Fractint, a formula that draws time-discrete dynamic system images. I have done very little investigation into this kind of stuff, though today's image shows that I might have been unnecessarily neglecting these images. Who knows, these images, which form regular repeating but ever-changing patterns, could be used as the basis for some award-winning quilting. The name "Patterns in Space" describes today's image, which is a pattern filling the otherwise empty space of the screen. The rating of a new-scale 8 indicates that I consider the image to be notably above average. The calculation time of 53 seconds will pass in a flash when the unexpected 'passes' algorithm begins working. The trip to a Hal's currently active web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> or my own new site at: <http://www.crosscanpuzzles.com/Archives.html> to see the finished image posted there will be equally as brief. The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Tuesday began glumly with a steady rain here at Fractal Central. The rain ended at 10am, and the sun appeared at noon, but by 3pm the clouds moved back in, and the rain returned by sunset. The temperature of 55F 13C was reasonable, though it would have seemed more spring-like with more sun. The ever-present fractal cats had a typical cat day. Nicholas had a moment of excitement when he got his foot stepped on, but a few consoling words let him know that no harm was intended. The humans also had a routine day. More of the same is expec- ted tomorrow. Now that the FOTD web site is finally off the ground, I am considering what to do with it. I am presently considering a picture gallery of the fractal cats in action. Yes, the fractal cats are real living cats, not simply invented fictions to fill space in the FOTD discussions. The next FOTD will be posted in 24 hours. Until then, take care, and is that a Boltzmann brain lurking over there in the shadows? Cosmologists tell us that such entities might not be total fantasies. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Patterns_in_Space { ; time=0:00:53.39-SF5 on P4-2000 reset=2004 type=dynamic function=sin maxiter=750 center-mag=0/0/0.0518672/1.3333 params=125/0.05/1/3 float=y bailout=7 inside=16 logmap=yes colors=000Wz0az0gz0pz6vsNzig6WNTYamamz0pz0sz3sz8vz\ EvzB0zH6zKKzQazWpzYzasKzz00z00z00z00z00z00z00v0Uc0\ zz3zUH00T00g00vc0z0m00c03WiNQzTWzYazcgzimmpsavyNyz\ Bzm0za0zN0zB0gT0Hi00yY0zz0zzcz00HK00z00m00T008800N\ 00TE0YT0cg6ivKpzWszgczmQzpBps0cy0Tz0Hz08z00Nc00z00\ z00i00T00B00000z0z00000600g00a00Y00z0mz0HKBQHKaBTi\ 8WsNYyaYzpmUc806T0Ti0sz0zz0zW00a00g00m00p00v00z60z\ H0zT0zzTzzYzzczzizzpzvszsYzsHzp0zp0zc0zW6zNKzEWzKi\ sNvgTzWWzcgziszszzyzzzzyzzvizzHWz00z00z00z0Ez0az0z\ z0zz0zz0zz6zzQmzgWzYHzQ6zH0y80m00a0Uzc0Hc08m00Q00i\ 00z00z00z80zH0zTpzQ8zYYzz0zzNcizigzmgzpgzsgzyczzcz\ zczzm0zi0zgTz0zz0zz0zz0zz0zz8zzKzzWzaB0gH3mKBpQNvT\ WyYgzap00a06g0Bi0HmENpYTspYv0z00z0Bz0Nz0Yz6ivQvmgy\ 0vz0yz6yzNy00z00zN0ziEz000000m00K03Y0HiBWvQi0s00p0\ 0m8HiQgggcTcmWisYpzavE00N00T00a00g06m6KvHYzTmK0Ni0\ gszYz0000z00zN0ziEz0yYNz0 } END PARAMETER FILE=========================================

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FOTD 12-04-11 (Attack of the Spiral [New 6, Old 7])
by Jim Muth 12 Apr '11

12 Apr '11

FOTD -- April 12, 2011 (Rating New 6, Old 7) Fractal visionaries and enthusiasts: Today's image features a wild spiral, with more nooks and crannies than the maze of the Minotaur. Perhaps I exaggerated a bit when I named it "Attack of the Spiral", but some of its nooks look absolutely threatening, not to mention its crannies. The image rates a 6, which is equal to an old rating of a 7. This is the last day I will list both the new and old ratings. >From now on I will simply list the new rating. But remember that images with new ratings will usually appear better than expected. For some reason I tend to avoid spirals, perhaps because they are so trendy, especially with contest participants, but occa- sionally, as happened today, even I fall prey to the temptation to check a spiral for hidden goodies. The goodies in today's image are not exactly hidden however. They are there on the surface for the whole world to see. The parent fractal came about when I calculated the Z^(1.5)+C Mandeloid as it appears 0.5 levels up the complex logarithmic hyperspiral when no function is applied. This parent fractal appears as a Mandeloid rotated so that its main bud faces north. Both its main bay and main bud are squashed, with a lively broad spiral extending from the northeast shore line of the main bay. Today's scene is located at only a small depth in this broad spiral. The calculation time of 34 seconds is surprisingly fast. The finished image may be viewed without the task of calculation, on the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> My own web site may now be accessed at: <http://www.crosscanpuzzles.com/Archives.html> but the site is still in the early stages, and today's FOTD will not be posted for a day or so. Suggestions for improvement will always be considered, so feel free to make helpful comments. You might also check FL's puzzles on the site. She deserves a little return for all the work she has done helping to get the web site up and running. With a high temperature of 81F 27C, Monday was the warmest day of the spring so far here at Fractal Central in central Pennsyl- vania. In fact, it was warmer outside than inside. The fractal cats considered the temperature just right, but their relation- ship must have left something to be desired. In the evening they were spotted at opposite ends of the fractal hallway in full sulk posture, their sulks directed at each other. The day of the humans was busier than expected. Most of the extra work involved making last minute tweaks to the FOTD web page. The next FOTD image is due to be posted in 12 hours or so. Until then, take care, and what will be, will be, but we don't have to sit down and helplessly take whatever comes. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Atack_Of_TheSpiral { ; time=0:00:34.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.76882629/+0.54538622/266/1/180 params=1.5/0/0.5/0 float=y maxiter=288 inside=255 logmap=27 periodicity=6 colors=200LNUKMTJLSIKRHJQGIPFHOEGNDFMCELBDKADJ9CI8\ BH7AG69E68D56B44955B57D58F5AH5BJ5DL5EN5GP5HR5JT5KV\ 5MX5NZ5P`5Qb5Sd5Tf5Vh5Wj5Yl5Zn5`p5ar5ct5dt5ft5gt5g\ t5gt5gt5gt5gt5gt5gt5gt5gt5gt5gt5gt5gt5gt5gt5gt5gt5\ lt5lt5lt5lt5lt5lt5lt5lt5lt5lt5lt5lt5lt5lt5lt5lt5qt\ 5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5q\ t5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5\ qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt\ 5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qt5qtBqt9qt7qt5q\ t9qtBqtDqtFqtHqtJqtLqtNqtPqtRqtTqtVqtRmtRmtRmtRmtR\ mtRmtRmtRntRntRntRntRntRntRntQptRotRntRmtRltRltRkt\ RjtRitRhtRhtRgtRftSesSesSdsScrSbrSarSaqS`qS_qSZpSY\ pSYpTXoTWoTVoTVnTUnTTnTSmTRmTRmTQlTPmTOmUNmTOmTOmT\ PmTPmTQmTQmTRmSRmSSmSSmSSmSTmSTmSUmSUmRVmRVmRWmRWm\ RXmRXmRXmRYmQYmQZmQZmQ_mQ_mQ`mQ`mP_mQ`mQ`mQ`mRamRa\ mRamSbmSbmSbmTbmTcmTcmUcm } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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 PARAMETER FILE=========================================

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Re: [Fractint] Multifractal_10
by Jim Muth 11 Apr '11

11 Apr '11

At 02:22 AM 4/11/2011 +0200, Albrecht wrote: >Hi, > > >To be honest, how many users are able to produce own images with your >sophisticated formulas? >The multifractal "mini-program" to use your expression is capable of >the same complexity even with a single formula. To prove this I have >included two pars using one formula only. >Also, of course, it creates images that in NO other way can be >obtained by adding several complexities to one that supersedes the >single ones. >For me fractals are part of my leizure time and should be fun to play >with. It´s even possible to just take any five numbers, like a >blind monkey - see what comes out and zoom in. You will get an >absolutely unique image within minutes. > >What do YOU think? The images in your most recent posting are impressive indeed. But I am even more impressed by the complexity and potential of the Multifractal-10 formula. JIM

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Multifractal_10
by Albrecht Niekamp 10 Apr '11

10 Apr '11

Hi, Qte Jim: Myself, I wonder what all the excitement over Fractint's demise is about. I have never lost the awe and wonder that came and still does come with every new image. All of my present-day images are not located in the Mandelbrot set, the fractal that brought the first fractal excitement, but most are created by a small group of simple, short formulas. . One thing I have never been tempted to do is write one of those mini-program formulas with hundreds of lines, which in the end draws just another complex fractal image. I am more concerned with the things complex numbers do on their own, without human intervention.unqte Of course you´re right, Jim, from your point of view. Also for me fractals are a big mystery, which possibly never can be fully explained on our level of existence. Maybe to understand we will have to go to the level of elementary particles, if ever. Imagine that everything is one big "fractal" unity and on this level there are no distances between systems... To be honest, how many users are able to produce own images with your sophisticated formulas? The multifractal "mini-program" to use your expression is capable of the same complexity even with a single formula. To prove this I have included two pars using one formula only. Also, of course, it creates images that in NO other way can be obtained by adding several complexities to one that supersedes the single ones. For me fractals are part of my leizure time and should be fun to play with. It´s even possible to just take any five numbers, like a blind monkey - see what comes out and zoom in. You will get an absolutely unique image within minutes. What do YOU think? ========================start par========================= Phoenix1 { ; Single Formula ; Time 0.12.00 ; XP DOS Shell ; Apr,11 2011 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=exp/sin/exp/sin passes=t center-mag=+0.10921424934341250/-0.56152114679917940/28\ 6.2014/1/-52.4999999999994742/-4.57613114068777804e-013 params=-0.05825983458967864/0.3785210730307932/60000.32\ 565700023/25234.0506030602/151024.0204808192/384.327685\ 24288/384.00482000595/256.1007683/512.1007683001/768.20\ 07680082311 float=y maxiter=1024 inside=maxiter logmap=5 periodicity=0 rseed=-2436 colors=WWSKKWGKSOGSKGC84848KKGSCGSGGOGGS884ckg_c_Wc_KOC\ __Wcc_SWcOW_OSOS_WGSWGKKGS_KSWOSWKOWGOSGGC_ScSW_GO_COOG\ OG8CCGCOGKWCGWCCOCCCCC4GCKCOS8CS8COC4C448_gcOSKkkgKSK8G\ 8C8KCKKKOKCG8GKGCGC8KOCKWCKSGOWKSS88KSScKO_GKO8GSCGOCCK\ KW_KS_CKO4CO4CC4C4CK_8GW8CK8CG44COKKKOGKKCC8CCC8CGG4044\ 8C804400GK84CGGOO8GG48G4840444880800408KWGGWCCS8GOCGK88\ G88C44G408004ggkcccWWWSSSKKKGGG888444000<12>000<4>000KK\ 8OOG_SWc_cC88OKCKGKGCCC84KGGG4COKGccgkokSKSc__G8GgggSOC\ GG4SOGcWcC48SKCSSKSSGkgkGSSKWW4C88GCkkkgkkW_WKKGOOKSOS_\ W_WOWWSSOKOW_cSO__Wc__cSOOGC8SKWKGOWWc_WWWO_C8G048SSO8C\ 4844KG8GCGkoo_ccgkgCG4CKG_ocSWWOSSGKCgko_Wg___SSWKKSKOO\ 4CKWW__S_WOSWOG440COWSOWWSWOOWOOSGGK8KSOKWKKOOKSGG884Cg\ oocggKSOcgkGOKCKCWScOS_W__OWWSWS8C8KK_WS_S__OWSKOS8GK88\ OSS_OO_OOOOOCCCGGK_ } Newton { ; Single Formula ; Time 0.06.49 ; XP DOS Shell ; Apr,11 2011 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=exp/sin/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.8857805\ 8618804789e-016 params=-0.05825983458967864/0.3785210730307932/70000.32\ 595700023/35234.0506030602/151024.0204808192/384.327685\ 24288/384.00482000595/256.1007683/512.1007683001/768.20\ 07680082311 float=y maxiter=1024 inside=maxiter outside=tdis logmap=2 periodicity=0 rseed=-2436 colors=200432<20>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<\ 3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<6>DDDFFF\ HHH<10>___aaaccc<3>iiijjjlll<3>sss<25>BBB999777<2>22200\ 0012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211 } Please use the formula file from my previous mailing. Sincerely, Albrecht

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FOTD 11-04-11 (Split Personality [New 8, Old 8])
by Jim Muth 10 Apr '11

10 Apr '11

FOTD -- April 11, 2011 (Rating New 8, Old 8) Fractal visionaries and enthusiasts: Today's image is an improved sample of the type of minibrot that appeared in yesterday's FOTD. It is located rather deep on the southern side of East Valley of the Mandelbrot set, so deep in fact that it requires arbitrary precision math, which increases the calculation time by a factor of around 1500. But, at least in my opinion, the extra time is worth the effort. The image is an obvious example that not all minibrots at this depth are surrounded by little more than concentric circles of elements. The outer parts are obviously characteristic of the elements in East Valley, while the inner part shares the sharp spikes of a scene on the main spike. The minibrot at the center is not fully resolved. I left it un- resolved to improve the spacing of the color bands. The name "Split Personality" comments on the schizophrenic mix- ture of East Valley and main spike features surrounding a single minibrot. The rating of a new 8 is equal to the old rating of an 8. The calculation time of a lengthy 44 minutes is perhaps more time for some than the image is worth. But the wait may be avoided by viewing the finished image on the active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD site may be accessed at: <http://www.Nahee.com/FOTD/> The address of my new FOTD web site will be posted in tomorrow's FOTD. The clouds continued here at Fractal Central on Sunday. The temperature of 59F 15C was about normal, but without sun the day brought little impression of spring. The fractal cats got into a spat during the afternoon, leaving Nicholas with a scratch on his head. A half-hour later all was back to normal however. The humans had an uneventful day, which is the way we like it. Most of the time was spent fine-tuning the new web site, a process that most likely will never be finished. The next FOTD will be posted in 24 hours. Until then, take care, and I'm waiting for the government to grant me equality, but I'm not sure what I want to be made equal to. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Split_Personality { ; time=0:44:14.38-SF5 on P4-2000 reset=2004 type=mandel center-mag=0.26758003792428\ 46212227875/-0.0039097831278057311114401/8.87e+020 params=0/0 float=y maxiter=5700 inside=0 logmap=2456 periodicity=6 colors=000GK_HK_IKZJKZKKZLKYMKYMKXNKXOKXPKWQKWRKVS\ KVTKVUKUVKUWJTXJTYJSZJS_JS`JRaJRbJQcJQdJQdJPeJPfJO\ gJOhJOiINjINkIMlIMmIMnILoILpIKqIKrIKsIJtIJuIIuIItI\ IsHHrHGqHGpGFnGFlGEjGEhFDgFDeFCcECbEB`EBZEAYDAWD9U\ D9TC8RC8PC7PC7OC7RE7UG7WI7ZK7aM7cO8fP9iQAkRAmRAkRA\ iQAgPAeOAcMAaKA_JAYJAWJAVIAVIAWIAWIAWHAXH9XH9XG8YG\ 8YG7TF9WE8YG7`J7bL6eN6gQ5jS5lU4oX4qZ3s`3q_4o_4n_5l\ _5jZ6iZ6gZ7eZ7dY8bY8`Y8_Y9YX9WXAVXATXBRWBQWCOWCSR9\ NWCI`FDeI8jL4uQ3rO3oN3lM3iK3fJ3cI3`H3YF3VE2SD2PC2M\ A2J92G82D72A5274243101222333443554664775885996AA6B\ B7CD8DE8FL`hoWzzUtqQrmSphUndVl_XjWZhS`fNadJcbEe`Ag\ Z6hY9fYBeYDcYGbYIaYK_YNZYPYXRWXUVXWTXYSX`RXbPXdOXf\ NUbNRZNOVNLRNJNNGJNDFNABN77N54N43R43U43Y43c43m43z4\ 3z43zDKzLizOkzRlzUnzXoz_pz_nz_lz_kz_izZhzcXecWgcUi\ cSkcRlcPnmOpmMrmFumHtvJtzLswNzwPzwQzrmzvmzzmzzmzzm\ zzmzzmzzmzzmzzmzzmzzmzzmz } END PARAMETER FILE=========================================

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FOTD 10-04-11 (Star of Something [New 4, Old 6])
by Jim Muth 10 Apr '11

10 Apr '11

FOTD -- April 10, 2011 (Rating New-4, Old 6) Fractal visionaries and enthusiasts: I have seen rumors floating around the area that Fractint is dead. Well, maybe it's not the program itself that is supposed to be dead, but at least the Fractint list, where the traffic sometimes slows to nearly nothing. And I also see regrets about the vanished 'good old days', when every new image was an object of wonder and every new scene in the Mandelbrot set, a major discovery. Myself, I wonder what all the excitement over Fractint's demise is about. I have never lost the awe and wonder that came and still does come with every new image. All of my present-day images are not located in the Mandelbrot set, the fractal that brought the first fractal excitement, but most are created by a small group of simple, short formulas. One thing I have never been tempted to do is write one of those mini-program formulas with hundreds of lines, which in the end draws just another complex fractal image. I am more concerned with the things complex numbers do on their own, without human intervention. A number of years back I experimented with the black-square- white-square capability of Fractint, which divides the screen into a checkerboard pattern and draws pseudo-multi-layered images like those created by some of those 'other' Windows-based fractal programs. But like what happened with the old Fractint 3-D transforms, my interest in the black-white checkerboard soon waned. All I saw was double exposures. So how can I regret the passing of the 'good old days' when fractals were new? Here at Fractal Central, the old days have never departed, and every fractal still is new. (If this were not true, what has kept the FOTD going for 14 years?) As for today's image, it is a scene in the Mandelbrot set, at just about the limit of the range of the conventional math routine. It is located on a filament on the northwest shore line of the main bay, just beyond the tip of the spike of a minibrot. The rating of a 4 on the new scale is equal to a 6 on the old scale. The calculation time of one second is insignificant. The name "Star of Something" refers to the star-like appearance of the pattern surrounding the central minibrot. The finished image is available on the FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> The address of my new FOTD web site will be announced April 12. As suspected, an antiquing trip did erupt on Saturday, which explains the lateness of today's FOTD. The weather on Saturday was cloudy and chilly, with a temperature of 48F +9C. With no one around FC to keep the fractal cats occupied, they spent most of the day doing what cats do best. They slept. The next FOTD, a much deeper and improved version of today's image, will be posted in about 8 hours. Until then, take care, and every person's idea of what made the 'good old days' so good is different. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Star_of_Something { ; time=0:00:01.43-SF5 on P4-2000 reset=2004 type=mandel center-mag=-0.6960909132026\ 418/+0.4750231045822381/1.412646e+013/1/-87.3/0 params=0/0 float=y maxiter=1800 inside=0 logmap=286 periodicity=6 mathtolerance=0.05/1 colors=00050I50J50K51L52M53N54O55P56P57P58P6AQ7CR8\ ES9GVAIYAJ_AKaALcAMeBNgCOiDPkEQmFUoGXqH`sIbtJdwKcz\ L_zKazIUqFKhDGZCEPBEFAGF9IF8JF7LFANFFPAKR5PS1U_CZg\ NcoYhvhmrZroQvkHzh8vdCr`GmYJhUNcQRZNUUJYPFaLCdIFZQ\ IUYLOeOJmRDuU8hNAWHCJBE65GB9HFDHKHHOLHSPHXTH`XHe`H\ idHmhHrlHvpHzsHvpIsmJpjKlhLieMfbNb_O_YPXVQTSRQPSNN\ TJKUGHVDFWCN_CUcCagChkConBniAme9ma8lY7lU6kP5kL4jH3\ jD2i91i53g65f77e89c9BbADaBF`CGZDIYEKXFMWGOUHQTISSJ\ TRKRLBPF3OK9NOFNSKMWQL`WLd`KhfKlkIecGZXESQCLJAECBH\ ABK9CN8CP7DS6DV5EX4E_3Fb2Fd1HVTJMtMNpOOlROhTPdWQ`Y\ QX`RTbSPeSLgTHiTDjZKkcRkhYlmdlrkmninjgogfpcdq_brXa\ sT_tPYtMXeM`SMdEMh0MlQIknFjpGdrGZsGTuHNvHHxHByH6tG\ 8oGAkGBfFDbFFYFGUEIPEKLELODMQCNTBOVAOX9P_8Qa7Rd6Rf\ 5Sh4Tk3Um2Up1Vr0Wt0Wr8TqGRoOPnWNmcKkkIjsGizEhxGhzI\ gzJgzLfzMfzOezQezRdzTdzUezTezSezSezRezRezQfzPfzPfz\ OfzOfzNfzNezUcz`bzgaznUzi } END PARAMETER FILE=========================================

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Re: [Fractint] MultiFractalZ
by JackOfTradeZ＠comcast.net 09 Apr '11

09 Apr '11

. They are awesome! The complexity is amazing - try zooming in. Too bad they take too long to generate, and so many parameters with complex numbers; I would like to try animating them but I dont think it can be done realistically. :( Cheers .

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Multifractal_10
by Albrecht Niekamp 09 Apr '11

09 Apr '11

Hi, this ends the series of multifractal mails. As I think, the Fractint Forum is dead- the lethal dose possibly was that "spam assasin", I dont expect any feedback. I´m doing this for myself and in order to have the finalization of my multifractal project stored in the fractint archives. A few words though about multifractal_10. It is the final version, it handles 8 basic fractal formulas and combines ANY 5 to one multifractal image. (1) Secant (Mike Wareman) (2) Mandel (Special version Puskas Istvan) (3) Bees (Ray Girvan) (4) Julia (Special version Puskas Istvan) (5) Many mods (Linda Allison) (6) Phoenix (Mike Wareman) (7) Newton (Special Version Puskas Istvan) (8) Spiderjul (John Horner). An easy tweak is real(p2) (Z-screen), just list 5 numbers of above list in front of the dot. Multiple entries of the same number or any other combinations are possible. To get the basic image just use one number followed by 4 zeros. The sequence of the five numbers defines following: Shape - outside - inside1 - inside2 - inside3. To activate S.Gallet´s "Lake Effect" type "1" in front the dot image(p5) and after the dot 6 digits as stated below. I did some exploring and testing, did not detect any fractint error. Exploring cant be complete. there are far too many possibilities, found that any combination delivered an image ready to zoom into. Inputs Multifractal_10: ; ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ;0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2: 2digits_many-mods 2digits_phoenix 2digits_spider ; 1digit_shapereset:0_no 1_dblmandel 2_iter-reset 3_both +5_warp ; 4digits reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 5digits_colour(bailout) number ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) 2digits_newt 4digits_colour1, 5digits_colour2 5digits_colour3 ;imag(p3) shape : factor (fn1), 5digits_colour4 6digits_colour5 ;real(p4) outside: factor (fn2), 4+1digits_bord-out 4digits+fract_bord-in ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2(7)_bord-out 3(8)_bord-in ; 5digits_factor3 (fn4) 4digits+fract_border3 ; optional: 1_lake effect, 2digits_frquency 2digits_level 2digits_ampl ;fn(1) shared by many-mods+bees ==================start par=============================== MFR345o { ; The Big Circle - basic shape ; Time 0.2.0 ; XP Dos Shell ; 1600/1200 ; Apr 7th, 2011 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=0.0016085/-0.00563554/0.5690132/1/-90/3.8857\ 8058618804789e-016 params=-0.05825983458967864/0.3785210730307932/15367.64\ 595767025/14235.4911030602/152048.0404808048/384.160489\ 4048/384.00482000595/256.1007683001/512.1007683001/768.\ 1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=200034022000<8>IF9KHAMJBOLCQMDSOE<8>icNkeOmfP<3>\ unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<2\ 5>C00A00800<3>000<11>LLLNNNPPPQQQSSSUUU<6>fffgggiiijjjl\ ll<3>sss<25>BBB999777<2>222000012<22>0_k0am0bo0cq<3>0jx\ 0kz0jx<27>056 } Phoenix { ; Big Circle Zoom ; Time 0.7.11 ; XP Dos Shell ; 1600/1200 ; Apr 7th, 2011 reset=2004 type=formula formulafile=mfr.frm formulaname=multifractal_10 function=sin/exp/exp/sin passes=t center-mag=-1.50145448596800800/+0.10016964702423030/18\ 65.617/1/75.0000000000048601/-6.20805490347819955e-012 params=-0.05825983458967864/0.3785210730307932/15367.64\ 595767025/14235.4911030602/152048.0404808048/384.160489\ 4048/384.00482000595/256.1007683001/512.1007683001/768.\ 1007683001 float=y maxiter=3071 inside=maxiter outside=tdis periodicity=0 rseed=-2436 colors=200034022000<8>IF9KHAMJBOLCQMDSOE<8>icNkeOmfP<3>\ unTwpVxqWzsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<2\ 5>C00A00800<3>000<11>LLLNNNPPPQQQSSSUUU<6>fffgggiiijjjl\ ll<3>sss<25>BBB999777<2>222000012<22>0_k0am0bo0cq<3>0jx\ 0kz0jx<27>056 } FRM:multifractal_10 { ; Albrecht Niekamp Jan2005 ; le=0 z=pixel da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+11111 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==4)+(d==5)+(d==8)+(d==9) d4=d3==0 vb=d>5 sc=d==2 mo=d==6 px=d==7 ab=px+(d==3)+(d==5)+(d==9) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>1 sc1=d==2 mo1=d==6 px1=d==7 v1m=mo1+px1 v1j=d>7 dd1=v1j+(d==4)+(d==5) ab1=px1+(d==3)+(d==5)+(d==9) d=trunc(dd/100) dd=dd-d*100 ex2=d>1 sc2=d==2 mo2=d==6 px2=d==7 v2m=mo2+px2 v2j=d>7 dd2=v2j+(d==4)+(d==5) ab2=px2+(d==3)+(d==5)+(d==9) d=trunc(dd/10) ex3=d>1 sc3=d==2 mo3=d==6 px3=d==7 v3m=mo3+px3 v3j=d>7 dd3=v3j+(d==4)+(d==5) ab3=px3+(d==3)+(d==5)+(d==9) d=dd-d*10 ba=imag(p5) mi3=trunc(ba) dd=(d>1)+(mi3>1) ex4=dd==2 sc4=d==2 mo4=d==6 px4=d==7 v4m=mo4+px4 v4j=d>7 dd4=v4j+(d==4)+(d==5) ab4=px4+(d==3)+(d==5)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 dm=(d==2)+(d==4) ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex1+ex0+ex2+ex3+ex4 ; d=real(p3) dd=trunc(d) da=(d-dd)*10000000000 pp=trunc(dd/10000) ba1=dd-10000*pp ba2=trunc(da/100000) ba3=da-100000*ba2 ; d=imag(p3) sfac=trunc(d) da=(d-sfac)*100000000000 ba4=trunc(da/1000000) ba5=da-ba4*1000000 ; d=real(p4) ofac=trunc(d) da=(d-ofac)*10000000000 bh=trunc(da/100000)/10 bl=(da-bh*1000000)/10 bs=bl/2 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) da=round((d-dd)*10000000000) d=trunc(dd/10000) dd=dd-d*10000 bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/1000) dd=dd-d*1000 bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/100) dd=dd-d*100 bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=trunc(dd/10) dd=dd-d*10 bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) d=round(dd) bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5) ; d=da p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 dp=p6+p0/100 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=d==3 fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=d==3 fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; if (mi3==1) d=(ba-mi3)*1000000 fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet d=d-fr*1000 lv=(trunc(d/100))/100 d=d-lv*10000 am=d/100 u=real(rotskew*pi/180) t=exp(-flip(u)) bo=1/real(magxmag) q=bo/0.75*imag(magxmag) dd=tan(imag(rotskew*pi/180)) da=2*q*t rs=2*bo*(dd+flip(1))*t zz=center+(-q-bo*dd-flip(bo))*t z=z-zz d=imag(conj(da)*z)/imag(conj(da)*rs) le=d<=lv if (le) dd=lv-d z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs endif z=z+zz else da=(ba-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=d==3 fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 endif ; if (vb) if (d3) if (ab) z=z*le+pixel*(le==0) ;Spider c=p1 else z=z*le+pixel*(le==0) c=p1 ;newton endif elseif (ab) c=z ;Phoenix z=z*le+pixel*(le==0) else c=0.4*log(sqr(z^mm)) ;many mods z=0 endif elseif (d3) if (ab) c=p1 ;Julia z=z*le+pixel*(le==0) else ;bees c=p1 z=z*le+pixel*(le==0) endif elseif (ab) c=z ;Mandel z=0 else c=z ;Secant z=z*le+pixel*(le==0) endif t=0 bo=|z| p=pp z0=p7 zold=(0.0,0.0) cb=p9 ba=bb0 : if (tt) t=t+1 if (ex0) ex0=t<mi1 if (bo>bs) u=2*(fn1(t/sfac)) ex0=0 if (ir0) t=0 endif if (d4) z=z*u if (mo) c=0.4*log(sqr(z^mm)) else c=pixel endif else z=z*le+pixel*(le==0) cb=p9*u c=p1*u p=pp*u endif tt=tt-1+ex0 endif elseif ((ex1)&&bo>bl) if (bo<bh) d3=dd1 ba=bb1 ab=ab1 ex1=0 tt=tt-1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif if (ir1) t=0 endif if (d3) vb=v1j if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif else vb=v1m if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo1) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) ab=ab2 d3=dd2 ba=bb2 ex2=0 tt=tt-1 if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif if (ir2) t=0 endif if (d3) vb=v2j if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v2m if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo2) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) ab=ab3 d3=dd3 ba=bb3 ex3=0 tt=tt-1 if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif if (ir3) t=0 endif if (d3) vb=v3j if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v3m if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(z^mm)) endif endif endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) ab=ab4 d3=dd4 ba=bb4 ex4=0 tt=0 if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (d3) vb=v4j if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif else vb=v4m if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif if (mo4) c=0.4*log(sqr(z^mm)) endif endif endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Quasinewton Puskas Istvan z2=p*z*z z=z-z1/z2 endif elseif (ab) z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman zold=z z=z1 else z2=fn1(z)+c ;Many_mods Linda Allison z1=cos(z2) z=c*(1-z1)/(1+z1) endif elseif (d3) if (ab) z2=z*z ;Julia Puskas Istvan z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) if (dm) z=z*z+c+c*c-dp ;Double Mandel else z2=z*z ;Mandel Puskas Istvan z=z2*z2+p6*z2+c-p0 endif else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<ba }

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correct FOTD 09-04-11 (A Trinity of Piece [New 5, Old 7])
by Jim Muth 08 Apr '11

08 Apr '11

FOTD -- April 09, 2011 (Rating new-5, old-7) Fractal visionaries and enthusiasts: Notice the big announcement below the address of the original FOTD web site. And also notice my new return email address. The fractal itself is a scene in the large minibrot on the west branch of the filament extending from the large north bud of the large minibrot on the main spike of the parent, which is almost a Mandelbrot set. On its surface, the parent fractal is a normal Mandelbrot set, but in its depths it gradually takes on quartic characteristics. Today's image lies at the extreme depth of 2*(10^12), a depth where the quartic nature totally predominates. The image also contains strong anti-minibrot trends. I'll leave it to the individual fractalist to find these trends. The image rates a 5, which is right at FOTD average and equals the old rating of a 7. The name "A Trinity of Piece" makes little sense, since I used another spelling of the final word to avoid unintended religious connotations. The calculation time of 1-1/3 minutes will pass in a flash, even for those with less-than-SOTA machines. And the finished image may be viewed on the currently active web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> without the need to calculate it. The original FOTD web site can be accessed at: <http://www.Nahee.com/FOTD/> BIG ANNOUNCEMENT! -- The debut date of my own FOTD web site has been set! The web address will be announced in the FOTD for April 12. Heavy clouds, steady rain and a chilly temperature of 41F +5C made Friday here at Fractal Central a day to be forgotten. Not only are the local farmers complaining that they cannot work their fields, but the schools are complaining that they cannot play their scheduled games. The fractal cats are just complain- ing generally. The day of the humans, (a good name for a sci-fi horror movie), was once again busy, but this is the way we like to see it. The next FOTD will be posted in 24 hours, that is unless it is post- poned because of an antiquing trip. Until next time, take care, and when things go wrong, make them go right. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Trinity_of_Piece { ; time=0:01:22.39-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.758922148621982/+0.01911085321254484\ /2.512392e+012/1/-45/0 params=4/200000/0/0 float=y maxiter=1500 inside=255 logmap=149 periodicity=6 mathtolerance=0.05/1 colors=000302403504605706807908A09C0AE0BG0CI0DK1EM\ 2FO3GR3HU4IY4J`5Kc5Lf6Mi7Nm7Op8Ps8Qv9Ry9SzBQvCOrDM\ mFKhGIcIGZLEUNCPPBLUCKYDKcEKhFKgEKbEK`EKZEKWEKUEHS\ ECQE8OEANGCNHENJGNKHNMJNNLNPNNQONSQNTSNVUNWVNXSOYQ\ PZNPZLQ_JR_GR`ES`CTa9Ta7Ub5UbBVcGWdLWeRXfWYg`YhfZi\ c`h`bgYdfVfeShdPjcMmbKnaIn_InYImWIlUJlSJkQJjOhjMhi\ KhhJhhHmgFmfDmfCmeAmd8md7mc5mb3mb2mc4mc5mc7zd8zdAz\ dBzdCzeEzeFzeHzeIzfJzfLzfMzfOzgPzgQzgSzhTzhVzhWzhY\ ziZzi_ziazibzjdzjezjfzjhzkizkkzklzfjzilzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhjzfizehzcgz\ afz_ezZdzXczVczTbvSarQ`mO_hMZcLYZJXPH`JF`JE_JCZJAY\ K8XK7WK5VK3UL1VK2UK2TK2TK3SK3SK3RP3VP4VP4UP4UP5TP5\ TP5SP5RP6RP6QP6QP7PP7OP7OP7NO8NO8CO8CO8BO9AO9AO99O\ A9OA8OA7OA7OB6OB6OB5OC5OC4OC3OC3OD2OD2OD1OD1PE3QE4\ QF5RF7RF8SG9TGATGCUHDUHEVIGVIHWIIXJJXJLYJMYKNZKOZL\ Q_LR`LS`MUaMVaMWbNXbNZmzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

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FOTD 09-04-11 (A Trinity of Piece [New 5, Old 7])
by Jim Muth 08 Apr '11

08 Apr '11

FOTD -- April 09, 2011 (Rating new-5, old-7) Fractal visionaries and enthusiasts: Notice the big announcement below the address of the original FOTD web site. And also notice my new return email address. The fractal itself is a scene in the large minibrot on the west branch of the filament extending from the large north bud of the large minibrot on the main spike of the parent, which is almost a Mandelbrot set. On its surface, the parent fractal is a normal Mandelbrot set, but in its depths it gradually takes on quartic characteristics. Today's image lies at the extreme depth of 2*(10^12), a depth where the quartic nature totally predominates. The image also contains strong anti-minibrot trends. I'll leave it to the individual fractalist to find these trends. The image rates a 5, which is right at FOTD average and equals the old rating of a 7. The name "A Trinity of Piece" makes little sense, since I used another spelling of the final word to avoid unintended religious connotations. The calculation time of 1-1/3 minutes will pass in a flash, even for those with less-than-SOTA machines. And the finished image may be viewed on the currently active web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> without the need to calculate it. The original FOTD web site can be accessed at: <http://www.Nahee.com/FOTD/> BIG ANNOUNCEMENT! -- The debut date of my own FOTD web site has been set! The web address will be announced in the FOTD for April 12. Heavy clouds, steady rain and a chilly temperature of 41F +5C made Friday here at Fractal Central a day to be forgotten. Not only are the local farmers complaining that they cannot work their fields, but the schools are complaining that they cannot play their scheduled games. The fractal cats are just complain- ing generally. The day of the humans, (a good name for a sci-fi horror movie), was once again busy, but this is the way we like to see it. The next FOTD will be posted in 24 hours, that is unless it is post- poned because of an antiquing trip. Until next time, take care, and when things go wrong, make them go right. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Trinity_of_Piece { ; time=0:01:22.39-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.758922148621982/+0.01911085321254484\ /2.512392e+012/1/-45/0 params=4/200000/0/0 float=y maxiter=1500 inside=255 logmap=149 periodicity=6 mathtolerance=0.05/1 colors=000302403504605706807908A09C0AE0BG0CI0DK1EM\ 2FO3GR3HU4IY4J`5Kc5Lf6Mi7Nm7Op8Ps8Qv9Ry9SzBQvCOrDM\ mFKhGIcIGZLEUNCPPBLUCKYDKcEKhFKgEKbEK`EKZEKWEKUEHS\ ECQE8OEANGCNHENJGNKHNMJNNLNPNNQONSQNTSNVUNWVNXSOYQ\ PZNPZLQ_JR_GR`ES`CTa9Ta7Ub5UbBVcGWdLWeRXfWYg`YhfZi\ c`h`bgYdfVfeShdPjcMmbKnaIn_InYImWIlUJlSJkQJjOhjMhi\ KhhJhhHmgFmfDmfCmeAmd8md7mc5mb3mb2mc4mc5mc7zd8zdAz\ dBzdCzeEzeFzeHzeIzfJzfLzfMzfOzgPzgQzgSzhTzhVzhWzhY\ ziZzi_ziazibzjdzjezjfzjhzkizkkzklzfjzilzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhjzfizehzcgz\ afz_ezZdzXczVczTbvSarQ`mO_hMZcLYZJXPH`JF`JE_JCZJAY\ K8XK7WK5VK3UL1VK2UK2TK2TK3SK3SK3RP3VP4VP4UP4UP5TP5\ TP5SP5RP6RP6QP6QP7PP7OP7OP7NO8NO8CO8CO8BO9AO9AO99O\ A9OA8OA7OA7OB6OB6OB5OC5OC4OC3OC3OD2OD2OD1OD1PE3QE4\ QF5RF7RF8SG9TGATGCUHDUHEVIGVIHWIIXJJXJLYJMYKNZKOZL\ Q_LR`LS`MUaMVaMWbNXbNZmzz } FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================

1 0