October 2005 - Fractint - mailman.xmission.com

FOTD 25-10-05 (Julia Variation-2 [7)
by Jim Muth 25 Oct '05

25 Oct '05

FOTD -- October 25, 2005 (Rating 7) Fractal visionaries and enthusiasts: Since posting the last FOTD, I have become fascinated with the low-order Julia images drawn by the JuliaBC formula, which I recently came upon in one of my discarded formula files. Today's image is a Julia set of the Z^(1.125)+C Mandeloid as it appears 11 levels up the complex logarithmic hyperspiral. I have named it "Julia Variation-2" and rated it a 7. Since the image shows the entire Julia set, it is at a very low magnitude and therefore is a very fast one, rendering in under 1 minute on my tired, worn-out old P200 clunker with 16mb of memory, a 2gig hard disk, an exhaust fan that must be goosed into turning by hand, and a CD drive that has not worked in 6 years. The central spirals and triangles are made of inside stuff brought to life by the inside=fmod option and a proximity of 0.025. The radiating outer spokes are a natural part of the image, which was rendered with the outside parts of the image set to the old-fashioned everyday 'iter'. The image is so fast that it should hardly be necessary to download the finished version, but those who wish to do so will find the finished product on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An article in the November 2005 issue of 'Scientific American' magazine speculates that life on earth might have originated somewhere in outer space and reached earth on a meteorite. The most likely source of such a meteorite is presumed to be the planet Mars. Of course, this theory does nothing to explain how living material originally arose from dead matter. It merely shifts the process to another world, and if the ultimate source of life is presumed to have been on a planet in a different solar system, gives a bit more time for the miracle to have happened. I thoroughly discussed this topic in a recent series of FOTD's, so I will not repeat my own views of the nature of life, but I once again wonder how it is possible that such an intellectually advanced species as our own is still debating its own origin, which one would think would be the first question to answer. Cloudy chilly conditions on Monday here at Fractal Central cut short the cats' outdoor time, but not the time they spent in a bad mood. When fractal cats get sulky, they squat down and scrunch up in the most obvious place they can find, usually in a doorway, where they must be stepped over. But thank goodness for tuna. Neither Tippy nor Thomas can remain sulky when tuna is near. Today is starting rainy, windy and chilly. It will not be a good day for the cats. In my department, the work is pretty much caught up, so the next FOTD should appear in 24 hours on schedule. Until then, take care, and is it possible for us to discover what we are? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Variation-2 { ; time=0:00:58.66--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC passes=1 float=y maxiter=255 center-mag=0.138015/-0.127115/0.9300138 inside=fmod params=1.125/0/11/0/0.03224847/-0.32755741/0/0 proximity=0.025 logmap=yes periodicity=10 colors=000zzZlgGg_UbSgYKuVNtTPsRRrPUqNWpLYoJ`nHbmF\ dlDgkBij9gi9ff9cd9_b9X_9TY9PW9LT9IR9EP9AM96K93I5AD\ 2H97NDCSHJXLQaPXfSckWjp_ovcsyfmrafhY_ZUSPPFGL37H4A\ I5DI7FI8IJALJCNJEQKFTKHVKJYLL`LMbLP_MSYNVVOYTP`QQc\ ORfLSiJTlHUkGVkFVjFVjEViDViDWhCWhBWgBWgAWf9Xf9Xe8X\ e7Xe7XcCWaGV`KUZOTXTSWXRU`QTdPO_MKVKGQHCLF8GC4CADL\ EMTHV`KchNlpQtxTswSswRsvQsvPruOruNrtMrtLqsKqsJqrIq\ rHqrGnqFlpEioDgnCdmBblA_k9Yk8Vj7Ti6Qh5Og4Lf3Je2Gd1\ Ed0Dc7CbDBaKAaQ9`W8_b7Zh6Zn7`j7bg7dd7f`8hY8jV8lR8n\ O9pL9rH9tE9vB9w8ArABmCBhECcGCZHDUJEPLEKNFFPFBQNAMU\ 9Ia8Fh7Bp67w54r88mBBhEEcGHZJKUMNPPQKRTQTQWVNaXKgZH\ m`EsbBxc9iZFVVKGQQ2MV2J_2Fd2CjSANF9GN8NV7Ua7_ZDZXJ\ YVPXTVW`c4R_WFcAIMwAJj3HYBJUILQQNMXPIaWEcRFeNGfJHh\ FIiBJk7Kl3Kg4Ib4GY5ET5CO6AJ69M87P96RB5UC3WE2ZF1kVD\ `G0cNAfUJjWNh_SgcXfgadjfcnkbrpauuRmjGf_9XT6_Q`L43a\ NAcTGeZNgdTij_kpelufjqfhm } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } END PARAMETER FILE=========================================

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Extra fractal; not an FOTD
by Jim Muth 22 Oct '05

22 Oct '05

Fractal fans: Today's posting is not an FOTD. I have no time today for a regular FOTD, but I have just turned up a formula that I had forgotten about, and I wanted to give an idea of the things it might do. I also have found that it was Andrew Coppin who originated this formula and apparently the basic idea for the MandelbrotBC2 formula as well. The image is a Julia set of the Z^(1.1)+C Mandeloid as it appears 100 levels up the logarithmic super-spiral. The next real FOTD will appear on October 25. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com ----------------------------------------------------------- Julia_Variation-1 { ; time=0:02:34.18--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC passes=1 center-mag=0.0738128/\ -0.0496634/1.036244 params=1.1/0/100/0/0.206/0/0/0 float=y maxiter=2600 inside=255 logmap=15 periodicity=10 colors=000EF8GC6I94J72L67N6CP6HR6LT6QU6VW6_Y6c_6ha\ 6mc6rd6ue8sfAqgBohDmiEkiGijHgkJelKcmMaoN_nSYnXWnaU\ oeSojQooOosMlrKirIfrKdqMaqNZqPXpRUpTRpVPpWNkVMfUKa\ TJXSHSRGNQEIPDDPFPCIRDLSENUEQVFSXFVYGX_G_`HabHdcIf\ eIifJkhJniKpkKslLunLxoMzpMskOlfQfaS_XUUTVWSUXRTYQS\ ZQR`PQaOPbOOcNNeMMfLLgLKhKJjJIkJHlIGmHFnHFlJHjKIhL\ KgMLeNMcOObPP`QRZRSXSTWTVUUWSVXRWZPX_NYaLZbK_cI`eG\ afFbgI_`LYVOWPRTJURDXP7ZN1YX2Yf2Xp3Xz3Ww7WuAVrDVpG\ UnJUkMTiPTfSSdVSbYR_`RYcQVfQTiPRlPOoOMrOKuPLsQMrQN\ qROpSPoSQnTQmURlUSkVTjWUhWVgXWfYWeYXdZYc_Zb__a```a\ a_aaZ`aU_aQZaMYaI`bGcbFfcDicClcBod9rd8ud7p_6kV6fR6\ aM5XI5SD5O95NC7ME9MGBLICLKEKNGKPHJRJITLIVMHYOH_QGa\ RGcTFeVFgWQiQ_jKjlEtm9oj8kg7fe6bb5Y`5UY4PW3LT2HR2J\ S3LT4MU5OV6QV7RW8TX9VYAWZBYZC__D``EbaFdbGebGcdEaeC\ `gBZh9Yj7Wk6Vm4Tn2So1Pl3Ni4Lf5Jc7H`8FY9RQCaJEmBHx4\ Jp9HiDFPVKQSIQPGRNESMCJWN } frm:JuliaBC { ; Formula by Andrew Coppin e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)), r=real(p2)-q, C=p3, Z=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|< p4+100 } ----------------------------------------------------------

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Zoom into Jim Muth's Oct 16, '05 FoTD.
by Hal Lane 19 Oct '05

19 Oct '05

########################################################### Here is a Zoom into Jim Muth's Oct 16, '05 FoTD. Damascena Korwen's Leather Gem color map is used in a rotated version. Creation time was 20 seconds on my older Pentium 400 machine. See my Oct. 13, '05 post on: "How to use a .PAR file" for instructions on how to use Fractint to generate this fractal. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### START PARAMETER FILE======================================= Mandel_Variation5A{ ; Hal Lane Oct 19'05 0:20 P400 1024x768 ; Zoom into Jim Muth's Oct 16,'05 FoTD. ; Damascena Korwen's Leather Gem ; color map rotated. reset=2004 type=formula formulafile=pastengo.par formulaname=wallpaper center-mag=0.693774/2.0912/2.933562/1/90/3.885780586188\ 04789e-016 params=-0.75/0.49/16/0 float=y maxiter=95 inside=255 logmap=yes symmetry=xyaxis periodicity=0 sound=off colors=YD0P61<2>S91fM5<3>iO5jP5kQ6<9>UB3S92Q82<3>I10931\ A00<3>VK0_P0dU0<3>zm0<3>zb0z_0zX0zU0<3>`F0UC0O80H40<2>A\ 4773A73C<3>56K47M48O39Q2AS<8>9QaASbATc<3>E`hFbiGdi<3>Jk\ lKmmJkj<7>CURBSOAQM<3>6GB5E86G9<9>EWHFYIGZJ<2>JdMKfNLhM\ <5>bmDenBhoA<3>ts3wt1sr2<5>Zf8Vd9SbA<3>DVF<4>CPCCNBCMA<\ 2>BI9BH8BH8<3>AE79D6DE6<3>UI9YJAaLBeMCgODjQF<3>nXFoZGp`\ G<2>seG<15>dL4cK3bI2aH1`F0`F0<5>UA0T90S80R80Q70P60<3>L3\ 0K30J20I10I10<16>UB2UB2VC2<3>YE3<5>M41N41000 } frm:Wallpaper { ; Author: ? ; use fp math, no periodicity, XY symmetry ; p1=location in M-set ; p2=magnitude z=c=p1+(1/p2)*(tan(cos(real(pixel)))\ +flip(tan(cos(imag(pixel))))): z=z*z+c, |z| <= 64 } END PARAMETER FILE========================================= ########################################################### -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.344 / Virus Database: 267.12.4/142 - Release Date: 10/18/05

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FOTD 19-10-05 (Mandel Variation-8 [NA)
by Jim Muth 19 Oct '05

19 Oct '05

FOTD -- October 19, 2005 (Rating NA) Fractal visionaries and enthusiasts: Today's image is a variation of yesterday's image. It was created by the same formula, and the only change is in the real p1 parameter, which has been raised from 1 to 10. I did not rate the image, since it is a virtual repeat of yesterday's. The name indicates that the image is the eighth in the series of Mandelbrot variations. The render time of today's image is slightly longer than yesterday's, though I doubt that anyone will complain about an additional 1/10 of a second. The finished image is available for viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> In yesterday's mail I received the November issue of 'Scientific American' magazine. When I opened it I found several interest- ing articles. The first article says that a deadly 'bird flu' epidemic is possible. I'll have to raise 'bird flu' higher on my list of other media-induced things to worry about. In the meantime, to take my mind off the ever-increasing list of things to worry about, I'll rush out and buy the sponsor's products. Another article in the magazine speculates that the force of gravity might be a kind of illusion arising from interactions in a lower-dimensional realm. (I thought there were supposed to be 10 or 11 dimensions in the world of supermembranes.) The last article tackles the question of how the very material brain generates the sense of the very immaterial 'self'. (Hope- fully it goes beyond merely measuring brain activity.) I have not yet found time to thoroughly read any of these articles, but I am already intrigued by the fact that in the same publication there is an article about physics, implying that the search for answers must extend beyond the intuitive range of our senses, and another article about neurobiology, implying that we need not search beyond the range of our senses for the answers. Come on guys, these are big mysteries. Let's have a bit of philosophical agreement here. Perhaps I don't even need to read the articles. The first article probably is another remotely possible idea that most likely will go the way of the luminiferous ether. The second is probably a study of what happens in the brain when a person is conscious. It almost certainly will not bridge the gap between interacting neurons and our inner sense of 'self' in a comprehen- sible manner. Turning to my own field, graphic design, a very large job has come in, which will leave me little time to ponder other things for the rest of the week. Due to the rush, the next FOTD will be delayed for several days. An unexpectedly pleasant sunny 77F 25C day on Tuesday made the fractal cats very happy. And even better, today promises to be equally as pleasant. For me the work has once again piled up and it will take several days to clear things away. The next FOTD will appear by next Monday or Tuesday. Until then I will be very busy but not too busy to keep up with the fractal lists. Take care, and if gravity, which seems very real, is only an illusion, how much more that appears real is only an illusion? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandel_Variation-8 { ; time=0:00:00.97--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=Test-01 function=cos/sqr center-mag=-0.459436/0/0.02901848 params=10/0/1/0/2/0 float=y maxiter=1000 inside=0 outside=summ logmap=yes periodicity=10 colors=000NIVR4XR4TR4QS3MS3JS3FS3CS39Q8APDAOHAMMAL\ QAKVAI_BHcBGhBElBDqBCuBHnDLgEP`FTVHXOI`HJdBKeHLfNM\ gSMhYNhcNihOjnOktPkyPdpTZhXS`_MTcGLfJP_LSTNVMQYFS`\ 8Uc1Re7OgCLhHIjNFlSCmXEhZFd_H_`IWaJSbHUcGWcFXcEZdD\ _dCadBcdAde9fe8ge7ie6kf5lf4nf3of9lbEiZJgWPdSUbOZ_L\ dYHiVDnTAhVFbXKXZPR`ULbZFdcAfgBjfCnfCqfGlbJhZMdVQ_\ RTWOWSKS7gO8dKAaGCZCDW8FT4GQEBcN6pOAnPElQHjRLhSOfT\ SdUVbUZaVa_WeYXhWYlUZoS_sQ_vPWsQSqRPnSLlTHjUEgVAeW\ 7cWJfXUiXdlXooXoeUoXSoOQiX`ddkffihghihgkifljenkdol\ cqmbrnato`up_sk`qfaoabmXclScjNdhIefDfe9fOYS7vEBtHF\ rKJpNNnQRmTVkWZiZbgaffdjdgnbjr`mu_oqYpnXqjWqgVrcUs\ `TsXStURtQQuNPvJOvGNwDMwIQrNTnSXjX_facbffYkjUpmQuq\ MztIYjS6a`4`X2_T0_P5ZR9ZSEYTIYUNXVRXWWXX_WZdW_hV`m\ VaqUbvUczUdyWcxYbx_aw``vb_vdZufYtgXtiWskVrmUrnTqpS\ ppRppRnnSmlSliTjgThdUfbUd`VbZUaYU`WU_VUZUUYTUXSUWR\ UVQUUPUTOUSNURMUQLUPKUOJU } frm:Test-01 {; Jim Muth z=real(pixel)+(p1*(fn1(imag(pixel)))) c=p2*real(pixel)+fn2(imag(pixel)): z=z^p3+c |z|<=100 } END PARAMETER FILE=========================================

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FOTD 18-10-05 (Mandel Variation-7 [7])
by Jim Muth 18 Oct '05

18 Oct '05

FOTD -- October 18, 2005 (Rating 7) Fractal visionaries and enthusiasts: What can be said about a fractal that takes less than one second to finish? Not much I fear. But today's soft, wavy image does just this. It renders in an impossible 7/8 of one second on my tired old machine. I doubt that it could render faster, even on the newest units, since it will take them about one second to shift into the chosen vesa video mode. Today's resurrected old formula, named Test-01, is something I wrote back in 1996. Having not seen it for nine years, I have no idea of what I was trying to accomplish when I wrote it. Possibly, I was investigating the four odd planes of the Juli- brot. After all, the small open area at the center of today's image does rather resemble the Elliptic slice of the Julibrot. But whatever its original purpose was, I soon laid the formula aside and forgot it -- until yesterday, that is. With its two changeable functions, the formula actually draws some quite interesting fractals. Today's image, which somewhat resembles a reflection in a puddle of water, is a sample of what it does. In keeping with the trend of recent days, I named the image "Mandel Variation-7" The rating of a 7 is largely due to the extra effort I put into the coloring, which, at least on my monitor, is almost but not quite perfectly smooth. There is little more to be said about the image, which speaks for itself, using light waves instead of sound waves of course. As I said earlier, the image is faster than light, but those without the 7/8 of one second to spare can visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and download the finished product from there. A temperature that was slightly too chilly and a wind that was a little too brisk kept the fractal cats from being perfectly happy on Monday. But they still managed over an hour in the holly patch, checking the holly berries, which are just starting to turn red. Once I finished the day's work, my day was equally satisfactory. Today is starting a bit milder, and with no wind. It looks like a better day coming for the cats. The next FOTD will appear in 24 hours. Until then, take care, and then have a bit of fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandel_variation-7 { ; time=0:00:00.87--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=Test-01 function=cos/sqr center-mag=-0.459436/0/0.02901848 params=1/0/1/0/2/0 float=y maxiter=1000 inside=0 outside=summ logmap=yes periodicity=10 colors=000NIVR4XR4TR4QS3MS3JS3FS3CS39Q8APDAOHAMMAL\ QAKVAI_BHcBGhBElBDqBCuBHnDLgEP`FTVHXOI`HJdBKeHLfNM\ gSMhYNhcNihOjnOktPkyPdpTZhXS`_MTcGLfJP_LSTNVMQYFS`\ 8Uc1Re7OgCLhHIjNFlSCmXEhZFd_H_`IWaJSbHUcGWcFXcEZdD\ _dCadBcdAde9fe8ge7ie6kf5lf4nf3of9lbEiZJgWPdSUbOZ_L\ dYHiVDnTAhVFbXKXZPR`ULbZFdcAfgBjfCnfCqfGlbJhZMdVQ_\ RTWOWSKS7gO8dKAaGCZCDW8FT4GQEBcN6pOAnPElQHjRLhSOfT\ SdUVbUZaVa_WeYXhWYlUZoS_sQ_vPWsQSqRPnSLlTHjUEgVAeW\ 7cWJfXUiXdlXooXoeUoXSoOQiX`ddkffihghihgkifljenkdol\ cqmbrnato`up_sk`qfaoabmXclScjNdhIefDfe9fOYS7vEBtHF\ rKJpNNnQRmTVkWZiZbgaffdjdgnbjr`mu_oqYpnXqjWqgVrcUs\ `TsXStURtQQuNPvJOvGNwDMwIQrNTnSXjX_facbffYkjUpmQuq\ MztIYjS6a`4`X2_T0_P5ZR9ZSEYTIYUNXVRXWWXX_WZdW_hV`m\ VaqUbvUczUdyWcxYbx_aw``vb_vdZufYtgXtiWskVrmUrnTqpS\ ppRppRnnSmlSliTjgThdUfbUd`VbZUaYU`WU_VUZUUYTUXSUWR\ UVQUUPUTOUSNURMUQLUPKUOJU } frm:Test-01 {; Jim Muth z=real(pixel)+(p1*(fn1(imag(pixel)))) c=p2*real(pixel)+fn2(imag(pixel)): z=z^p3+c |z|<=100 } END PARAMETER FILE=========================================

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FOTD 17-10-05 (Mandel Variation-6 [6])
by Jim Muth 17 Oct '05

17 Oct '05

FOTD -- October 17, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's old forgotten formula is an early attempt to examine the odd planes of the Julibrot. In a way it succeeds, but its extra baggage makes its use more difficult than need be. For today's fractal, the formula has created a very unusual variation of the Julia set of East Valley of the Mandelbrot set. The artistic worth of the image is un-notable, but the mathematical interest raises the total worth to a rating of 6. The p1 parameter places the scene in East Valley of the Mandel- brot set, while the p2 parameter slices the 4-D Julibrot in a direction very close to the Julia orientation. The p3 parameter adds the extra decoration that makes the image mathematically notable. The overall effect is one of an endless spiral, only one level of which appears on the screen. I named the image "Mandel Variation-6". A name like 'Julia Variation' might have been more appropriate, but names are names, and the name I have given the image will be its name for all eternity. Except for those with internet-proficient-but-Fractint-chal- lenged computers, rendering today's image will be no problem, for it finishes in only 26 seconds, and that is on my tired old P200 workhorse machine. Those with amnesiac machines that have forgotten how to run DOS programs can see the image by down- loading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday turned out milder than expected here at Fractal Central, with a lot of sun, a fresh breeze, a few scudding clouds, and a high temperature of 66F 19C. The cats were satisfied, though not overjoyed. Today is starting sunny but chilly. The cats are still sleeping and have yet to comment. The next FOTD will appear in 24 hours. Until then, take care, and see the new world revealed by fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandel_Variation-6 { ; time=0:00:26.26--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=ManJul2CPwr inside=255 center-mag=-0.000916065/0.00366617/0.507824/1.0765 params=0.255/-0.0006/1e-010/0.001/-50/10 float=y maxiter=10000 outside=real periodicity=10 colors=000SXkZYheZek_bcT`WMZOFYG8W82VB4UE5TH6SK7RM\ 8RP7MS7HV6CY67`62b58c5De4If4Nh3Ti3Yk2bl2gg4ec6dZ8c\ VAaQC`ME_W8`d3a_RNVn9YiB`eDcaFfYHhUIjYKk`MldNmgPoj\ RpnSqqUrtVilWaeXUYYMRZEKZIbZMtZMuZNuYNuYNuYOvYOvYO\ vYOvYPuZPuZPtZPtZPsZQsZQrZQrZQqZQqZQqZRpZRpZYYZRoZ\ RoZRnZSnZSmZSmZSlZSlZSlZTkZTkZTjZTjZTiZUiZUhZUhZUg\ ZUgZUgZVfZVfZVeZVeZVdZWdZWcZWcZWbZWbZWbZXaZXaZX`ZX\ `ZX_ZY_ZYZZYZZYYZYYZIP1JQ2JQ3JQ3JQ4KQ4KQ5KQ5KR6LR6\ LR7LR7LR8MR8MR9MS9MSANSANSBNSBNSCOSCOSDOTDOTEOTEPT\ FPTFPTGPTGQUHQUHQUIQUIRUJRUJRUKRUKSVLSVLSVMSVMTVNT\ VNTVOTWOTWPUWPUWQUWQUWRVWRVWSVXSVXTWXTWXUWXUWXVXXV\ XYWXYWXYXYYXYYYYYYYYZlXgkYfkYfkYfkYfjYfjYfjYfjYejY\ eiYeiYeiYeiYehYehYehYdhYdhYdgYdgYdgYdgYdgYdfYcfYcf\ YcfYceYceYceYceYbeYbdYbdYbdYbdYbcYbcYbcYacYacYabYa\ bYabYabYabYaaY`aY`aY`aY``Y``Y``Y``Y_`Y__Y__Y__Y__Y\ _ZY_ZY_ZYZZYZZYZYYZYYZ000 } frm:ManJul2CPwr {; Jim Muth ; Creates and rotates ^2 Hyperbrot Figure ; P1 sets point of rotation, P2 sets angle of rotation ; P3 sets power of C z=c=pixel: z=sqr(z)+p1+(p2*(c^p3)), |z| <= 100 } END PARAMETER FILE=========================================

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FOTD 16-10-05 (Mandel Variation-5 [4])
by Jim Muth 16 Oct '05

16 Oct '05

FOTD -- October 16, 2005 (Rating 4) Fractal visionaries and enthusiasts: Can a fractal be used as a wallpaper design? Today's image shows that the answer is yes. The old formula I resurrected for today is named "Wallpaper", and the only thing it aparently does is create a wallpaper-like pattern. Since the formula is based on the Mandelbrot set, I named the image "Mandel Variation-5". Like is true of so many of these old forgotten formulas, I have no idea where it came from or what it was originally supposed to do, though with the way the functions are piled on in the iteration part, I doubt that I wrote it. The (p1) parameter is set to a point some distance north of Seahorse Valley. Bits and pieces of this valley form the smaller, more intricate parts of today's wallpaper sample. The larger flat diamond shapes are simply parts of the iteration bands in the area. Is there a market for wallpaper with a fractal design? Who knows. Maybe it has already been tried. I myself prefer the peaceful feeling a smoothly painted wall induces, expecially when the color is a pastel tint of blue. But some people enjoy the liveliness that a busy wallpaper pattern can create. There might be a place for fractals on the walls of our homes, but surprisingly enough, not here at Fractal Central. After giving today's image careful consideration, I rated it a below-average 4. This is no reflection on the worth of the formula. The formula might have far better images in it, but wallpaper is just not my thing, so I will not work with the formula long enough to find out. One very good point however is the speed of the image, which with its XY-axis symmetry, renders in an incredible 3 seconds. It will take several times as long to stop by the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and download the completed image from there. Lots of sun and a high temperature of 75F 24C here at Fractal Central on Saturday was just what the cats have been waiting for. Only a rather brisk wind kept the day from being absolutely perfect. Today is starting sunny but not quite as warm. The day will probably be good enough for the duo. For me things look peaceful. Hopefully they will stay that way until the next FOTD appears in 24 hours. Until then, take care, and spare no fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandel_Variation-5 { ; time=0:00:03.18--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=Wallpaper center-mag=0/0/0.04266667 params=-0.75/0.49/16/0 maxiter=95 inside=255 float=y logmap=yes symmetry=xyaxis periodicity=0 colors=000qmmnibkdSSEKYMJcUIQXR1NTNUNrp3ol7mhAjdEb\ KIXr8_mBbiDedFjAciOSmrWjiONGXYRPim4hi8hfBhcEiqWhkR\ heM6vlQkXgmWhiSjbelikecXZZIWi9Tt0MPgnN6ZYPJggKx_TX\ k`5w`Wq`ukwzokyp`xqPwrEvrAnZ7gGF_KMTNTMQ_FTaKNbPId\ UCeZ7rwllmcgcWaUNXKFPLKHMP9MUDQLGUCJY3RX5ZX7fW9nWA\ xCvZpTViaRbiNWrJPzLcqNqhGbg9Pg2Bgt3Ih8MhIKhSITRzZH\ oj23iKA40EIDFWPGt0jnJWoZVl_Qj`LJpaSjV`eOasEdlFffGt\ zUpqPlhL1KBGQDVWF0OqFTdUXTZBMlAhJSfQV_WXUbZNAV7PkP\ WgMbcJkXIiZHuMypRjlWWvSSrVPoXMkZJcGmeNbgUSsh8pfBmd\ DjbF7UCAMMJQKSUJ`YIjTViWQhZLpO9lVD4_NLTsTWf`ZU2htD\ fjOd`ZbRqY8f7OgFMgMKhUIReIWcH_bHdaHVEbaQS`xbdlSVgr\ ih6heAhbEhXThYQhZNh_KyYlp_XZM0cU9nholecjbSemF8eELy\ TXlNGUxQXi_ZVhEehMXhUPCczLbnTac``SWhEkpkOSFVVGaYHE\ xLPpJZhIvFWoQOj5DiGFhRGIr6Pm9WiCbdF6meJhXWdPRHa_RR\ RMo_UYy1usDgmPUJJJQOIWSIbXHjnligXbvXdpTekPgeLo2kkK\ Wv1YoJPNb6aeaccWebRgaMtry } frm:Wallpaper { ; ; use fp math, no periodicity, XY symmetry ; p1=location in M-set ; p2=magnitude z=c=p1+(1/p2)*(tan(cos(real(pixel)))\ +flip(tan(cos(imag(pixel))))): z=z*z+c, |z| <= 64 } END PARAMETER FILE=========================================

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FOTD 15-10-05 (Mandel Variation-4 [5])
by Jim Muth 15 Oct '05

15 Oct '05

FOTD -- October 15, 2005 (Rating 5) Fractal visionaries and enthusiasts: When sleep will not come, or sometimes just for fun, I like to imagine myself exploring the surface of a four-dimensional hyperplanet. I start at the zero-zero-zero point and travel west along the equator. These three coordinates are needed to mark the starting point because the surface of such a hyper- planet is a curved three-dimensional space. Since my imaginary self still has only three-dimensions, I can never see the entirety of the planet, but I can scan any chosen section, using time as the missing dimension. The equator of such a hyperplanet is a great circle around the planet, the same as it is on earth. But the equator does not separate the hyperplanet into two hemispheres as earth's equator does. It is merely a line around the surface, which may easily be bypassed completely by taking a route that does not intersect or even come near it. I move west along the equator until I have gone 90 degrees from the starting point. Then I stop. There is now a big decision to be made. I want to leave the equator to check the higher latitudes, but I must decide in which direction I wish to travel. On earth the decision would be simple. The surface is two-dimensional and, setting out at a right angle, I could go only directly north or south. But on the hyperplanet the surface is three-dimensional and there is a full 360-degree circle of directions in which I could leave the equator at a right angle and move directly toward the pole. Something is wrong. By definition, the pole is 90 degrees from the equator and if I have a choice of 360 degrees in which to move directly toward it from one point on the equator, the pole cannot be a point. This is true. On a four-dimensional planet, the pole is a great circle, which circles the planet exactly like the equator, and every point of it is 90 degrees from every point of the equator. Does this mean that frigid arctic conditions form a ring around the planet? Not necessarily. Planets rotate. The equator of our hyperplanet rotates on itself exactly as earth's equator does. But it rotates around the polar circle as its axis. As the planet rotates, every point of the polar circle remains fixed in position and rotates in place, exactly as the two points of earth's north and south poles do. Things get even more interesting. The polar circle does not just sit there, its points turning in place. It can rotate around the equatorial circle just as the equatorial circle can rotate around the polar circle. A four-dimensional planet can be subject to two independent rotations at the same time, and planets being planets, if rotation is possible, it will almost certainly be happening. In my mind, this raises the question of the path the sun would take in the three-dimensional firmament of the hyperplanet. The points of a 4-D hypersphere subject to double rotation trace out paths that are impossible to visualize in 3-D space, but some- what resemble a curved helix with its ends joined into a circle. This is where I now stand. Would the equator of our 4-D planet be a circle of heat, while the polar circle is a circle of cold? Maybe or maybe not. The sun would travel a kind of spiral path in the sky, which at first would seem chaotic, but after a while a pattern would become evident. At times, the sun's path might or might not take it away from the equator and high over the polar regions, warming them and giving the entire planet a temperate climate. Right now I am not sure, but I expect many more nights of good sleep trying to find the answer. Oh, and before I forget, we have another fractal for today. It was created with an old formula written back in 1998 by Jay Hill (I wonder what happened to him). Since the image is part of a distorted Mandelbrot set, I named it "Mandel Variation-4". Its extreme magnitude made the mathtolerance entry necessary in the parameter file. The image rather resembles a scene far out on the negative stem of the M-set when the bailout radius is set to 4. Due to its appearance of familiarity, I could rate the image no higher than a 5, but the render time of under one minute means that little time will be lost in rendering it. Those who do not render can find the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An unexpected amount of sun and an unexpected high temperature of 73F 23C kept the fractal cats' mood in the good range on Friday. They enjoyed several hours in the holly thicket, watching the birds fly by. Today is starting even better. The cats will be overjoyed. I expect my day to be acceptable, but it will be even better if the next fractal turns out well. The next fractal will appear in 24 hours. Until then, take care, and listen to the message of the fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandel_Variation-4 { ; time=0:00:56.08--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=MixUp passes=b center-mag=-1.963594365754721/0/1.044777e+013/0 params=1/0/2/0/0.0700000002/0 float=y maxiter=500 inside=255 outside=real symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=000h9tFkmKnlOqkStjWviU`ZSGPQEOODOMBNKANJ6GJ\ 29O3FS4KW5Q_6Vc7`g8ek9ko9ppQ_peJogKnhLmiMljNkkOjlP\ imQceNYYLSQJMIHGAFJBKMCQPDWSE`VFfXGkSDjNAiI8iD5h82\ g40gD9dLHaTPZaYWieTqmRbqWPu`BxdGt_KqVOmRSjMWfI_cDc\ `9KB8gT7hP6jM5lI4mE3oA2p71jOGedV`tiarjapjanjaljajj\ ahjafjbVdcK_c9VVLTNWRFfPN_RUTSaMThGUfMWeRYdW_ba`af\ b`kd_peXfZVYTSRNQNHRKBQI5R78TBAVFCWJEZNH`RJcVLeYNf\ aPgdRhgTijVjmXmoSppOrrJusFwwBzzJpsRmrZjrfgrnUeVUcO\ U`HUYAUW4dWOoWfzWytYso_nj`iebd`c_WeVRfQZaPeXOlTOsO\ NzKNyTby`rrVnkPjdKfYEbR8ZK3WHDVEMUBVU8cT5lS2uS3rT4\ oT5lT6iU7fU7cUMpETqDZrDdsDjtDpuDvuDXaT8Jg7NZ6QQ6TI\ 6RH6QG5OF5NE5LD4KC4IB4HA3F93D82C72A629517416314203\ 1010KM5NV2gb3d_2aY2_W2XT2VR2SP1PM1NK1FRqB`q7kq4uqe\ XI_NXUDkP4zXFqcPhj__qiRxsJwtOwtSwuXwu`ttWqtRnsMlsH\ jcQhOYg8eZDhQHjHMl9Qn8Tl8Vk7Yj7_i6bh6dg6ffRpejzdPm\ j4apIVbWPPiJChHLhFUhDb000 } frm:MixUp {; (c) Jay Hill, 1998 ; make sure p1 <> p2 and p3 <> 0 u=p1, v=p2, w=p3, c=pixel/w, x=v-u, z=(-u/v/w)^(1/x): z=z^u + w*z^v + c |z| <= 1000 } END PARAMETER FILE=========================================

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FOTD 14-10-05 (Mandel Variation-3 [6])
by Jim Muth 14 Oct '05

14 Oct '05

FOTD -- October 14, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's old long-unused formula is named "Test0622". It is so simple that it barely deserves being called a formula. It draws only the Mandelbrot set with a changeable parameter and function added to initial C. But as today's image shows, in the world of fractals, little initial changes can produce great final results. Despite its unlikely appearance, the segmented worm-like shape filling today's cropped image is the Mandelbrot set. The shape and proportions have been changed, but topologically the set is unchanged. Nothing has been added or taken away. It is the exponential function and parameter which have been applied to C that are responsible for the craziness. I'm not certain how, but when this function is applied to C, the effect is to enlarge the designated point to infinity, resulting in an image something like what one might see if he were actually in the world of the Mandelbrot set, standing at the point and looking at the scenery surrounding him. In today's image the point is in a remote valley on the northern shoreline of the main bay of the M-set. The main bay itself is the open area farthest to the right, where East Valley and the main negative stem are vaguely visible. The wide-screen effect does not mean something is wrong with your monitor. I have changed the proportions of the image to avoid repeating parts of the distorted M-set. A single outzoom will reveal that today's image is part of an infinite repeating series of identical images. In order for the image to render properly in the vicinity of the central point itself, the periodicity must be turned off. I have done this in the parameter file. The maxiter of 45000 would seem to be far beyond what is necessary for an image of the entire Mandelbrot set, but carefully check the left edge of the image. The maxiter there is barely adequate. Though most of the value of today's image is mathematical, it has enough artistic worth to rate a 6. The name "Mandel Variation-3" is a simple description. The render time of 9 minutes is reasonably fast, but the image may be seen much faster by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A most unpleasant chilly drizzly day here at Fractal Central on Thursday made the Fractal Central cats most unhappy. Extra tuna in the evening made them less unhappy. Today is starting the same as yesterday, but without the drizzle. I expect little happiness to come the cats' way. My work is reasonably caught up, so I am neutral. The next FOTD will appear in 24 hours. Until then, take care, and look for the fractal lining. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandel_Variation-3 { ; time=0:09:15.85--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=Test0622 function=exp center-mag=-6.53\ 755/1.20746/0.2636167/0.6249/14.1598813307994735/\ -1.23373533611470521e-014 params=0/0/-0.2217009427\ 4/0.79843333763 float=y maxiter=45000 inside=0 logmap=yes periodicity=0 viewwindows=1/0.5/yes/0/0 colors=000IYTIZVJ_WK`YL`_Ma`NbbOccPdePefQfhRgjShkT\ imUjnVkpSkrUkqVjqWiqXhqYgqZeq_cqaaqb_qcZqdXqeWqfUq\ gTqhRqjPqkOqlMqmLqnJqoIqpGqrEqsDqtBquAqv8qw7qx5qz2\ sy3ry4qy5py6oy7ny8ny8my9lyAkxBjxCjxDixEhxEgxFfxGex\ HexIdxJcwJbwKawLawM`wN_wOZwPYwPYwQXwRWvSVvTUvUTvUT\ vVSvWRvXQvYPvZPv_Ou_Nu`MuaLubLucKudJudIueHufGugGth\ FtiEtjDtjCtkCtlBtmAtn9to8to8sn9rm9qm9pl9ol9nk9mj9l\ jAliAkiAjhAigAhgAgfAffBeeBeeBddBccBbcBabB`bC_aCZ`C\ Z`CY_CX_CWZCVZCUYDTXDSXDRWDRWDQVDPUDOUENTEMTELSEKR\ EKREJQEIQFHPFGPFFOFENFDNFDMFCMGBLGAKG9KG8JG7JG6IG3\ HH5IG6IG7IG8JGAJGBJFCJFDKFFKFGKFHKFILEKLELLEMLENME\ OMEQMDRMDSNDTNDVNDWNDXOCYOC_OC`OCaPCbPCdPBePBfQBgQ\ BhQBjQBkRAlRAmRAoRApSAqSArS9tT9uU9vV9wW9xX9yYAzZAz\ _Az`BzaBzbBzcCzdCzeCzfCzgDzhDziDzjEzkEzlEzmEzmFzmF\ zmFzmGzmGzmGzmGzmHzmHzmHzmIzmIzmIzmIzmJzmJzmJzmKzm\ KzmKzmKzmLzmLzmLzmMzmMzmM } frm:Test0622 { ; Jim Muth z=p1, c=fn1(pixel)+p2: z=sqr(z)+c |z| <16 } END PARAMETER FILE=========================================

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How to use a .PAR file; Zoom into Jim Muth's Oct 13, '05 FoTD
by Hal Lane 13 Oct '05

13 Oct '05

########################################################### Here is a zoom into Jim Muth's Oct 13, '05 FoTD (Fractal of The Day) with a rotated HITENSN2 (High Tension 2) color map. Jim says this about the original fractal: > the borders between the iteration > bands have broadened into narrow open lanes, with bits and > pieces of something else showing through. I located a place and a color map that brings this 'something else' out as clearly as I could. The 'something else' is shown primarily as yellow features. The features 'showing through' appear to be of similar iteration count (and, therefore, color) to the lightning-like features in the base Mandelbrot set but the 'showing through' features are not lightning-like in form. The fractal only takes 15 seconds to calculate on my Pentium 400 for a 1024x768 (SF7) version of the fractal. How to use a .PAR file ---------------------- For those who don't calculate fractals from parameter files every day I give instructions here: Create the parameter file: -------------------------- - Copy and paste the parameters and formula (below) into a text file in the same directory that Fractint is in. Omit the "START (and END) PARAMATER FILE ====" text. - Name the file F051013A.PAR (F=Fractal of the day series, 05=2005, 10=Oct, 13=13th day, A=First variation on Jim Muth's original parameter file). - Save the file. Make *sure* that the file is in the same directory that Fractint is in. (Although seeing the digits of dates in YYMMDD order may seem strange at first this is done for a reason. Multiple files named with two digits each for the Year, Month and Day *in that order* will sort in correct date order in a directory. The initial 'F' groups these files together.) Calculate the fractal: ---------------------- - Start Fractint and (if necessary) press <Enter> until the Mandelbrot set begins to be calculated. - Press the <@> key to 'Run a saved command set', that is, a parameter file. - Press the <F6> key to get a list of parameter (.PAR) files in the Fractint directory. - Use the arrow keys to highlight the file name F051013A.PAR you created above. - Press the <Enter> key. - Parameter files can contain more than one named group of parameters, so a list of named parameter groups is presented. In this case there is only one set of parameters in the file named: Mandel_Variation-A so you can just - Press the <Enter> key and - The fractal will be generated. - If you like the fractal you can save it by pressing the <s> key while viewing the fractal. Since there are several steps to do in a specific order, if you have not done this before consider printing out this list of instructions -- or making a few quick notes so can get the sequence of operations right: E.g: @, F6, choose .PAR file, <Enter>, <Enter>, ... <s> [Optional -- Set the file name to save the image as:] ----------------------------------------------------- - I like to control the names of some of the fractal images I save. To do this: - While viewing the image to be saved press the <x> key. - Use the down arrow key to highlight the 'Savename' field (eighth field down). - Type in the file name you want to save the image as when you press the <s> key later. E.g: F051013A The ".GIF" will be supplied by Fractint. This is a DOS file name so it must be eight or less characters and contain no spaces. - Press the <Enter> key. - You will be returned to viewing the image. - Press the <s> key. The fractal will be saved using the name you supplied above. Remember, you don't have to settle for the fractal that the parameter file generates! After it is created you can zoom into or out of it, pan around within it and find other interesting images. And different color maps bring out different features within fractals. Enjoy! I would appreciate a quick email from anyone who calculates this fractal to get an idea of interest in variations on Jim Muth's Fractal of The Day (FoTD). I would also be interested in knowing if my instructions of how to calculate a fractal from a parameter file were useful to anyone. Thanks, Hal Lane ######################### # hallane(a)earthlink.net # ######################### START PARAMETER FILE======================================= Mandel_Variation-A { ; Hal Lane Oct13'05 14.5 P400 1024x768 ; Zoom into Jim Muth's Oct 13,'05 FoTD ; with a rotated HITENSN2 color map. reset=2004 type=formula formulafile=pastengo.par formulaname=mytestagnew center-mag=-0.174842/1.07723/21.96437/1/67.500000000000\ 0568/-1.23373533611470521e-014 params=1.414213562373/1/1/1.414213562373 float=y maxiter=100 inside=0 logmap=yes symmetry=xaxis sound=off colors=000bJ5<4>UB3S92Q82<3>I10931A00<3>VK0_P0dU0<3>zm0\ <3>zb0z_0zX0zU0<3>`F0UC0O80H40<2>A4773A73C<3>56K47M48O3\ 9Q2AS<8>9QaASbATc<3>E`hFbiGdi<3>JklKmmJkj<7>CURBSOAQM<3\ >6GB5E86G9<9>EWHFYIGZJ<2>JdMKfNLhM<5>bmDenBhoA<3>ts3wt1\ sr2<5>Zf8Vd9SbA<3>DVF<4>CPCCNBCMA<2>BI9BH8BH8<3>AE79D6D\ E6<3>UI9YJAaLBeMCgODjQF<9>tgGuiGvjG<2>ypGzrFzrK<3>yufxu\ kxvqwww<3>rhh`F0`F0<5>UA0T90S80R80Q70P60<3>L30K30J20I10\ I10<16>UB2UB2VC2<3>YE3<3>Q82O61M41<3>Q71R81S91fM5<4>jP5\ kQ6jP6<2>dK5 } frm:MytestAGnew {; Jim Muth z=c=pixel, a=flip(real(p1)), b=flip(imag(p1)), d=real(p2), f=imag(p2): z=(d*(z^a))^(f*(-b))+c, |z|<=100 } END PARAMETER FILE========================================= ########################################################### -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.344 / Virus Database: 267.11.14/131 - Release Date: 10/12/05

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