December 2001 - Fractint - mailman.xmission.com

Re: [Fractint] FOTD 28-12-01 (Festive Holiday [6])
by Multiple Bogeys 28 Dec '01

28 Dec '01

> FOTD -- December 28, 2001 (Rating 6) The heck is going on? The December 27 FOTD isn't on the Web site yet -- it's over a day late! Meanwhile here's the December 28 FOTD, early -- by which I mean, according to the timestamp it was posted 20 minutes in the future... What does this new mailman listserver do, send messages through wormholes? :P <hr>MSN Photos is the easiest way to share and print your photos: <a href='http://go.msn.com/bql/hmtag3_etl_EN.asp'>Click Here</a>

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Slice layering and hypercomplex M-set.
by Multiple Bogeys 28 Dec '01

28 Dec '01

If you want to get the same layering effect and exactly choose what areas to overlap, don't bother with hypercomplex. Instead, just write code that will simultaneously iterate two points for every pixel and bail out if *either* of them escapes, to decide the iteration count, where the two points are determined by separate zoom-mapping. It can be done in a Fractint formula file, but with difficulty -- one of the superposed images would be determined by zoom, and the other by entering center-mag coordinates or corners or something into the formula parameters. <hr>MSN Photos is the easiest way to share and print your photos: <a href='http://go.msn.com/bql/hmtag3_etl_EN.asp'>Click Here</a>

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Whither the FOTD CD?
by Multiple Bogeys 28 Dec '01

28 Dec '01

There was a lot of discussion about making a FOTD CD and it seemed the project would go ahead, right before all hell broke loose on September 11. It seems to have gotten completely forgotten since then. Anyone know what's up with it? <hr>MSN Photos is the easiest way to share and print your photos: <a href='http://go.msn.com/bql/hmtag3_etl_EN.asp'>Click Here</a>

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FOTD 28-12-01 (Festive Holiday [6])
by JimMuth＠aol.com 28 Dec '01

28 Dec '01

FOTD -- December 28, 2001 (Rating 6) Fractal visionaries and enthusiasts: Today's fractal image has more colors than one can shake an iteration at. In fact, it is so colorful that, at this festive time of year, I had no choice but to name it "Festive_Holiday". The colors actually are a bit overpowering, and for this reason I could rate the image no higher than a 6. The image was created by that overworked but not overvalued formula, MandelbrotMix4, which today combines two negative powers of Z and turns the resulting inside-out image right-side- out by adding 1/C instead of C. To achieve the brilliantly colored effect, I colored the outside with the <tdis> option. Curiously enough, the width of the brilliant yellow band immediately surrounding the midget can be controlled by adjusting the maxiter of the image. The greater the maxiter, the narrower the band. The render time of the parameter file falls 1/100 second short of 5 minutes on my struggling, out-of-shape P200 machine. On a well-tuned machine with washboard abs and bulging biceps, it should finish in less than 2 minutes. The alternate choice is to download the completed GIF image from the W.W.Web at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday here at HQ was once again just about what would be expected at this time of year -- brisk breezes and a temperature that barely reached freezing. This meant that the fractal cats could not venture outdoors in comfort. When the fractal cats want to go outdoors and cannot do so in comfort, they become quite irritable. No surprise then that the normally friendly brothers got into a heated argument that ended with them rolling on the floor, fighting. When they settled their dispute, I treated them to left-over turkey, and peace prevailed for the rest of the day. The only damage is a nick on Thomas's ear and a couple scratches on Tippy's head. It's now time to shut down fractal HQ and call it a night. The cats are still at peace, and a small snack will keep them that way for the rest of the night. Until next FOTD, which will happen in about 24 hours from now, take care, and be prepared for philosophical pondering. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Festive_Holiday { ; time=0:04:99.99--SF5 0n a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.64306827113377100/+0.752710917997295\ 30/536805.2/1/-60/-2.13414834415726062e-010 params=0.4/-14/-4/-1.4/0/525 float=y maxiter=920 inside=0 outside=tdis colors=000mw0mca_MaZLaaMedNh\ fNkiOokOrnPupPxoQuoQroQooQmoQjnRgnRdnRbnR_nRXmSUmS\ SmSPmSMmSKkOHiKEgGBeC8c85a43Z67X7AU8ES9HPAKNCOKDRI\ EUFFYDG`BHcGMZKQVOVRSZMWcI_gEcl9gp5kt1mn3ni5od7qZ9\ rUAsPCuJEvEGw9HuCNtFSsIXqLbpOgoQllSdjUXgWPeYHTNIGC\ J31JMVEcx9btDapH`mK_iOZfSYbVXZZWWbVSeUPiTLmSIpNOZI\ UIdhIfkJhmJjoJkqJmtJovJqxJrzJmuMiqPdlR`hUXdWS_ZOWa\ JRcFNfBJh8df6yeBwhFujKslOqnSopXmr`kteivigxmfzfit`k\ oVnjOpdIs_CuV6wQAvREuSHtTLtUOsVSrVWqWZqXbpYeoZin_l\ n_ikbfidcgg`eiZckW`nTZpQXsNVuLTwNSqPRkRQfTP`VOWXNQ\ ZNL`UTb``dfhfmpgsxervcqtbqs`pq_ppYonWnlVnkTmiSmhQl\ fPleRkdSkdUjcVjcXicYib_hb`hbbgacgaef`ff`he`ie_kd_l\ d_ZgZLjY8lX9eWA_WAUWBOWCIWCCWBFYBIZAL`AOa9Rb9Ud8Xe\ 8_f7bh7ei7gj7eg7de7cb7b`7aZ7`W7_U7ZR7YP7XN8VO9UOAT\ OBSPBRPCQPDPQEOQFNQFMQnQ9USH9TOOBmPIoQOpRUqS`rTfsU\ ltVruXjtZbt`WsbOsdGrf9rWBcLDPKIPJMPIQPHUPGYPFaP } 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 27-12-01 (Hypercomplex Magic [7])
by Jim Muth 27 Dec '01

27 Dec '01

FOTD -- December 27, 2001 (Rating 7) Fractal visionaries and enthusiasts: The first of the two holidays of the season has passed. It was not as bad as feared here at Fractal Central, but neither was it as good as hoped. One of my gifts was an electronic device -- a VHS video recorder. (I would have preferred a 1.5ghz computer for faster if not better fractals, but that's another story.) I assume the VCR device works perfectly. I must assume this only because I have not yet figured how to use most of the features. And the remote, with its 50 mysterious buttons, just makes matters worse. To make things even more confusing, the 64-page instruction manual is no help at all. When I consult it, I am flooded with so much cryptic information that I don't know where to start looking for what I need. To begin, I find that there are at least 7 different ways of connecting the antenna system. And if I hit the wrong button on the remote, sub-titles appear on the screen, which are almost impossible to get rid of. Or even worse, the screen goes totally blue and the machine just sits there defying me. As of yet, I have not discovered how to receive the UHF over-the-air channels. Presumably, the unit is tuning the cable frequencies, but since I have digital satellite rather than cable input, this does me no good at all. Then there are those settings that lock out certain channels, so that the young ones do not see the material that offends their adults. There are also lights that begin flashing for no discernible reason. I think this is connected with automatic tracking correction when a less-than-perfect tape is playing, but I'm not sure. All in all however, the device is a success. It plays tapes exactly the same as my old VCR machine, which is far simpler and has worked perfectly for almost 4 years. (I need tape-playing ability because I would be lost without a junky old sci-fi or horror movie fix a couple times a week. And those junky oldies are all on tape.) But, even while playing with my new toy, I am left wondering what ever happened to the electronic devices of the good old days -- the devices that were connected, plugged in and turned on, and worked perfectly. They came with 4-page instruction manuals which were usually discarded with the packing. After the holiday, which was neither best nor worst, it's back to the FOTD, and a trip to the fourth dimension. In this case, the four-dimensional object is the 4-D Mandelbrot hyperslice of the 8-D Julibrot. I named today's image "Hypercomplex Magic" because the effect of widely separated parts of the Mandelbrot set superimposed in the same scene is almost magical. In the image, we once again have a Mandelbrot midget filled with features from a distant part of the M-set. This image is far better defined that the similar one that appeared on December 20. In fact, today's image is good enough to rate a 7, which is above average. The render time of 7 minutes is acceptable, though the download from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will be significantly faster. The fractal weather Wednesday was normal winter fare for this part of the world -- some sun, some clouds, chilly winds, and temperatures in the mid 30'sF, which translates to around 2C. And there was no white Christmas the day before. The fractal cats, still recovering from the catnip mice they received for Christmas, were happy to pass the day indoors, stretched by their favorite radiators, complaining only when the heat temporarily cut off. As usually happens at this time of year, I have been thinking very deep philosophical thoughts the past few days. It will take a day or two to get them written down and posted to the philofractal list, but when they do appear, the stagnated list should see a little activity. At the moment, it's late evening of the day after Christmas, and time to shut down the fractal shoppe for another day. But I'll return in the customary 24 hours with more fractal fun. Until then, take care, and if you doubt that fractals can be fun, just try having a conversation with one. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Hypercomplex_Magic { ; time=0:07:05.94--SF5 on a P200 reset=2002 type=hypercomplex function=sqr passes=b center-mag=-0.1726670305042/+0.20143746331292/5321\ 9.92/1/-95/9.16385023419508116e-013 params=0/0/0.2\ 05/0.44 float=y maxiter=12000 inside=255 logmap=98 colors=000KUeLVdMWeNXfOYePZdQ_dRafSegTihTmfSrcRqbQ\ paPmaMjaLhaKeaHbaG_aFYaCVaBSa8Pa7Ma5Ka3Ha2Fa1Ca0Aa\ 07a00_03a05a08a2Ba5Da8GaCIaFLaIOaLQaPUaSWaWZaZaabc\ aefaiiallapoassazwazzbzvapoVfgMYYGOR8FK2740850870A\ 71A82B83BA5BA7CB8CBADCBDCCFDFFDGFFHGFIGGKHGLHHOIHP\ IIQIKSKKUKLWLLYLMZMM_MOaMObOPeOPfPQhPQiQSjQSlQUoSU\ pSVrUVsUWuMUzQVzUWvWWr_YmbZieZeh_alaWoaSrbOvcKycGz\ eCze8zcAzbByaCwaCv_DuZFsYFrYGpWHoVHmUIlUKjSKiQLhPM\ fPMeOObLPaKP_HQZFSYCSWBUV8VU5VS3WQ2YP1YO0ZM0_L0_K0\ aI0eI0iK0mL0rM1vO2zM3zM4zL5zL5zL7zK8zKBzKCzIFzIHyI\ KyHLyHOyHQyGSyGSyGUyFVyFWwFWwDYwDZwD_wCawCbwBcwBew\ BfvAhvAivAiv8jv8lv8mv7mv7ov7pu5ru5ru5su4uu4vu4vu3w\ u3yu3yu7zrAzpCzoFzmIzlLzjOziQzfVzeYzc_zbbzafz_izZl\ zWozVszUvzSyzQzzPzzOzzPzzPzzPzzQzzQzzQzzQzzSzzSyzS\ yzUyzUwzUwzUwzVvzVvzVvzVuzWuzWuzWszYszYszYrzYrzZrz\ ZpzZpzZpz_oz_oz_ozamzamza } END PARAMETER FILE=========================================

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Looking for "Kay" ???
by Tony Parker 24 Dec '01

24 Dec '01

Someone called "Kay" uploaded a a large 3 Meg Fractal File to my server on December 7th. She mentioned that her PC had crashed (Virus???). I've sent here several e-mails and haven't gotten a reply. Is she back online? What does she want me to do with her file? Shall I delete the file? Please advise! Merry Christmas, Happy New Year, and best wishes to all of you "Fractalieri" Tony

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FOTD 22-12-01 (Textured Midget [4])
by JimMuth＠aol.com 22 Dec '01

22 Dec '01

FOTD -- December 22, 2001 (Rating 4) Fractal visionaries and enthusiasts: With almost no time to spare, I will have to keep today's notes brief. The scene is one of a midget in the Seahorse Valley area of a small M-set on the outskirts of its rambling parent fractal. I named it "Textured Midget" and rated it a 4. The render time of 15 minutes can be avoided 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> The fractal weather Friday was once again cold and breezy. Combined with a temperature of 39F 4C, these conditions kept the cats confined indoors for the entire day, where they sulked under the Christmas tree, (seasonal tree for those who are PC), until I lured them out with a treat of tuna. As for me, I am totally overwhelmed by the things that need to be done, so I'll have to take a 4-day break from the FOTD. Until December 27, when I'll return with new goodies, take care, and have a good time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Textured_Midget { ; time=0:15:41.86--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-2.68766176414265900/-1.002382144093885\ 00/673122.9/1/-35/3.26222118623986646e-008 params=-0.05/-9/-0.5/-0.9/0/525 float=y maxiter=2400 inside=0 logmap=204 colors=00049jACuGFzLIzQLzXOzaQzgTzmXzr_zgcz_fzPizG\ my6pv0ss0vr0xl6xfFx`MxVVxQcyLjyFsy9zy3zy0zz1zz3zr3\ zyizulzrmzoozlrzgszduzavz_yzXzzSzzPzzMzzJzzGzzIzzI\ zzIvzJszJoyJjxLgvLjuLmsMprMspMvoOymOzlOzjSziVzgYz9\ azAfzCjzDmzFrzGvzIzyJzxOyySvzVrz_ozcjzfgzjczo`zrXz\ vTzzPzzMzuQzmTzlVyjVviVsiVogVlfXidXddXacX_aXV`YS`Y\ P_YLYYIYYFT`JQaOMcSJdXGf`Cgd9ig6ll1mp0ou0py0rz0sz0\ uz0pz0lz0gy3cu7_pCVmGQiJOfGMcFL`DL_CJXAIT9IS6GP4FM\ 3FL1DI0CF0CD1FC3GA4J96L79O6AQ4CT3D_1Ld0Sj0_p0fv0ms\ 4upMvmLvjJvgIxdGxaFx_DyXCyTAyQ9zO7zL6zI4zF3zD1zA0z\ 90y71v74s66p69m4Cj4Dg3Gd3Ja1L_1OX0QT0SQ0VO0YL0_I0a\ F0dC0fC0fA0d0lf0cc0X_0PX0GT09Q01O03M03L03J03I03G03\ F03D04C04A049047046044043FJ6YY9pjArfDscGu_IuXLvTMx\ YPyaSyfTzjXzoYzs`zxazzXxzQuzLrzFpz9mz3jz0gz0fz0fzz\ _zzSzpLzfFzV7zJ0z90z00z00z00z00z40z90zF0zL1zP3zV4z\ `7zd9zjAzp0zz0zz0zz0zz0zz } 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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Government Grants For You.
by c11132＠371.net 21 Dec '01

21 Dec '01

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FOTD 21-12-01 (Krakatoa [5])
by JimMuth＠aol.com 21 Dec '01

21 Dec '01

FOTD -- December 21, 2001 (Rating 5) Fractal visionaries and enthusiasts: I hate days like today, when I have no chance to find a proper FOTD image or write a proper discussion. But there is simply too much to be done and, since I'm trapped in linear time that moves with a will of its own, I have too little time in which to do it. Today's image rates a liberal 5. It reminds me of an erupting volcano. I named it after that huge eruption toward the end of the 19th century, which obliterated the island of Krakatoa and was heard 3,000 miles away. The formula behind the image is a very simple Z^1.19+C. The midget in the scene is located on a long meandering filament of a larger midget. The larger midget lies on a long meandering filament of the parent fractal, which lies 5.4 turns (whatever that means) up the logarithmic spiral. The parameter file runs in less than 9 minutes, so not too much patience is required to view the image this way. An even more efficient way of viewing the image is to download it from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday was milder than what is expected at this time of year, but still very uncomfortable for the fractal cats. The wind was too strong, the sky was too cloudy, and the 43F 6C temperature was too cold. The cats, being particular about what they find acceptable, spent the day indoors, alternating between their radiators and their lookout shelf by the window. Well, the holidays are getting close, and much remains to be done. I'd best get busy doing those things that need to be done. But I'll return tomorrow with another FOTD. And the philosophy has been lagging lately. To rectify the situation, I might have a bit of wisdom to share in a few days time. Until tomorrow, take care, and stay warm, (unless you're living in the Southern Hemisphere or the northeast U.S., where you're not cold in the first place.) Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Krakatoa { ; time=0:08:49.98--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-5.59395897219679400/+8.262575269499850\ 00/6787487/1/32.5/4.9630024465119327e-008 params=1\ .19/0/5.4/525 float=y maxiter=18000 inside=255 logmap=192 colors=000hFEgGGfHIeIKcJMbKOaLQ`MS_NUZO\ WYPYXP_ZR``TaaUbcWceXdfZdh_eiafkbgmdhnfipgiqijsjku\ llvmmxonypnsihncchYYcSTZMOTGIOADJ48P56U55Z54U65P76\ K86K97KA7KA8aB8ZC9XD9UEARFBPFBMGCKHCHIDFJDCKEAKECL\ CELBGL9IL8JL7LM5NM4PM2RM1SM0TR8UVFVZMVcTWg_XkfXomY\ moZlqZjr_it`gv`fwZdsYcoWakV`gUZcSY_RWWQVSOTONSKMRH\ LQGKPGJOGINFHMFGLFFKFEJEDJECIEBHDAGD9FD8ED7DC6CC5B\ C5BC6DD6FD7GE7IE8JF8LF8NF9OG9QGARHATHBUIBWIBYICZJC\ `JDaKDcKDdKCbNB`QA_T9YV8XY7V`7Ub8PT9LKAHBAD2FJKJOa\ IQbIRcHSdHTdHUeGVfGWgGXgFYhFZiF_jEajEbkEclDdmDemDf\ nCgoChpCipBjqBkrBlrLhqVdqTemRfiPfeNgaLgYJhUHhQFiMD\ iIBjEAjAAkCAkEAlFAlHAmIAmKAnLAnNAoOAoQAoRApTApVAqW\ AqYArZAr`AsaCscEtdGtfItgKteMtcOtaQt_StZUtXWvVYwT_x\ RayQczOezMgzKizJkzFmzBoz7qz4sz8uzCwzGyzKzzOzzSzzVz\ zSzzPzzNzzKzzHzzFzzCzz9zz7zz8zz8zz8zz8zz8zz8zz8zz8\ zz8zz8zz8zz8zz6zz6zz6zz6zz6zz8zzAzr0 } 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 20-12-01 (HyperMandel Madness [5])
by JimMuth＠aol.com 20 Dec '01

20 Dec '01

FOTD -- December 20, 2001 (Rating 5) Fractal visionaries and enthusiasts: On Tuesday, Jon K. posted a letter to the Fractint list, commenting on the FOTD of December 17, which is a scene in the hypercomplex Mandelbrot set. In the letter he asked whether an easy way exists to find the locations of the top layer and bottom layer in the hypercomplex set. This question is more complex than it seems. To start, the appearance of different layers in the FOTD of December 17 is an illusion. The hypercomplex M-set is 4-dimensional indeed, but only a single 2-dimensional slice of it can ever be displayed by the hypercomplex formula. (The julibrot formula can display 3-dimensional slices.) What is happening in the 12-17 image is that the hypercomplex figure has been sliced in an area where different parts of it are merging, actually trying to occupy the same points of hyperspace, with the higher-iteration features being obliterated by the lower-iteration features. In the 12-17 image, we are not looking through an eroded Mandelbrot shaped hole at features that lie on the other side, we are seeing all that remains of the higher-iteration features, the rest having been obliterated by the surrounding low-iteration stuff. Jon asked whether I know of an easy way to find scenes such as 12-17's. The answer is no. Both 'layers' move in an unpredictable manner as the parameters are changed. The only way I know to find such scenes is to track them down by trial and error bracketing and to fine-tune the image with the Fractint evolver. As I noted in the 12-17 discussion, the hypercomplex formula of Fractint does not draw all possible slices of the hypercomplex Mandelbrot set. The formula I wrote for today's image draws more, though not all slices. Today's formula has a drawback however in that the periodicity must be shut off in order for it to work correctly. The p3 parameter of today's HyperMandelbrot formula works the same as the cj and ck parameters of the hypercomplex formula. (I have no idea what the unused parameters of the hypercomplex formula are eventually supposed to be used for.) The p1 parameter of today's HyperMandelbrot formula works roughly the same as varying the initial Z parameters of the Mandelbrot set. The p2 parameter does strange things indeed, things that are almost unbelievable. Since it alters the effect of the other parameters, it is changed only at the risk of the user. Enjoying risk, I set it to 0.5 for today's image, and when I set p3 to 0.008, just look at what it did to our Mandelbrot set. I named today's image "HyperMandel Madness" as a poetic description, and rated it at an average 5. With a running time of 12 seconds, today's parameter file is virtually instantaneous. As always, the completed GIF image is also available at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> With a little more sun and a little less wind, the fractal weather Wednesday was somewhat improved over the day before, but the dynamic duo still would have preferred a temperature of 77F 25C rather than the 54F 12C that actually happened. They were in a surly mood until the sound of some stray cats fighting somewhere in the brush sent them dashing to their lookout shelf by the window, where they spent more than an hour. Then, when their evening mealtime arrived, they completely forgot their troubles. It's now time to accomplish something a bit more practical. Until next time, take care, and don't get hyper. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ HyperMandelMadness { ; time=0:00:12.14--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot center-mag=-0.546672/1\ .33227e-015/0.9318636 params=0/0/0.5/0/0.008/0 float=y maxiter=480 inside=0 logmap=yes periodicity=0 colors=000KAcKAbKAaKA`KA_KAZJAYIAXHAWGAVFAUEATDASC\ ARBAQAAP9AO8AN7BM6AL6AK000AQlBSlCTlDVlEWlFYlGZlG`l\ HblIclJelKflLhlMilNklNllR`lVPmZDmb1ma4na6n`8n`Ao`C\ o_Eo_Go_IpZKpZMpZOpYRqYTqXVqXXrXZrW`rWbrWdsVfsVhsV\ jsShpPgmMfjJegGdeDcbAb_7aX4`U2_S3aQ4cO4eM5gK6iI6kG\ 7mF8oD8qB9s9Au7Aw5By3Bz2Ew5Gu7Is9KpBMnDOlFRiITgKVe\ MXcOZ`Q`ZScXVeUXgSZiQ`kObmLdpJgrHitEkvCmxAom8qcSoP\ RpUQpPPpKOpFNpKMpGLpIKpKJpMIpOHpQGpSFpUEpWDpYCp_Bp\ aBpcEneGlgIjiKhkMfmOdoQbqT`sVZuXXwZVy`TzbRzdPzfNzg\ PzgQzhSzhTziVziWzjYzjZzk`zkazlczldzgbzcaz__zWZzRYz\ NWzJVzFUzKRzPOzTLzYJzaGzfDzjBzfDzcEz`FzYGzVHzSJzPK\ zMLzJMzGNzFRzFUzEYzE`zDdzDgzDjzFhzHgzJfzLezNdzOczQ\ bzSazU`zW_zXZzZ_z`_zb_zd_zf_zh_zj_zk_zm`zo`zq`zs`z\ u`zw`zy`zz`zz_zz_zzZzzZzzWzzTzzQzzNzzKzzHzzEzzBzz8\ zz5zz2zz0zzBzzLzzVzzdzzbzz`zzZzzXzzVzzUzzSzzQzzOzz\ MzzLzzFzzPzzQzzRzzSzzTzzU } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } END 20.0 PAR-FORMULA FILE==================================

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