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FOTD 01-06-09 (Seahorse Valley-01 [6.5])
by Jim Muth 01 Jun '09

01 Jun '09

FOTD -- June 01, 2009 (Rating 6.5) Fractal visionaries and enthusiasts: Very slow image alert!! Run parameter file at your own risk! We have not had a FOTD theme month for quite a while, so I have decided to make Seahorse Valley the FOTD theme for the month of June. Not only will we explore the well-known Mandelbrot and Julia aspects of the valley, we will check the four remaining aspects as well. Seahorse Valley of the Mandelbrot set is actually a four- dimensional thing, which includes not only all its Julia sets, but the scenes in the Oblate, Parabolic, Elliptic and Rectangular directions, as well as the oblique scenes sliced at unimaginable four-dimensional angles. I have included a short chart of the six mutually perpendicular planes of the Z^2+C Julibrot: real(C) and imag(C) = Mandelbrot aspect real(Z) and imag(Z) = Julia aspect imag(C) and real(Z) = Oblate aspect real(C) and real(Z) = Parabolic aspect real(C) and imag(Z) = Elliptic aspect imag(C) and imag(Z) = Rectangular aspect The names of the four additional aspects are my own invention. The orientation of today's image is within 1/100 of one degree of the Julia orientation. The tiny rotation is toward the Rectangular orientation. The outer edge of the fractal is the familiar Julia set with a C-value of -0.75,0. Cut the maxiter to 100 to see it. The strange-looking stuff inside the familiar Julia set is a gross enlargement and distortion of the Mandelbrot aspect of Sea- horse Valley. As far as I know, this is the smallest deviation from the actual Julia orientation of Seahorse Valley that I have yet seen. The familiar Julia set of Seahorse Valley calculates in a few seconds, but today's slight rotation raises the calculation time to over three hours. The incredible increase in time is due to the stuff on the inside of the fractal, most of which has an iteration count in the millions, and also to the fact that the periodicity must be turned off for the image to generate properly. The name "Seahorse Valley-01" is a catalog number, since I will be doing many more Seahorse-Valley images in the month to come. Luckily, no more images will take anywhere near today's 3 hours to calculate. The rating of a 6-1/2 implies that I feel there is too much mathematical interest and too little artistic worth in the image. Also, I have posted several images very similar to today's in the past, though the images were nowhere near as extreme. Those with a few hours to spare may see the image by starting the included parameter file and coming back several hours later. Those with more pressing things to do may see the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Another perfect day prevailed here at Fractal Central on Sunday, with sunny skies and a temperature of 77F 25C. The fractal cats spent most of the day in the side window, watching the other cats in the neighborhood wander by. My day was pleasant enough. If all goes well, the next FOTD image will be posted in about 6 hours. Until then, take care, and when does the beginning end? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Valley-01 { ; time=3:09:55.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/0/0.862069 params=90/0/89.99/90/-0.75\ /0/0/0/2/0 float=y maxiter=3500000 inside=0 logmap=yes symmetry=yaxis periodicity=none colors=000HazJczLezNgzPizRjzTkzVmzXnzZoz`qzbszduzf\ wzhzzjzzlzznzzpzzrzztzzvzzxzzzzzzzzzvzzrzzmzzhzzcz\ zZzOj_NibMidLifKihJhkIhmHhoGhqFgtEgvDgxCgzIfuOepTd\ kZdfccaibXnbTi`Vd_X_YZVX__YZdZZi_Zn`ZsaZwbZtYRqUJn\ QCpVKqZRrbYsgdtkkuorrmmpkinjdlh`jgXdi_ZjaTkcNmfHnh\ Boj6pl7mk8jk8gj9ejAbjA_iBYiBVhCShDQhDNgEKgEIgILiLN\ jOPkRRlUTmXWn_YoNfLcfZtfkp`lmWliQlfLlbGl_AlW5lT0lQ\ 6nOBpLGqJMsGRtEWvC`wFdqHgkJjfLm`OpVQsQSvKUyFTuKTqP\ SmTSiYReaRafRZjPWhNTfLQdKNbIK`GIZEFXDCVB9T96R73P61\ O76R8BU8GX9L_9QbAUeBZhBckChnCmqDrtDvvFruHotJksLhrN\ dqPapRYoSVnUSmWPlYMk_JjaDicAhd7g`CeYHdULcRQbNUaKZ`\ HcZDgYAlX6rW3xV0zU2xS3tR4pP5mO6jM7gL8eJAbIB_GCXFDU\ DERCFOAGM9KPBORCSTDWWE_YFc_GgaHkdIofJshKvjLulOumQu\ nTuoVupYuq_trbtsdttgtuitvltwnnxmiymczlczlczlczkczk\ czjczjczjczkczlhzlmzmrzmvznzznzzozzpzzpzzqzzqzzrzz\ rzzizz`zzSzzJzzBzzIzzOzzU } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 31-05-09 (A Bud in Trouble [No Rating])
by Jim Muth 31 May '09

31 May '09

FOTD -- May 31, 2009 (No Rating) Fractal visionaries and enthusiasts: There are many Julia sets but only one Mandelbrot set. Not true. Just as there is a unique (totally perpendicular) Julia set associated with every point of the Mandelbrot set, there is a unique (totally perpendicular) perturbed Mandelbrot set associated with every point of every Julia set. But this four-dimensional stuff is best left for another day. Today we have a hastily-found scene in what is left of Seahorse Valley of the perturbed Mandelbrot set with an initial Z value of 0.6669953+0.6670071i. The obvious ghost bud in the background is almost totally obscured by a spectacular foreground spiral. I named the image "A Bud in Trouble" because of the distressed bud. Since I have done this type of image so many times in the past, I gave it no rating. The calculation time of 37 seconds can hardly be beat. The trip to the FOTD web site also is hard to beat. The web site may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The fractal cats enjoyed the near perfect weather here at Fractal Central on Saturday, while FL and I enjoyed an antiquing trip. The total sun and temperature of 77F 25C was perfect for almost any activity, indoors or out. The next FOTD will be posted in about 18 hours. Until then, take care, and wonder why the world is the way it is. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Bud_in_Trouble { ; time=0:00:37.36-SF5 on P4-2000 reset=2004 type=mandel passes=1 float=y center-mag=-0.7526914332/-0.0383381323/44718.06/1/\ -121/0 params=0.6669953/0.6670071 maxiter=150000 inside=255 logmap=-500 colors=000KAAKAAKAAKAAKAAKAAKAAKAAKAAKBAKCAKDAKEAK\ FAKGAKH9KI9KJ9KK9JL9HM9GN9EO9DP8BQ8AR88S87T85U84V9\ 3VC6XF9YIC_LE`OHbRKcUNdXPf_SgbVieYjh_kkXinVgqSetQc\ wNkzLjzIhzGfzDdzBczFcz9cz1cz3cz5cz7cz9czBczDczFczH\ mzJmzLmzNmzOmzQmzSmzUmzWmzYtz_vzayzczzezzgzzhzzamz\ VmzOmzImzKmzLmzMmzNmzOmzPmzQmzSmzTmzUmzVmzWmzXwzYw\ z_wz`wzawzbwzcwzdwzjwzewz`wzWwzRwzMwzJwzIwzHwzGwzG\ wzFwzEwzDwzDwzCwzBwzAwzAwz9wz8wz8wzAwzHwzIjzJlzJmz\ KozLqzLrzMtzMuzFazHczJdzLezNfzPhzRizTjzVkzXmzZnz`o\ zbpzdrzfszhtzjuzlwznxzpyzuzzrzzpyznxzkwzivzguzdszb\ rz`qzZpzWozUnzSmzPkzNjzLizIhzGgzEfz7gzCezHczLbzQ`z\ VZzZYzcWzeSzgVzhXziZzj`zkbzmdznfzoizpkzqmzsoztqzus\ zvuzwwzxpzxjzxdzxZzxTzxNzxHzxBzvCztCzsDzqDzpEznEzl\ FzkFziGzhGzfGzdHzcHzaIz`IzZJzXJzWKzUKzTKzUPzUTzUYz\ UazUfzUjzTnzUnzVnzWnzXnzXnzYnzZnz_nz`nz`nzanzbnzcn\ zdnzdnzenzfnzgnzgnzfizzzc } END PARAMETER FILE=========================================

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FOTD 30-05-09 (Beyond Redemption [7.5])
by Jim Muth 29 May '09

29 May '09

FOTD -- May 30, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is a variation on the theme of Z^(3.5)+C. The parent fractal is a Mandelbrot set with chewed-up buds. Today's scene is found on the western side of the Seahorse Valley of the parent fractal, which is curved in toward the main bay. I named the image "Beyond Redemption" for no particular reason. Then I rated it at a 7-1/2. I really did put some extra effort into the coloring. Most of the effect is a result of rendering the image with the inside set to fmod with a proximity of 0.035. The calculation time of 1-5/6 minutes is well with the realm of reason of even the most devoted rationalists. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image there is equally reasonable and a lot more fun. Almost 3 inches (7cm) of rain fell here at Fractal Central on Thursday night, but Friday turned sunny and warm. When the temperature reached 79F 26C, the fractal cats turned quite happy and attacked their catnip toys viciously. My day was normal -- neither good nor bad. The next FOTD will probably but not certainly be posted in 24 hours. Until then, take care, and I saw on one of those pop-science TV shows that we are no more than the string of our memories. Somehow, this still leaves me wondering what we are. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Beyond_Redemption { ; time=0:01:53.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot passes=1 function=recip center-mag=-2.330270308555342/+0.1626775182503306/\ 5765275/1/-85/0 params=3.5/3.5 float=y maxiter=1500 inside=fmod proximity=0.035 periodicity=10 colors=000clzcmzdmzdnzenzeozfpzfpzgqzgqzhrzhrziszi\ szjtwjstksujqwkqukqskprkppkookomlnllojloilpglpfzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzyzyxzxwzwtzuqzsnzqkzo\ hzmezlbzk_zjXziUzhRygOwfLueIsdFqcEobEmaEk`Dj_DiZCh\ YCgXCfWBeVBdUBcTAbSAaR9`Q9_P9ZO8YN8XM7WL7VK7UJ6TI6\ SH5RG5QE5PD4OC4NA3MB4LB4KC5KC5KC6KB6KB7KA7KA7K98KA\ 8K99K99K9AKAAKBAKEBKGBKHCKJCKJDKKDKLEBMEBOEBNFCOFC\ OGCPGCPHDQHDQHDQIERIERJESJESKFTKFTLFULGULGVMGVMHWN\ HWNHXOHXOIYOIYPIZPJZQJ_QJ_RK`RK`SKaSKaSLbTLbTLcUMc\ UMdVMdVLcUMdVMdVMdVMdVMdVMdWMeWMeWMeWNeWNeXNeXNfXN\ fXNfXNfYNfYNfYOgYOgYOgZOgZOgZOgZOhZOh_Oh_Oh_Ph_Ph_\ Ph`Pi`Pi`Pi`Pi`PiaPiaQjaQjaQjaQjbQjbQjbQkbQkbQkcRk\ cRkcRkcRlcRldRldRldRldRldWndTmdRldPkWNjNLiEGl4Ij5J\ h5Kg5Le5Md5Nb5O`5P_5QY6RX6SV6TU6US6VQ6WP6XN6YM6ZK7\ _J7`H7aF7bE7cC7dB7e97f87g98gA9hA9hBAhCAXXbYXcYYcZY\ d_Ze__e`_f``ga`gaahbaibbi } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 29-05-09 (Deep in a Lost Valley [7])
by Jim Muth 28 May '09

28 May '09

FOTD -- May 29, 2009 (Rating 7) Fractal visionaries and enthusiasts: Sometimes I get an urge to return to the beginning, so in today's image we return once more to the greatest of all fractals, the Mandelbrot set, where we check rather deep in the second valley inside a tiny bud on the northern shore line of the third bud out the negative stem. With the ultra-fast math of the type=mandel, (I think it uses pure machine language.), the image finishes in a mere 13 seconds despite the maxiter of 32767. (This was the maxiter limit of the first version of Fractint I tried.) I named the image "Deep in a Lost Valley", which describes its location quite accurately. Considering the dark colors and somber mood, the rating of a 7 could be a bit liberal, but that is what I think it's worth. The calculation time of 13 seconds seems almost impossibly fast. That's how fast the parameter file runs on the P4-2000mhz unit however. Out of curiosity, I checked the time on the old 200mhz machine and found it to be 3-1/2 minutes, about 16 times slower. This means the type=mandel algorithm works especially well with the P4-2000mhz processor. (Strangely, type=formula images run only 4 times as fast on the 2000mhz unit.) Why not forget all this nerdy stuff and trek out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the completed image in total comfort there. Heavy clouds and frequent showers spoiled the very pleasant temperature of 75F 24C here at Fractal Central on Thursday. The fractal cats were more concerned with the unwanted stray cats prowling the area than with most of the day's weather, but when the showers culminated in a heavy thunder-shower at 8pm, they grew a bit apprehensive. My day was about average. The next FOTD will be posted in 24 hours. Until then, take care, and despite appearances, I'm not really that much of a nerd. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= DeepIn_A_LostVally { ; time=0:00:13.12-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-1.3819196009748/+0.014504692704645/\ 6.637531e+009/1/140/0 params=0/0 float=y maxiter=32767 bailout=9 inside=0 logmap=-3314 periodicity=10 mathtolerance=0.05/1 colors=000XqvWqvVqvVpvUpvTpvSovRovRnvQnvPnvOmvNmvN\ mvOksOipPgmPejQcgQadR_aRYZRWWSUTSSQTQNTOKUMHUKEUJC\ SIBRHBPG0OF0ME0LE0KD0IC0HB0FA0E90D90B80A7086075065\ 0GA0mUOzwYzrczmmvjhrgcmdZhaUcYQZXPUWOQVNNUMOUKOTJO\ bIOjHPfGPcFPVEPSDQMCQLBQKAQK9RJBSQzSczTUzTKzUFzVEH\ VEIWDJWCKXBLYBMYANZ9OZ9Pa8Nd8Lg8Jj8Hm8Fp8Ds8Bv89kE\ 8`J8QP8GU8FZLEcXEghFdfGbeH`dIZcIXbJVaKS_LQZLcYMcXN\ cWOcVOcUScSWcQZcPbczecziczmczpcztczwczwczzczzczzcz\ zczzczzczzczzczzczzcLzcMzcOzcPzcRzcSzcUszzzzXzzYzz\ _zz`zzbzzczzezzfzzdzzczzbzz`zz_zzZzzXtzztzztzztzzu\ zzvzzwzzxzzyzzzzzzzzzzzzzzzzzzzzzzzzzFzzEzzEzzDzzC\ zzBzzAzz9zz9zz8zz7zz6zz5zz5zz6zz7z78z99zAAzCBzDCzF\ DzGDzIEzKFzLGzNHzOIzQJzRKzTLzULzWMzYNzZOz`PzaQzcRz\ dSzfTzgTzfSzeRzdRzcQzbQzaPzaPz_OzZNzXMzWLzUKzTJzRI\ zQHzOGzNFzLEzKDzICzHBzFAzE9zC8zB7zEAzGCzJFzLHzOJzQ\ MzTOzVQzYTz_VzbXzd_zgazic } END PARAMETER FILE=========================================

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FOTD 28-05-09 (Fiery and Furious [7])
by Jim Muth 27 May '09

27 May '09

FOTD -- May 28, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the same parent fractal that held yesterday's image. But today, instead of checking the northwest shore line of the southernmost bay, we check the area around a small bud on the west shore line of the middle bay. What we find there is of mild to moderate interest, a scene which, in my opinion, rates a 7. I named the image "Fiery and Furious", but even though it's a rather fiery scene, I can find nothing very furious in it. The calculation time of 2-1/2 minutes will pass in the blink of an eye, which is probably around 1/25 of a second. This means that around 3,750 eye blinks will be required to finish the calculation. With this many blinks in mind, I recommend going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and saving those blinks by viewing the already-finished image posted there. The rain ended and the temperature rose to a more seasonal 64F 18C here at Fractal Central on Wednesday. But the heavy low clouds hung tough and the fractal cats showed their displeasure. As for work, I finished it in half a day. FL spent a good part of the day working in the garden. The next FOTD will be posted in 24 hours. Until then, take care, and be of sound mind and light body. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fiery_and_Furious { ; time=0:02:35.53-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.4326946656431548/-0.578103614769745/\ 316648.8/1/132.5/0 params=-5/-1.5/-1.5/-5/0/0/0/0 float=y maxiter=3200 inside=0 periodicity=10 colors=000xR7xN7wQ7wQ7vP7vP7vN8uO8tN8tN8sM8tM8sL8p\ L9rK9qK9rJ9pJ9nI9oIAoHAoHAnGAlGAmFAmFAmEBlEBkDBkDB\ jCBkCBiBCiBChAChACi9Cg9Ch7Df8Cg9CjABiABiBBjCAkCAlD\ 9mE9hF6pE7oE8kE8mE9hD9jDAiDBhDBgDCeCCdCDcCDdCEaCF_\ BFZBGYBG_BHWBIUAITAJSAJRAKP9KO9LN9MM9ML9NJ8NI8OH8P\ G8PF8QD7QC7RB7RA7S97T76T66U56U46V25U36V36V36V37W47\ W47W48X48X48X59Y59Y59YCAZKAZ6EZ6B_6B_MFYUK`BP_6B_d\ FYGJXcUVPXUUUSoYRb`PmcOlZMrjMtkLtkLwiKv_KwkKxkJylJ\ zlIzfIzlIzlHzlHzmGzmGzmGzmFzmFznCzmEzmFzlGzlHzkIzk\ JzjKzjLziMziNwhOwhPwgQwgRwfSmfTmeUmeVmdWmdXgcZgc_g\ b`hbahabhaci`di`ei_fi_gjZhjZijYjkYkkXlKAKlWnlWoQAN\ mUpKAKmUqmUqPANkUnKAKjSjjRgOAMiPcKAKhNZhMXNALiLWKA\ KgKVfKUMAJcJTKAKaIS`IRLAHYHQKCKWGPVFOKAFSFNLEFQEMP\ DLJAGNCKLCGKCJJBIHBFHAHWAGE9GD9FC9FB8Ec8D87D77C66C\ 56Bi5A46B77CB7CE8Do8DL9EP9ESAFWAFuBGbBGeCHiCHlDIyH\ IrY8sX8tV7tU7zM7uR7vQ7yS6 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 27-05-09 (Elusive Flutterby [7.5])
by Jim Muth 26 May '09

26 May '09

FOTD -- May 27, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image came about when I took a second look at the parent fractal that results when various portions of negative 1.5 and negative 5 are combined and (1/C) is added. Like most fractals that combine negative exponents, this parent is beyond descrip- tion, though it is quite simple to reproduce. I chose to investigate a tiny valley on the northwest shore line of the southernmost large bay, which appears to have the best developed Mandelbrot characteristics. In a matter of minutes I found a minibrot very near the limit of resolution, which became today's FOTD. I named the image "Elusive Flutterby" when for some reason it reminded me of a butterfly. I believe this class of insects were originally called flutterbys. The rating of a 7.5 might stretch the truth a little, but what the heck. Sometimes I stretch the truth quite a lot. At least the calculation time has not been stretched. It took an entire 5 minutes to calculate the image on the fast 2000mhz machine. And don't forget the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is or momentarily will be posted for immediate and absolutely total gratification. Heavy clouds, steady rain, and a chilly temperature of 54F 12C kept things well dampened here at Fractal Central on Tuesday. The fractal cats' spirits were especially well dampened, but an extra treat of tuna and cheddar took their minds off the bad weather, and a dose of fresh catnip kept their minds off the weather. For me it was a back to work day. Luckily, the work was not very heavy, and was out of the way just after lunch. To fill the afternoon I watched one of the junkiest of junky old sci-fi movies, "The Creeping Terror", which is so bad that it must be seen to be believed. Actually, the movie's awefulness gave me just the push I needed to find today's image. The next FOTD image will be posted in 24 hours. Until then, take care, and since dreams happen inside the brain, how is it possible to dream of something too large to fit in the brain? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Elusive_Flutterby { ; time=0:05:05.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.06238493615275089/-1.513718825559952\ /2.08e+012/1/-37.5/0 params=-5/-1.5/-1.5/-5/0/0/0/0 float=y maxiter=7200 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000YZZb`YgcXleWVUiDIvCKrCLoCNkCOhCQeCRaCTZC\ UWCWSCXPCZLC_ICaFCbBCd8Ce5Dc9EbCF`FG_IHYLIXOJVRKUV\ LSYMR`NPcOOfPMiQLlRKoPJkNIgLHcJH_IGWGFSEFOCEKBDG9D\ C7C85B44B159757D55J53P51V82XA2ZC2_E2aG2cJ3dL3fN3hP\ 3iR3kT3lR7gPBcNFZMJVKNQIRMGVHFZDDb8Bf4Ai0Fj2Jj3Nj4\ Sj5Wj6_j7dj8hj9ljAmiDniGniJoiMpiPphSqhVrhYrh`shcsh\ f000WNMKCB821C50G80KB0NE0RG0VJ0YM0aP0eR0hU0lX0p_0s\ a0mU6hNCbGHY9NT2S5nA6jD6fG6bJ7ZM7VP7RS8NV8JY8F`8Bb\ 9A_9AX9AUAARAAOAALAAIBCJBDJBEJBFJBGJBHKBIKCKKCLKCM\ KCNLCOLCPLCQLCRLHTJLVIPXHUZFY`EaaDY`CV_BSZAPY9MX8J\ X7LSGMOONJWPFdQAlR6t_GhgPXoYLZJn_PkaVib`fdfcelaZie\ TghNekHbnB`q5Zt7`o8bkAdgBfcChZEjVFlR2mT7nRBnPGnNTu\ 9QrENpIKnMHkQEiUBgY3eaAjZCnW8vRErTKnUQkVWgWadXg`YO\ qxkMJmYZsfyqgupgqnhmmhitqnpljlhfhcbd_Z`VVXRRTMNL7C\ NDGPIKRNOSSRUYVWbZYgbPonUmiZleck`mqNjmSgjXefabcfPS\ x``jkiXvBGvXIEPbJRaOU`TW_ } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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The Fractals Journal
by Paul N. Lee 25 May '09

25 May '09

For over 16 years, the Fractals journal has been published every three months. And the World Scientific Publishing Co. hosts information about this journal: http://www.worldscinet.com/fractals/fractals.shtml The past volumes are available online at: http://www.worldscinet.com/cgi-bin/details.cgi?id=jsname:fractals&type=all Where the most recent issue includes a 14 page article by BENOIT B. MANDELBROT and MICHAEL FRAME. Some of the most accessed articles are: • Estimating The Fractal Dimension Of Plants Using The Two-Surface Method: An Analysis Based On 3D-Digitized Tree Foliage Frédéric Boudon, Christophe Godin, Christophe Pradal, Olivier Puech And Hervé Sinoquet • Estimation Of The Fractal Dimension Of Fracture Surface Patterns By Box-Counting Method Manabu Tanaka, Atsushi Kayama, Ryuichi Kato And Yoshiaki Ito • A Generalized Mandelbrot Set For Bicomplex Numbers Dominic Rochon • Structural Scaling In Bach's Cello Suite No. 3 Harlan J. Brothers • Fractal Analysis Of Dendritic Arborisation Patterns Of Stalked And Islet Neurons In Substantia Gelatinosa Of Different Species Nebojša T. Milošević, Dušan Ristanović, Jovan B. Stanković And Radmila Gudović Most issues contain around a dozen articles, where each article is several pages long. And there is a lot of good material to be found for those with the time for reading. Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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Re: [Fractint] ???
by JackOfTradeZ＠comcast.net 25 May '09

25 May '09

. This particular type of fractal is a favorite of many a fractal enthusiast. Here is another one of interest: http://www.fractalforums.com/gallery/?sa=view;id=154 . Awesome! Looks gothic, almost H.R.Gigerish - like something from the "Alien" movies. Give me a fractint par for it ......... .

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FOTD 26-05-09 (World-Wide Webs [7])
by Jim Muth 25 May '09

25 May '09

FOTD -- May 26, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image is filled with things that look like spider webs. This is why I named it "World-Wide Webs". The parent fractal is what happens when the formula Z^(1.83)+C is calculated 18 levels up the logarithmic hyper-ladder, (or hyper-spiral). This parent resembles a partially-eroded Mandelbrot set rotated about 180 degrees, with a very large disconnected minibrot just inland on the northwest shore line of the main bay. Today's scene is located in what I take to be East Valley of this minibrot. The rating is limited to a 7, mostly due to the colors, which have an annoying muddiness that I couldn't get rid of. But the image is still an example of some of the unexpected scenes in the fractals with exponents of Z between 1 and 2. The calculation time of 1-2/3 minutes is blessedly brief. Equally brief is the trip out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the already-calculated image may be viewed at leisure. Tons of sunlight prevailed here at Fractal Central on Monday, and the fractal cats made the most of every photon of it. Nicholas got a bit testy when a wandering tomcat made a litter box of the side walkway, but Cassie calmed him in a hurry when she started playing with the catnip rat. My day was slow and lazy, which is the way I prefer days to be . . . up to a certain point, that is. The next FOTD will be posted in 24 hours. Until then, take care, and how do we know for sure that anything is real, or even if such a thing as reality actually exists, for that matter? (My guess is that it's a leap of faith necessary to make science work.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= World-Wide_Webs { ; time=0:01:42.19-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=-0.8745118926611518/+0.566229601300528/\ 283049.1/1/-55/0 params=1.83/0/18/0 float=y maxiter=1750 inside=0 logmap=133 periodicity=10 colors=00050050050250950F50K50Q50X50VB0TH0OM0OT0MY\ 0IiBgvazzzzzvzzozzizzdzzXzzQzzKzzFzz9zz_zxzzozzzXz\ z0zz0zt2zdFzOQz9dz0oz5goFaVOX9YQ0gK0eV0dd3a_2_Y0YX\ 0XV0XT0VQ0TO0QM0QK0OI0QH0VD0_A0eA0hA0mA2pA5sA7vEBx\ IFzMIzQKzSOzUOzWOzYOqTOgOOY0OO0OF0O50O00O00O00O00O\ 00O20O95OF9OMFVVK_aQgiXno_vxezzlzzqzzxzzzzIz_QzXXx\ VdxQlvMqvKztHztFzqBzq9zzezzzzzzxqoideXOVIBK50B0020\ 000000002303905F07K09O03H00B003000000700D00I00O00T\ 00X00_00d00g53lB9oHFtMIxTOzYVzdYzidzngz_QzM9z90zD2\ zF7zIDvKInOOeQVYV_QXeI_lBaq3ex0gz0lz0zzzTzzzzz0zzz\ zz0zzzzz0zzzzz0zzzzz0zzzzzzzzzzzzzz2zz3zz7zz9zzBzz\ Q0zM0zI0zH0zDBz9Mz7Xg3gO2qI0za0zi9zoOzvdzztzzzzzzz\ zzvdz_0Xqd0zz7znFzIMz0Bz30lH0XXzFiz0xz0zz0zz0zz0zz\ 0zz0zz7dzFHzK0zV0zd0zn0zx0zz0zz0zz0zz0zz0zz7zzHzzO\ zzKzzHzzDzz9zz5zz2zz0zz0zz0Kz2ez3zz5zzYzzzzzqzzizz\ azzVzzMzzFzz7zz0zz5nzngzo } 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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FOTD 25-05-09 (Inside the Nucleus [8])
by Jim Muth 25 May '09

25 May '09

FOTD -- May 25, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image, which is a slight reworking of an earlier FOTD image, reminds me of what one might see if he could shrink himself to the size of an atomic nucleus. In my earlier years I pictured the nucleus as a boiling raspberry, but this was before I realized that things like atomic raspberries and tiny solar systems are mere ideas, models that help us think logically about the atomic realm. Atoms and sub-atomic 'particles' cannot be pictured because they lack the attributes we associate with 'reality', including appearance. The mere fact that we sometimes wonder whether atoms are truly tiny real 'objects' or mere mental fantasy shows that we have no conception of what lies beneath the classical world of the five senses, another fantasy world, upon which materialists have bestowed the exalted status of 'ultimate reality'. Today's image is definitely virtually real and it has a definite appearance. It is the Julia set of the Z^(1.3) Mandeloid as it appears 3 levels up the logarithmic ladder. Most of the action was achieved by rendering the scene with the inside set to bof61. The name "Inside the Nucleus" refers to my impression of the image. Even though the image is a virtual repeat, in my opinion it still rates an 8. And the calculation time of only 16 seconds will seem to pass in a chronon. The finished image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Oppressive heat and humidity here at Fractal Central on Sunday was interrupted at 5pm by a heavy but otherwise harmless thunder- shower, which dropped the temperature from 86F 30C to 68F 20C. The fractal cats paid little attention to the rain. My day was spent mostly in recovery from Saturday's trip to O.F.C. The next FOTD will probably be posted on schedule in about 8 hours. Until then, take care, and what do we mean by meaning? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Inside_the_Nucleus { ; time=0:00:16.66-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC center-mag=-0.00327762/0.00070\ 084/9.34161 params=1.3/0/3/0/-0.74930081/0.3777896\ /0/0 float=y maxiter=1000 inside=bof61 logmap=6 periodicity=10 colors=00000N00s00s00O00K00K00L00N00S00T00V00P00V0\ 0b01e04Y16U47h78v9B_CCUFEjIHjKIbMKjQMjTOlRQiUSlbVl\ eWmcYmlamobmscovgoyoozjozlozmqzzzxmsvmstmssxtqotoo\ vmrzlzzhzzgzzezzczzzzzzzzzzzzzzzzzzzzzzzzzz1lz0hz0\ sz0ex0bt0`q0tz0Yj0Ve0Tb0gs0OW0MT0LQ0az0KM0KL1IL1Qe\ 3HK3HI4FI04H3EH6EFcCF7CE7CC8BCcBB09B999B89c88078C7\ 7E67E66C13E66F87HB9IEBKHELKFMMIOQKQTMSWOT_QzYOzWOz\ WMzVMzVMzTLzTLzSKzQKeQKgOIhOIjMHzMHzLHzKFzKFzIEzIE\ zHEzHCzFCzEBzEBzCBzCAzB9zB9y9Cx9Ev9Ft9Hs8Ko8Lm8Ml8\ Oj7Sh7Te7Vc7Wb7Y`6`_6bW6cV6eT4hS4jQ4lM4mL4oK3sI3tH\ 3vE3xC1zB1z91z81z84z71z60z40t30m10g00`10b10c11e17g\ 3Ch3Hj3Ml3Tm3Ym6Vo7To8SqBQqCOsEMsHLtIKtKItMHvOFvQE\ xTCxVByW9yY8y`6zb4zc3zg1zh0zj0zm0zo0zq0zt0zv0zx0zz\ 0zz0zz0zz0zz0zz0zy0vx0sv0ms1hTOQSKOSHMQELOBIO8HM4F\ L1EL0CK0BK09I0BH0CF0CE0EC0FB0F90H80I70I60K40L30L10\ M00O00O00Q00S00S0PY0cc0vY } 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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Re: [Fractint] ???
by JackOfTradeZ＠comcast.net 25 May '09

25 May '09

. Anyone ever hear of, or see, the "burning ship" fractal? It looks awesome, I see it around but never with formulas. Is there a FRACTINT PAR or FRM for this? Might make a good animation, like sinking or getting torpedoed .... .

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Wolfram Alpha Boots Up
by Paul N. Lee 24 May '09

24 May '09

Friday evening (May 15, 2009) was the debut of Stephen Wolfram's "Wolfram Alpha". It officially went public on Monday (May 18, 2009) from the web site at: http://www.wolframalpha.com/index.html According to this article: http://www.hpcwire.com/features/Wolfram-Alpha-Boots-Up-45364022.html Wolfram Alpha employs HPC clusters for its computational hardware. And at launch time, the application had access to about 10,000 x86 CPUs spread across five data-centers. Apparently there are still a few problems to work out, based upon what the article states, but it is interesting to see that queries for fractals can be generated with varying iterations specified. Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

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FOTD 24-05-09 (Primary Splat [No Rating])
by Jim Muth 24 May '09

24 May '09

FOTD -- May 24, 2009 (No Rating) Fractal visionaries and enthusiasts: With a calculation time of almost 8-1/2 minutes, today's image is too slow for what it is worth. But it's still worth a peek on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The parent fractal is a kind of Mandeloid with a double-lobed main bay that came about when I combined various portions of (1/Z) and Z^(-13) and added (1/C). Today's scene is located rather deep on the western shore line of the north branch of the pseudo-Seahorse Valley of the parent. The first dozen or so color registers are set to solid black to give the effect of a minibrot hanging in endless space. The name "Primary Splat" can mean anything one wishes. With such a hasty yet slow image, I could not find a proper rating, so I simply let it go with no rating at all. Talk is cheap, but all curiosity may be satisfied and questions about the appearance of the image answered on the above mentioned web site. Light rain showers fell at New Fractal Central on Saturday, but at Old Fractal Central, 150 miles to the south, the weather was perfect, with blue skies and a temperature of 84F 29C. The fractal cats were lazy while I was away. The next FOTD will be posted in about 16 hours. Until then, take care, and unless you are a photon, you can't be in two places at the same time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Primary_Splat { ; time=0:08:27.97-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.951346025334112/+0.5908106245004408/\ 1.6e+007/1/35/0 params=0.096/-13/0.96/-1/0/525/0/0 float=y maxiter=7500 inside=0 logmap=1100 colors=0000000000000000000000000000000000000000000\ 000003ES3DL7BQAAVE8_H7dL6iO4nS3sV2wT5tR8qQBoODlNGj\ LJgJLdIObGR_FTYD__Bfa9mc8seFr`MrWTqS_qNfpImpEtg9zo\ 5zU8zUAz0CzKFzKHbJJZDMV8OS3QT2PT1OU2NU3NU3MV4MV4LV\ 5LV5LS4NP3PM3RJ2TG2VD1XA1Z70`50b85_BAXEFUGKSJPPMUM\ PZJRcHUhEXmB_r8aw6_v7Yv7Wv7Uv7Sv7Qv7Ov7Mv7Kv7Iv7Gt\ BErEDpIBnLAlP8jS7hW5fZ4da6cb8cc9cdBceCceEbfGbgHbhJ\ biKbiDeP6g47h67h77i97iA8jB8jD8jE8kF8kH9lI9lJ9mL9mM\ 9mNDnLHoKKpIOqHRrFVsEZtDauBevAhw8lx7oy6mvCktIirNgp\ TenYclcbjh`hi_gjZekYdlXcmWanV`oUZpTYqSXrRVsQUtPSuO\ RvNQvUbw_owWruS_sOTqKazGDmC6kD0KD0iELhEQgEUgGScIQ`\ JPYLNUMLROKOPIKRGHSFEam6`z5`j5zi5_h5Zg5Zf4Ye4Yd4Xc\ 4Xb4Wa3Z`3Z_3cZ3cY3hX3hZ8m`DmbIrdNrfSvhXvjazlfznkz\ ppzruzsyzowzlvzhuzetzaszZrzWqzSpzPozLnzImzFlzIhzKd\ zNazPYzSVzURzXOzZKzaHzcDzfAzh6zj3zWDzHNz2Xz7WzBWzF\ VzJVzLkzKkzJlzIlzHlzGezFZ } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 23-05-09 (Primary Aversion [6])
by Jim Muth 22 May '09

22 May '09

FOTD -- May 23, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today's image is an improvement over yesterday's, though not as much of an improvement as I had hoped for. It's an evaporated scene in the parent fractal that results when various portions of Z^(-1.15) and Z^(-5.5) are combined and (1/C) is added. The obvious flaw is the raggedness. I was a bit too enthusias- tic with the magnitude and went too far beyond the limit of resolution. But the jagged edges can actually be taken as a part of the texture, so I inserted the mathtolerance entry into the parameter file and let it go. Like so many of the names I give to the FOTD images, the name of today's image, "Primary Aversion" means nothing more than what the viewer might put into it. The rating of a 6 is 2 points higher than yesterday's abysmal 4, but still only the slightest bit above average. The calculation time of 3-1/2 minutes is true on the 2000mhz unit. On other machines the parameter file will run faster or slower. And as always, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Midsummer arrived in full force here at Fractal Central on Friday, with near total sun and a temperature of 88F 31C. The fractal cats spent most of the day watching the local stray cats attacking the catnip mint plants FL planted in her garden the evening before. By the end of the day, the catnip was gone and the neighborhood cats were quite happy. My day was near average. The next FOTD might not be posted until midday Sunday, since I'll be making a short trip back to Old Fractal Central on Saturday. Until whenever, take care, and have a good time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Primary_Aversion { ; time=0:03:29.68-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+2.299459189430742/-1.308475692667019/\ 1.22481e+013/1/-102/0 params=-5/-1.15/-1.5/-5.5/0/\ 1e+100/0/0 float=y maxiter=2500 inside=bof61 periodicity=10 mathtolerance=0.05/1 colors=000Q40D2020000000000002004606F08M0BS0Da2Fg2\ Hp4Jw0Hz4Mz8OzBQyFSwJVuMXrQ_pSanXcjaegcgegjcllann_\ rpXurVzp6zz0zn0z_0zJ0z44z00z04y0Bw0Hr0Op6VnD_jJegO\ leVraay_gzMrzSnzXlzajzegzjezncwrarw_pzXlzjpzVjlFer\ HzS0a00000020680JH0XO0j20zH0yV0uj0py0pw0lu0gr2cp2_\ n4Vl6Sj8Og8JeBFVeeVzOXpVXaa_Jg_4n_0r0z00z00u00n00e\ 00_00S00J00D0000020260DD4OHBXOHgSQr_Xzcczjjzlwznpz\ plzrgzrczu_zwVwwQryMlzHgzDcz8_z4Vz0Qz0Mz0Hz0zz0zz0\ wz0pu0lj0ea0aQ0VH0Q60J00F00B00H00M00S00X40cB0gF0lM\ 0rS2w_6zeBzlFzeHnQFrSDeJB_FBQB8H46F4400400V00020n0\ 0000200200O00200400400400404600N00PV660O4e64062062\ 2g0S60H60H60OS0S6Dn6jX6SFSB0600600n0za0zz00l0zr00z\ 00z0zz0zz0zz00z00z0zz0zz00z4zz62z8zyDBuFFpHHlJzgDB\ c68_06V0zS00O00J00F0zD06F0nH0SH0cJ4pMDzMOzOXzQgzQp\ zOnzMlzJlzHjzFgzDgzBez8cz6cc4zXSzSSzVSzXSz_Sza6Oc6\ Me8Jg8HjBFlBDzHMyDFnBBa84 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 22-05-09 (No Discontinuities [4])
by Jim Muth 21 May '09

21 May '09

FOTD -- May 22, 2009 (Rating 4) Fractal visionaries and enthusiasts: Due to a very busy day on Thursday, I had no time for a proper fractal search, so I dredged up an image that I was working on when I shut off the fractal machine for the day Wednesday evening. The image is typical of the stuff I throw in the trash bin several times every day. The name I gave the image, "No Discontinuities", is not true. I thought it was true when I named the image, but a closer examina- tion revealed a subtle break extending west-southwest from the west end of the minibrot. But considering that the image is a mixture of Z^2 and Z^4.5 features, the existence of only this single minor fault line is unexpected. The scene is obviously in the Seahorse Valley area of a larger parent fractal, in this case a grossly inflated Mandelbrot set, which takes on new and unusual characteristics in its depths. A barely noticeable fault line does not make a great fractal image. Since I could find little else of worth in the scene, I rated it at a humble and below-average 4. The calculation time of 3 minutes may be cut to 2 minutes, with only a slight loss of accuracy, by rendering the image with the passes set to 'g' instead of the '1' in the parameter file. The image may be seen in full accuracy in even less than 2 minutes by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is posted for instant satisfaction. Total sun and a temperature of 86F 30C made Thursday seem like a July day here at Fractal Central. The fractal cats had their thrill when they spotted two pigeons cooing and doing naughty things on the side walkway. My thrill came when I finished the unexpectedly heavy work and chose the unexpectedly lackluster fractal. The next FOTD, certainly no burning ship, will be posted in 24 hours. Until then, take care, and try to fill the hollow inside. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= No_Discontinuities { ; time=0:03:01.59-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=-149.5262833418637/+23.25272903656032/\ 26715.09/1/-40.25/0 params=4.5/200 float=y maxiter=25000 inside=0 logmap=140 periodicity=10 colors=0008gz9hzAhyBhvChsChpDimEijFigGidGibFjdFkfF\ lhFljFmlEnnEopEorEptEqvCszEqxGpwIovJnsLmqNkoPjmQik\ ShiUggWeeXdcZca`a_b_YbZXbYVaXSaWRaVP`UN_TL_SLZRKYQ\ JXOIXNHWLGVKF`G8VJFFC5QLL_T_i`nbVeXPYRKPLEHF88930C\ 62F93IC4LE5OH6RK8UN9XPA_SBbVCeYEh_FkbGneHsgHpgIngJ\ kgKigLfgMffLdgNchObiPajR`kS_lTZmVYnWXoXWpZVq_Ur`Ts\ bStcRudNthQueSubUu`XuYZuW`vTbvRevOgvMivJkwHnwEpwCr\ w9tw7qu7nt7kr7hq7eo7bn7_l7Xk7Ui7Rh7Me5Pg7Sh9UiAXkC\ _lDamFdoGgpIiqJelHbhG_dFX`DUXCRTBOP9LL8IH7FD6KEBPE\ GTEKYEPaETfEYg8YjEamKepPigPcZPZHKVRPU`UTjZSsdMtcSu\ bXvabw`gx`luZjsYiqXhzVgmUfkTdiScgQbePacO`z3ZzN_zf`\ zz`zyZzwYzuXzsWzqZGo`zmbzmdzmfzmhzmrzmjzmbzoVzqNkt\ Fzw7zz0zz2zz4zz6zz8zzAzzCzzFzzDzzCzzBzzAzz9zz8fz7z\ z6zz5zzNzzOzzOzzOzzOzzOzzOzzOzzPzzPzzPzzPzzPJzPzzP\ zzPzzazznzz6zzzzztzzozzizzdzz_zzUzzPzzJzzVzzVzzVzz\ XzzZzz`zzazzczzezzfzzhzzj } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 21-05-09 (Holey Seahorses [7])
by Jim Muth 20 May '09

20 May '09

FOTD -- May 21, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today we take a journey into one of those oversized Mandelbrot sets generated by the NewDivideBrot formula, which are Mandel- brot only on the surface. In its depths, today's M-set develops distinctly Z^(77)+C characteristics. In the image we delve into the Seahorse Valley area of the parent M-set. Near the limit of resolution we find a scene that by all rights should have a quadratic minibrot at its center. All the quadratic trimmings are there, but at the center we actually have a Z^(77)+C minibrot. Since we are at the limit of resolution, it is not possible to go any deeper into the image, but from studying similar scenes at lesser magnitudes, I can state that there are no discontinui- ties in the scene. The sharp cutting-off of the quadratic elements is a total illusion. It all blends smoothly. The name I chose for the image -- "Holey Seahorses" -- refers to the apparent hole in an otherwise pretty normal appearing Sea- horse Valley scene. It is not a call to the god of seahorses. The rating of a 7 is just far enough above average to make the calculation time of 2-1/2 minutes worth the effort. A trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image is always worth the effort regardless of the calculation time. An absolutely perfect day prevailed here at Fractal Central on Wednesday, with a cloudless sky, light winds, low humidity and a temperature of 84F 29C. The fractal cats purred in delight. My day was mildly busy taking up the slack while FL busied herself in the fractal garden. If all goes well, tomorrow will be the same. The next FOTD will be posted in 24 hours. Until then, take care, and how important is an individual person to the uni- verse as a whole? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Holey_Seahorses { ; time=0:02:34.08-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=-149.5299161466038/+23.24859716591299/\ 4.869088e+010/1/-2.75/0 params=77/200 float=y maxiter=3600 inside=0 logmap=302 periodicity=10 mathtolerance=0.05/1 colors=000hFagFZeGWdGTcGQbHNaHK`IH_IEZIBWJCUKDSLDQ\ LEOMFLNFJOGHOHFPHDQIBQIDMEEIBFE8GA5LC7QD8UE9ZFAbHB\ gICkJDpKEtLFsPGsTHsXIs`JsdJshKslLspMstNsxNowPkwQgv\ SdvT`uVXuWTuXQtZMt_IsaEscBseKsgUri`qkcom`ooannZmnW\ lmTklQjlNikKhkKbfKXaKRXKMTKGOKAJK5FL4IM4KM4MN4PN4R\ O4TO4WP4YQ3_Q3bR3dR3fS3iS3kT3mT3oU9lUFjULgUReUXcUb\ `UhZUmXUgZUb_UY`UTaUObUJcUEdU9eY8g`7ic7jg6lj5mm5oq\ 4pt3rw3sv4qv5pv6ov7nv8lv9kvAjvBivChvDfvEevFdvGcvGb\ aBaI7`GAZFCXEFWDHUCKTBMRAOQGPVMP_RPdXPhaPmgPrlPvjR\ phTjfVdeXZcZTa`N`bHVYJPTKKOMEJN8EP39Quy6ovEisLcqSY\ nZSkeMilGfsAdzF_xKWwOSvTOuXJtaFseBrj7qn3pY8VX8XW8Y\ V8_U8`T8bS8cR8eR8fQ8hP8iO8kN8lM8nL8oL8pIAcFBSCDFAE\ 3LBBV8Jd5Rn3Yp4`q5cr5fs6it6lu7ov7qrCioGbkLWhPPdUIa\ YBZa4`_8bZBdXEeWIgVLiTOjSRlRVnPYpO`qNdsLguKjvJmwLj\ wMgwNewObwP_wRYwSVxTSxUQxVNxXKxYIxZFx_Cx`AAsRCqPEo\ NGmLIlJKjHMhFNgDPeBRc9Tb7 } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 20-05-09 (Candy For The Eyes [6])
by Jim Muth 19 May '09

19 May '09

FOTD -- May 20, 2009 (Rating 6) Fractal visionaries and enthusiasts: Fractals are candy for the eyes, which is what I named today's image. (Of course, fractals can also make a kind of music, though I have yet to hear any fractal 'music' that I would like to listen to a second or third time.) Today's image is evaporated, which means the bailout radius is so large that no points at all ever escape, a thing that is possible only with fractals created from negative exponents of Z. But an evaporated image does not necessarily mean a blank screen. When a fractal evaporates, it leaves a ghost behind that can be made manifest with certain active inside fills, such as the 'bof61' fill of today's image. I rated the image at a 6 -- an adequate rating. The calculation time of 1-3/4 minutes is quite brief, almost as brief as the time required to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoy the completed image posted there. Wall-to-wall sunshine and a temperature of 73F 23C made Tuesday all that could be asked for here at Fractal Central. The macho fractal cats enjoyed the sun on their shelf in the sunny south- west window. My day was about average. The next FOTD will be posted in 24 hours. Until then, take care, and be the first to solve the ultimate paradox. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Candy_For_The_Eyes { ; time=0:01:45.08-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+206.0879684531/+359.192822455/204.418/\ 1/85/0 params=2.5/-1.05/0.35/-5.05/0/1e+100/0/0 float=y maxiter=12500 inside=bof61 periodicity=10 colors=000NZ`KZWG_QD_LA`G7`BD_HI_MNZRSZXXYaaYffYke\ e`dlRctGbz6_t9XmCVgFS`HQVKNONLIPOHQRHRUGRXGS_FSbFT\ eFT070TYLNfHGoDAx94z6GzMSzabwpYvrUvsQuuMuvIwwEywBz\ wUlwkZwjYriXnhWihVegUafTXeSTeSP`UTXVWTX_PYbL_fH`i0\ 70LVlMSmOQnQNpRKqTHrUFs`NtgUtn`tugtn_`gTIdXOa_TZcY\ WfbTjgQmlNqqKtvRiwY_wdQwkGwfEhbCUYAFU90SB1QC2070MF\ 4KH5II6GJ7NQKTXXZcidjunuhwzXkmR`WLQFFYKVmOzmZmfNr`\ TlVDeP8_QEN7JB9RJAZRBfZCnfDvmBol9hk7aj5Vi3Pi8MhDJh\ IHgNEgSCfX9fp7f`Ec_LaZR_YYXXdVWjTzzzzzzzzrzzmzzczz\ UzzKzzGzzGzzFzyFzrEzkEzdIzYMzRQzRTZhXWd`TadRZgTYcV\ X_WWWYVT_UP`TLbSHdREeQAgP6hP3fO7eOBcNEbNI`MM_MPYLT\ XLWWK_UKcTJfRJjQInOIqNHuMHxKMuJQs070GZnEblDfjHggKh\ eOicRjaVk_YlYalWdmUhnSkoQopOrqMuqKjrL`sMQtNGuO6vO8\ tMAsLCqKDpJFoIHmGIlFKjEMiDNhCReAUc9Ya7`_6dY4gW3kU1\ nS0mW2l_3kc4kg6jk7io8isAhwBgzCgzDanFWZGZYJaYLcYNfY\ PiYSkYUnYWpYYhcTYagUXkQYe } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 19-05-09 (Tardy Technicality [7.5])
by Jim Muth 18 May '09

18 May '09

FOTD -- May 19, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: The parent fractal of today's image is a Mandelbrot set caught in the act of devolving into the circular hole created by the iterated non-formula Z+C. This halfway fractal is shaped like a tear drop with a tiny extra bay on the smooth shore line of its pointed east end. (I suspect that this tiny extra bay is actu- ally the extremely shrunken main bay.) The west side of the parent fractal has the expected Mandelbrot buds along its shore. Today's scene is located near the tip of a filament extending from one of these buds. The shape of the parent fractal is symmetrical with respect to the X-axis, though the bands of the outside=imag coloring feature are not. Therefore, changing the sign of the Y coordi- nate while keeping the absolute value unchanged brings an entirely different color scheme to the mirrored same scene. The name "Tardy Technicality" has little meaning. And why must a name have meaning or even make sense. (Remember the song 'Stairway to Heaven'.) The rating of 7-1/2 indicates that the image is good but not exceptional. One half of the rating is a reward for the effort I put into the coloring. The calculation time of 7 minutes is slightly slow, but nothing that will cause civilization to grind to a halt. And even the small effort of running the included parameter file may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The partly cloudy skies were compromised by an unusually chilly temperature of 57F 14C here at Fractal Central on Monday. The fractal cats made themselves comfortable by the heat, which came on again for an hour. My day was quite busy, but concluded successfully. The next FOTD will be posted in 24 hours, with or without the approval of the cats. Until then, take care, and be careful of what you think. Your thoughts are being monitored for illegal traces of hate. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Tardy_Technicality { ; time=0:07:01.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=-0.8127135141137847/+0.8410592011071745\ /4.98609e+010/1/-167/0 params=1/2 float=y maxiter=15000 inside=0 outside=imag periodicity=10 mathtolerance=0.05/1 colors=000mzzIIzMGzPEzTCzXAz_8zc6zg4zj2zn0zr0zu0zK\ 2dK0cK0cK0cK0cK0cK0cK0cQ2eWBfaLggUhmciwrntolrljpih\ nfflddjabgZaeW_cTYaRW_OUYLSWIQTFPRDNPALN7JL4HJ1FC0\ EE0EF0EG1EH3EJ1EL3EN5EP7ESAEUCEWFEYHEZHC_JE`LG`OIb\ QKbQMdTOeVQfXSg_Uh`WibYle_phavndysiztjzzpzzzzwqzzn\ zslwrhrr`nnZjnXfmUbjT_jSXjRVjQUjOTjNRiMQiLPiKNiIMi\ HLiGJiFIiEHiDGgGGfJGeMGdOGcRGbUGaWG`ZG_aGYcGXfGWiG\ VkGUnGTqGSsGRvGQyGPzGPzHQzIRzISzJTzKUyKVyLVyLWyMXy\ NYxNZxO_xP_xP`wQawQbwRcwSdwSevTevUfvUgvVhuViuWjuXj\ uXkuYltZmtZnt_ot_otYluXiuVguUdvTbvR_vQYwOVwNTwMQxK\ OxJLxJNzILzIKyIJxIIxHHwHGvHFuHEuGDtGCsGBr6EpACqDBr\ GArK9sN8tQ7tU6uX5v_3vb2wf1xi0xl0yp0zs0zv0zw0zx0zy0\ zy0xz0uz0rz0oz0lz1iz2fz3cz4`z5Yz6Vz7Tz6Uz6Uz6Uy6Ux\ 6Uw6Uu6Ut6Us6Ur6Up6Uo6Un6Ul6Uk6Uj6Ui6Ug6Uf6Ue6Uc6U\ b6Ua6U`6U_8TZASYCRYDQXFPWHOAXiAWjBVlBUmBToBSpCRrCQ\ sCQuDPvDOxDNyEMzELzEKzANz } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 18-05-09 (Gear Train [6.5])
by Jim Muth 17 May '09

17 May '09

FOTD -- May 18, 2009 (Rating 6.5) Fractal visionaries and enthusiasts: Today's over-magnified image lies in the nascent Seahorse Valley of a parent fractal that is rapidly morphing from the Z^9 Mandeloid to the Z^2 Mandelbrot set. The image actually lies in a little offshore debris. I named the image "Gear Train". One glance will show why. Then I rated it at a mediocre 6-1/2, one-half point of which is due to the coloring. Another glance will show why. Most of the image's effect is a result of rendering it with the outside set to 'tdis' and the inside set to 'fmod', with a proximity of 0.6902. The calculation time of just under 3 minutes will pass in the blink of an eye, or more likely in a couple thousand blinks of an eye. The best way to avoid tired eyelids is to hurry to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and gaze in unblinking delight at the finished image posted there. The partly cloudy skies let through just enough sun here at Fractal Central on Sunday to keep the fractal cats happy. The temperature of 61F 16C was a bit chilly for the middle of May, but warmer times are coming. The next FOTD is also coming. It will be posted in its full glory in 24 hours, give or take a few. Until then, take care, and when will we shed some light on dark matter? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Gear_Train { ; time=0:02:54.71-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=t center-mag=-2.822641591053055/-0.03235449428571077\ /8.942979e+012/1/24.9/0 params=9/4 float=y maxiter=1500 inside=fmod proximity=0.6902 logmap=68 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=000WrzRjkSkjTkjVliWliXlhYmh_mg`nganfbnfdoee\ oefpdgpdipcjqckqbmvdlqblmaki_kdZj`YjXWiSViOThKShFR\ gBPg7Og3Ne4Ld5Kc5Jb6I`6H_7FZ7EY8DW8CV9BU9ATA8RA7QB\ 6PB5OC4MA2NC3ND4NE5OF6OG7OH8OI9PJAPKAPLBPMCQNDQOEQ\ PFQQGRSHRTIRUISVJSWKSXLSYMTZNT_OT`PTaQUbQUcRUdSUeT\ VgUVhVViWWjXWkYWlYWmZXn_Xo`XpaXqbYrcYsdYte_yfYueXr\ dWncVkcUgbTdaS`aRY`QU_PR_QQ`QQ`QP`RP`RO`RO`SN`SN`S\ M`TMaTMaTLaULaUKaUKaVJaVJa0IaWIb0IbWHb0HbXGb0GbXFb\ 0FbYEb0EbZEc0DcZDc0Cc_Cc0Bc`Bc0Ac`Ac0Ada9d09db8d08\ db7d07dc6d06dd5e06dc6c07cb7b08aa8a09``9_`A_`AZ_BY_\ BYZCXZCWZDWYDVYEUYEUXFTXFSWGSWGRWHQVHQVIPUIOUJOUJN\ TKMTKMTLLSLKSMKRMJRNIRNIQOHQOGPPGPQFPSEUQEOVDaQ8OV\ BcRDhTFNUHmWJMXLrZNL`PvbRIdUkcTvcSMmRzbQOpPzaOQsNz\ aMTwLz`KVwJz_IXsHzZGZpFzZEamDzYCcYBzXAeX9zX8gW7zW6\ iW5zSBhPHzMNhITzFZhCdz8jh5ph2uU4cg6cU8cfAcUCcfEcUG\ ceIvUKceMcUNcKhnMimNilOjl } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 17-05-09 (Sincerely Segmented [7.5])
by Jim Muth 16 May '09

16 May '09

FOTD -- May 17, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: I did go on an antiquing expedition with FL on Saturday, but we arrived back at FC by 4pm, in plenty time for a hasty fractal search. I chose to search the fractal that results when 0.4 part of Z^(-0.8) is subtracted from Z^2, and (1/C) is added. Today's high-magnitude image with its floating citrus-like segments lies in this fractal, which consists of a Mandeloid bay with two large buds, surrounded by a huge spider-like network. The scene is located on a filament near the southwest shore line of the main bay of the Mandeloid. Not surprisingly, the filament is sprouting citrus segments like those in the image. I named the image "Sincerely Segmented" when the segments sincerely reminded me of a peeled orange. The rating of a 7-1/2 owes 1/2 point of its value to the coloring work. The calculation time of 1-2/3 minutes on the 2000mhz machine is about the same time it takes to surf to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and gaze in awe and wonder at the finished image posted there. Saturday began with low clouds here at Fractal Central. The clouds cleared out by 10am, leading to a sunny, humid afternoon in central Pennsylvania with a temperature of 82F 28C and occa- sional showers. The showers culminated in a brief but noisy and gusty thunder-storm at FC at 6pm, followed by a cloudy and pleas- antly cool evening. The fractal cats took most of it in stride, but grew a bit wide-eyed when the thunder crashed too loud. My day was fair enough despite the antiquing trip. I think I'm actually starting to appreciate these trips. The next FOTD will be posted in 24 hours. Until then, take care, and wait for the best that is yet to come. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SincerelySegmented { ; time=0:01:42.10-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.000125895457505/-0.1044759082479428/\ 1.01995e+013/1/-24.5/0 params=1/2/-0.4/-0.8/0/0/0/0 float=y maxiter=1200 inside=0 logmap=133 periodicity=10 mathtolerance=0.05/1 colors=000_XaZW`YV_XUZWTYVSXURWTQVSPUROTQNSPMROLQN\ KPMJOLHNKGLJEJIDHHBFGADF8BC8ABC9AF99I98L98P87T8KX8\ U`8zd8zm7zr7zu7zz7zn7UjLKgZKdzIbzHarG`nFXmEWhDUfCT\ eBQcANd9Je8IeN5ga_xocyjewefv`gtWhsRiqMipHinCimEjlG\ okIokKpjMpjOpiQliSlhUlhWmgYmg_mfanfcneenejY`oNWtBR\ y0Nx2Pw3Qw4Sv5Tv6Uu7Wu8Xt9ZtA_sB`sCbrDcrEdnWpec`Xk\ MOs7Qq6Rp5So5Um4Vl4Wk3Xj3_l4bm5eo5gp6jq6ms7pt7ru8u\ w8xx9zy9vxCsxFpxHmxKjxNgwPdwSawVZwXWw_TwaHzXczVgzR\ kzNozJpzHqzFrzDszCvzBxzBzzBzzHzzMzzRzzSzzSzzxzzizz\ Vzz4zzAzzszzIzzgzz`zzUzzNzzmzzwzzlzzazzRzzAzzDzzQz\ zLzzHzzGzzGzzGzzXzzSzzOzzKzzrzzhzzfzzPzz6zz9zzBzzE\ zzIzzHzzGzz1zz5zz9zzDzzHzzGzzAzztzmPzmMzmKzmIzmfzm\ jzm_zmQzmlzmWzmazmRzmEzmAzmCzmEzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 16-05-09 (Unity and a Half [6.5])
by Jim Muth 15 May '09

15 May '09

FOTD -- May 16, 2009 (Rating 6.5) Fractal visionaries and enthusiasts: The complex logarithm is multi-valued, so how then do we know which value is the correct one? The answer is that they are all 'correct'. The square roots of 4 are plus-2 and minus-2, and they are both 'correct'. We use the root that works best in the situation at hand, which is almost always the plus-2 root. The same is true with the complex logarithms, but the other values are always there, and they also make fractals. The MandelbrotBC3 formula makes use of these other values of the complex logarithm. Each value draws a different fractal, even when the exponent of Z remains unchanged. In today's image we have gone 30 levels up the logarithmic ladder to a level where the Z^(1.5)+C parent Mandeloid is totally changed. Today's image is located in the 'Seahorse Valley' of its parent. Since most of the effect is a result of the coloring, which I put at least 10 minutes work into, I have added the usual 1/2 point bonus for the coloring, bringing the overall rating to a less-than-inspiring 6-1/2. The name "Unity and a Half" refers to the exponent of Z. The calculation time of a shockingly fast 44 seconds will bring no discomfort to even the most fastidious. The trip out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to see the finished image there will be equally enjoyable. The showers moved out of the Fractal Central area early Thursday night, leading to a foggy start for Friday. By 10am the fog cleared out however, and the rest of the day was near perfect, with blue skies, puffy clouds, and a temperature of 77F 25C. The fractal cats enjoyed the weather conditions, but they were not happy when a lovesick tomcat wandered by and sprayed the wall right beneath their favorite window. A quick squirt from the hose removed the offensive odor and restored the cats' good moods. My day was busier than expected, in fact it was barely under control. Unless FL gets an antiquing urge, the next FOTD will be posted in 24 hours. Until then, take care, and be conservatively liberal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Unity_and_a_Half { ; time=0:00:44.80-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=+0.1641879378341295/+0.775442975243285/\ 200823.9/1/-5/0 params=1.5/0/30/0 maxiter=1800 inside=0 logmap=105 periodicity=10 colors=0000HU000K0U0000KU000N0U0000HU000K0Ul0fi1cf\ 2`c3Y`4VY5SV6QS7NP8KM9HJAEWU2UR4SP5QN6OL7NJ8LH9JFA\ HDBzm8wi9te9qb9n_AkXAgUAcRB_NBWLBSICOGCKDCoMMfJJYG\ HPDEZOFYNEXMEWMEVLEVLEUKETKESJERJDRIDQRzPHzOGtNGmN\ KcMFcLEZKEUJDPJDKICFHCCGBCcuAaqB_mBYiBWeBUaBSYBQUC\ OQCMMCKICIECz5Az6Bz6Bz6Bv6Br7Bm7Bh7Bc7BZ8BU8BP8BK8\ BJ9CI9CI9CI9CIACHACHACHACGBCGBCGBCf5Ga6FY7ET8EP9DK\ ACH09G2AG3AG5BG6BG7BG9CGACPu`OrZOpYNnXNlWMiVMgTMeS\ LcRL`QKZPKXNJVMJSLJQKIOJIMHHJGHHFGFEGDDF5mG6lH7lJ9\ lKAkMBkNDkOEkQFjRHjTIjUJiVLiXMiYNh_Ph`QhaRhm`kxjnv\ hotgosfoqeopdoncombokaoj`oh_ogZoeYocXpbWp`Vp_UpYTp\ XSpVRpUQpSPpROpPNpOMpQOnRQlSSjTUhUWfVYdW_bXa`Zc__e\ Y`gWaiUbkScmQdoOeqMfrLeqKeqKepJdpJdpJdoIdoIcoIcnHc\ nHcmGbmGbmGblFblFalFakEakEakEdzMezOezPezQfzRfzSfzT\ gzUgzVgzXhzYhzZhz_iz`izaizbizc`zYSzSJzM0z7LzuJzeHz\ RZzEXzDWzDVzDTzDSzDRzDQzD } 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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FOTD 15-05-09 (The Elephants Go West [5])
by Jim Muth 15 May '09

15 May '09

FOTD -- May 15, 2009 (Rating 5) Fractal visionaries and enthusiasts: We have just seen the weird rectangular things that appear on the negative stem of the Z^2.003 Mandeloid. But what would happen if the parent fractal were rotated 180 degrees so that East Valley lies on the negative stem? At a height of 1050 steps up the logarithmic hyperladder, the MandelbrotBC3 formula does just that. When East Valley lies on the negative stem it spreads out into a wedge, while the elephant stuff along its north and south edges breaks up into a series of circular herringbone things. Today's scene with its circular herring bones lies in the debris between two larger herring bones. Unfortunately, the image proved almost impossible to color satis- factorily. It is far too chaotic to produce any kind of smooth- ness to contrast with its over abundance of chaos. As a result, I could rate it no higher than a 5. More work might have found better colors, but I had no time to search. The name "The Elephants Go West" describes the 180-degree trip taken by the normally eastward-bound elephants before they reached today's state of decay on the west end of the fractal. The calculation time of 6 minutes, 6 and 66/100ths seconds has a lot of sixes in it. I guess it could be a sign that the beast is prowling nearby. To avoid the wrath of the beast, it is best to calculate the parameter file with caution. The image may be seen risk-free by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is or soon will be posted for immediate bliss. Heavy clouds, high winds and frequent heavy showers spoiled the otherwise pleasant temperature of 68F 20C here at Fractal Central on Thursday. The fractal cats were so distracted by two prowling tomcats that got into a fight in the side yard that they never noticed the inclement weather. My day was acceptable, but FL got a bit cranky when dirty pictures started popping up on one of the computers. I think the bug has now been cleared out, but only time will tell. The next FOTD will be posted in 24 hours. Until then, take care, and I didn't realize the 666 beast was into fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheElephantsGoWest { ; time=0:06:06.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=-0.254082178434463/-0.0011403938506048/\ 7.2428e+007/1/-105/0 params=2.003/0/1050/0 float=y maxiter=4000 inside=0 logmap=286 periodicity=10 colors=000UccUcbUcaUc`Uc_UcZUcYUcXUcWWcV_cUbbSfaQi\ `Om_NpYLtWJwUItQHrNGoKFmHEkEDhDGfCIcCKaBN_BOXAPVAQ\ T9SQ8TO8VM7YJ7_H6`F6aJBaNFcQJeUNgXSh`Wic_kgcmjgnjh\ kjhhjhdnh`rhXvhTzhPzhLzhHzhEzjGznHzrJzvKzzMzzNzzPz\ zQzzRzzTzzUzzWzzXzzZzz_zz`zzazzbzzczzdzzezzfzzgzeh\ zcizajzZkzXlzVlz`ezf_zStzVszXrvZqr`pmbohdncfmZhlQj\ kOljLniJphHrgFtfDveEw`FwWGxSGxNHyJIyEIyAMxDPwGTwJW\ vM_uPbuSftVitYms`prctrfwqizqkthao_SjSJTOUBLdAQfAUh\ AYiAakAelAjnKnpUrqcvsmmtmgqzcozalz_jzYhYWeaUceSaHP\ hDKdAG`7CX48TH6`U5hPDeLLcHSaD_Z9fX5nV1uT5pU8kVBfWE\ aXIXYLSZON_RI`KLbDOd5Rc7Qe8Pg9OhANjBMlCLmDLoEKiFJc\ GIcHHcIGcJGcKFcKEcKDcKCcLCcLBcLAcL9qL8pM8pM7oM6nM5\ mM5mO8jPBhQEfSHdTKbUN`WQZXTWYWU_US`UQaUOcUMdUKhUMe\ UIcUFaUCWUFRUIMUKHUNCUQ7USBU_E`g5muHgnTbgcY`o`UzcO\ shPmmQgrRavSWzTQzUKzVEzW0z`8zXGzTNzQVzMazJ`zI_zHZz\ GYzF`z2XzETzQPzaJznuzWxzc } 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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FOTD 14-05-09 (Counting Troubles [6])
by Jim Muth 13 May '09

13 May '09

FOTD -- May 14, 2009 (Rating 6) Fractal visionaries and enthusiasts: I named today's image "Counting Troubles" because I have never seen such a confusion of number series surrounding any minibrot. The image is supposed to have a mixture of order-7 and order-2 elements around the minibrot. What then are the *5* brilliant white points doing in the scene? I guess it's no problem however. The image, dark and somber as it is, is still worth the minute or so required to run the parameter file. And as always, instant relief is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image is posted, ready for viewing. Lots of sun and a temperature of 72F 22C here at Fractal Central on Wednesday gave the fractal cats much to enjoy. Unfortunate- ly, they wasted most of the day quarreling over the catnip rat and had little enjoyment. My day was quite busy. The next FOTD will be posted in 24 hours. Until then, take care, and I heard that the world will end on December 21, 2012. I hope I don't miss it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Counting_Troubles { ; time=0:01:21.83-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=-8.877891510454265/+0.00383125274875986\ /1.414258e+011/1/165/0 params=7/5 float=y inside=0 maxiter=1800 periodicity=10 mathtolerance=0.05/1 colors=000upNuqNuqOuqOrlNphNncNl_NiWNgRNeNNcJNhRVl\ ZaqehumozzzohkeX`MeQQZQTSQhPfcO`kCHiHIgLJeQJcUKaYK\ _bLzfLWjzzoMSmNzwNSmzzuKWmIzsH_mzaqEmmCzoBzn9zm8zl\ 6zk5zj4zbAsWFuOKxHPzAUsDXmG_fJb`MdUPgOSjHVmBXoBakB\ fhBkdBpaBuZHtVNsSTrOZqLdpIjoEpnBum8qoHnqQkrYckWWeU\ PZSHTQ9MO2GM2JN2MO2OP2RP2TQ2WR2YS2`S2bT2eUJQBNSBQU\ BUWBXYA__AcaAfcAieAjdHjdNjdUzzzzvzmhmmWYf7RgCPf4Nd\ 5Mb5L`5KZ5KX5JV6IT6HR6HP6GN6FL8EJ9EHADFBCDCCEDFEEI\ EFLEGOFHRFIUFJXFKZGM`HNaIPcJQdKSfLTgMUiNWjOXlPZmQ_\ oRapSbrTcs`VihN`pERx6Iv7Ht7Hr7Hp7Gn7Gl7Gk7Fi7Fg7Fe\ 7Ec7Ea7E`7EaBFbFGcJHdNIdRJeVKfZKgbLhfMhjNinOjrPkvQ\ kzQjwTitViqYhn_hkaghdgeffbif_keXmjUziRziOzfNzcNz`N\ vYNpUNlQNgNMcJMZGMUEMRBMO8ML6MJ8JGAHECECECAGA7I75K\ 53M31P74SA7UDAXGD_JGaMJdPMgTPiWSlZVoaYqd`tgcwjfymh\ 6Ce8I`9NXBSSCYOEbJFgFLhFRhFXiFaiFgjFmjFrjFskGskHsl\ HslIsmItmJtnKtnKtoLtoLupM } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] Rectangle Holiday
by Jim Muth 13 May '09

13 May '09

At 03:00 AM 5/13/09 +0000, you wrote: >""There are very curious rectangles in one of the Julia sets of >the Z^(2.003)+C Mandeloid. To see one of them, calculate the >Julia set with a C-value of -1.7435 and check the Z-coordinates >at 0.00019+0.07388i at a magnitude of 75. "" > > >Like, exactly how do I do that? Someone want to clue me with a PAR or FRM? Here is the parameter file: ========================================================= Mystery_Rectangle { ; time=0:00:40.50-SF5 on P4-2000 reset=2004 type=julzpower periodicity=10 center-mag=+0.00019/+0.07388/75 params=-1.7435/0/\ 2.003/0 float=y maxiter=1500 inside=0 symmetry=none colors=000NWvOZqPalPdgQgcRjZRmUSpPSsLTrOTqRTpUUoXU\ n_UmbUmeVlhVkkVjnWiqWhtWgwWgzZfy`exbewddvfdvhcujct\ mbsoarqars`qu`pw_oy_oxWlwTjvQgvNeuKbtH`sEYsBWr8Tq5\ Rq2PvwkjvmZunNtoCtpBqjBodAm_AkU9iP9gJ9eEEdJIcOMbSQ\ aXUaaY`ea_jeZoiZsd_n``jX`fTabObZKbVGcRCdN8dJDfNHhQ\ LjTQlWUnZYpabrdftgjvjnxmoukoripphpmfqkeqhcrearc`s`\ ZsZYtWWtUVsQWrMWqIXqFXpBYo7Yn3Zn0Zm5XmAVmFUmKSmPQm\ UPmZNmcLmgKjfNheQeeScdV`cXZc_WbaUadRafP`iM_kK_nHZp\ FYsDYuGXuJWuMVuPVuSUuVTuYSu`SucRufQuhQuzzszzrzzqzz\ ozznzzmzzkzzjzzizzgzzfzzezzdzzfzzhzzizzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzMzsPzoRzkUzhWzd\ Zz``zXczUezQhzMjzImzFozBrz7tz4oz8kzCfzGbzKYzOUzSPz\ WLz_GzcCzg7zk3zo2zZ1zI0z1lztWzaGzJHzlCz_8zO4zCvzHr\ zFnzEjzDfzCbzBZzAVz9Rz7Nz6Jz5Fz4Bz37z23z1GzWEzSCzO\ AzL8zH7zE5zA3z71z3Bzv9zp8zj7zd6zZ5zT4zN3zHzzBzz5zz\ lzzhzzezzbzzZzzWzzwzzvzzv } ========================================================== JIM

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Re: [Fractint] Rectangle Holiday
by JackOfTradeZ＠comcast.net 12 May '09

12 May '09

. ""There are very curious rectangles in one of the Julia sets of the Z^(2.003)+C Mandeloid. To see one of them, calculate the Julia set with a C-value of -1.7435 and check the Z-coordinates at 0.00019+0.07388i at a magnitude of 75. "" Like, exactly how do I do that? Someone want to clue me with a PAR or FRM? .

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FOTD 13-05-09 (Rectangle Holiday [8])
by Jim Muth 12 May '09

12 May '09

FOTD -- May 13, 2009 (Rating 8) Fractal visionaries and enthusiasts: There are very curious rectangles in one of the Julia sets of the Z^(2.003)+C Mandeloid. To see one of them, calculate the Julia set with a C-value of -1.7435 and check the Z-coordinates at 0.00019+0.07388i at a magnitude of 75. The orderly simplicity of the rectangle makes it an impressive fractal thing, especially when the surrounding railroad-track chaos is considered. And its fragility makes it all the more interesting. If imag(c) is changed even the slightest from zero, the rectangle distorts, fills with debris and disinte- grates like a soap bubble. And if the orientation within the Julibrot is changed by as much as one degree in any direction, the rectangle also distorts and disintegrates. Such rectangles are pure Julia objects . . . or this is what I thought until I found today's image, which shows a minibrot in the area of the 2.003 Mandeloid that corresponds to the Julia rectangle. To my surprise, I found that the area surrounding the minibrot is filled with rectangles exactly like those in the Julia set. In today's image, these rectangles appear as tiny open areas where the bulky arms appear to branch out into smaller arms. A single enlargement reveals them to be perfect rectangles however. I have not yet done much investigation of these Mandelbrot rec- tangles. Maybe some of them are not so perfect. Maybe some squares, trapezoids, parallelograms, or even more exotic figures with more than four sides, such as octagons, lie hidden in the scene. Too bad we're already near the limit of resolution. We may never find out. But I don't give up so easily, especially when it comes to fractals, and I have a funny feeling that many more surprises lie nearby. So I'll be doing a lot more exploration in the area. Stay tuned. Who knows what might turn up. I named the image "Rectangle Holiday" for the fun of it. I rated it at an 8 because I think it's pretty good. The calcula- tion time of 3-3/4 minutes will pass in a few flashes, or the flashes may be escaped by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and seeing the finished image posted there. Tuesday produced enough sun to keep the fractal cats happy. The temperature of 68F 20C was a little chilly for the date, but well within reason. My day was just eventful enough to prevent boredom. The next FOTD will be posted in 24 hours. Until then, take care, and when you find the ultimate truth, what will you do with it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rectangle_Holiday { ; time=0:03:45.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=1 center-mag=+0.00002587319771205/+0.000021904280298\ 92/3.8e+010/1/67.5/0 params=0/0/0/0/-1.7435/0/0/0/\ 2.003/0 float=y maxiter=3600 bailout=10000 inside=0 logmap=516 periodicity=10 colors=00089K9AM9BO9CQADTAFVAGXBJZBL`BObCRdCUfCWhD\ ZjD`lD`nCboCeqCfsCguChwCixCjyCkwBlwBmwBnwBowBowBow\ BowBqzAqzAqzFqzKqzMqzOqzQqzSrzUrzWrzYrz_rzarzcrzer\ zgrzirzkrzmrznszotzpuzqvzrwzsxztyzuzzvzzwzzwzzwxzw\ vzurvsnrqjmofhnbdnZanVZnTWmPUmLRmHOmDLl9Ji9Kg9KiAK\ cALaAL`BL_BMZBMXCMWCMWCNVDNUDNTDOTEOSEOREPQFPQFPPF\ PUScZdr`cqabpbapcaod`ne_ng_mhZmiYljYkkXklWjmWjlXjl\ YjkZjk_jj`jjajibjicjhdjhejgfjggjghjfijfjjekjSziOzj\ KzkHzlGycFtWEoNDjFDe7HZBLSEPLH`IQlFYwDeqKhkQjfXl`b\ nVipQorKvtFzvEvwEpwEjwEdwJ`rNXnSUjWQf`Ma`JYaFUcCQg\ IRmQRr_RvdSwjSypSzwSzzYzzmzzz4zn3ph3fb3YX2OR2EL25G\ Agn2_q6`o9`nC`lFH`YvzI`iL`hOIKezLauRYnWUg`5M79PDDR\ JGlPKzVmz`U9kTEjTJiSNhSSgRXfmLJrONmQQcSTYVXVX_TZbV\ AFTOT0pz4nz7lzBjzEmzHrzLwzzzzzzzzzzzzzzzzzzzzzzzzd\ zzdzzezzezznzzlzzkzzjzzizzhWzgTzfdz7_zJVzVPzOQzURz\ _EzlLzhyzwsztmzqgznHzj9zi } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 12-05-09 (Knowledge Lost [Optional])
by Jim Muth 11 May '09

11 May '09

FOTD -- May 12, 2009 (Rating Optional) Fractal visionaries and enthusiasts: So many flat patches give a kind of pop-art look to today's image, which lies in the area way out on the main spike of an oversized Mandelbrot set that has been corrupted by some quintic elements. Most of the effect is a result of the closeness of the scene to the bailout radius, where everything cuts off. This is exactly the same effect that appears far out near the tip of the negative spike of the classic Mandelbrot set when the bailout is set to 4. But in today's case, the minibrot at the center is not quadra- tic, it is quintic, and the number of elements surrounding it is a mixture of 2 and 5. I let the rating be optional. Some might like the image, others might consider it too elementary, more like what the newbie frac- talist would find. The name "Knowledge Lost" has little meaning in relation to the image. When I thought of the name, I was wondering what happens to the information that is swallowed by a black hole. The calculation time of 25 seconds is about 60 times as fast as yesterday's image. Since today's image has somewhat more than 1/60th the worth, this makes today's image the better value for the time spent. But why not forget all this stuff about image worth by viewing the image in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> With some sun, some clouds, little wind, no rain, moderate humidity and a temperature of 64F 18C, Monday had little to comment on here at Fractal Central. The fractal cats got in a short spat to decide who would control the catnip rat for the morning, but Cassie soon won and Nicholas retired to the window shelf to console himself watching for intruding cats. My day was average, as are most days. I'll have no complaints if tomorrow is the same. The next FOTD will be posted in 24 hours. Until then, take care, and we actually know only a small part of what we think we know. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Knowledge_Lost { ; time=0:00:25.32-SF5 on P4-2000 reset=2004 type=dividebrot5 passes=1 center-mag=-99.99995480655251/+0.0000000490712611/\ 7.153044e+010 params=5/50 float=y maxiter=300 bailout=10000 inside=0 logmap=34 periodicity=10 colors=000AIQ89DmIjzFxzBrp7U03A024013012c0RhLZMAHh\ zUGp9dcHZWGWK8Y7lzP1VO0LG0A80dCPqLxUEcF7KOixCNUUtC\ Ka8AJ4xAiwp1U006Sp4LF3EA17522011JfHtWCeL8SA4EKj`FZ\ RfVL_a8a_EcZKeYQgXWaO_WFcR6gg7px7xVRV2i1GUCTFNe0Yq\ IXR9GE8b95Q42DpJLQ9ANQHzz1zz0zzRzzZzzczzUzzKzzAzzB\ zz7zz3zzzzzazzPzzCzzszzBzzlzzOzzEzz5zz2zzbzzILz9sz\ HSz8Lz0Az0lzwWzcGzKezQLzD7z4mzXXzMGzBEzjAzZ7zN3zBy\ zpizbVzQFzDhznjzvNzTXz8Gz4xzLUzAOzvCzTFzOBzI7zC3z6\ 0zD0z80z4QzGDz8izTNzE0zD3zL2zE1z71zn0zPVzTmzN`zHPz\ BCz5RzXDzGlzUWzKGzA6zI4zC2z6nzhjzrNzRDzO8zG4z8sz5e\ z3Sz2Ez16zT3zEhztMzSuzefzVTzLEzAZz5Hz2tzZezQSzHEz8\ `zuRzfIzT9zEqzsRzSXz1Oz0Gz08z0yzyZzOjzJNz9KzTDzJ6z\ 92zA1z54zM2zBOzQCzDuzFazAJz5AzR6zI3z9Ezm9zX4zG9z94\ z49zm6zX3zG3zFCzu9zf6zT3zEEzOAzI7zC3z64zXVzeFzLXzf\ 5zDLzFEzA7z5jzjVzVFzFYz4Mz2Bz1pzSQzE_zRRzKIzD9z6oz\ oYzYHzHjzTZzLNzEBz7ZzpQzb } END PARAMETER FILE=========================================

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FOTD 11-05-09 (Valley of the Shadow [No Rating])
by Jim Muth 10 May '09

10 May '09

FOTD -- May 11, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's nearly unbearably slow image shows what happens to an order-11 minibrot when it mixes with the quadratic stuff deep in Seahorse Valley of the Mandelbrot set. I spent several minutes simply observing the curious blending of different orders of fractal material. Unfortunately, I never got around to rating the image, though it appears worthy of about a 6. IMO, the colors are a bit too pale and pastel-ish, but in the world of fractals, one person's paleness is another person's perfection. The name "Valley of the Shadow" is not nearly as ominous as it sounds. The image is actually quite bright and cheery. The calculation time is by far the most troublesome aspect of the image. The problem here is the unusually high iteration count of the elements in the image, most of which have an iteration count well above 5,000. The image may be viewed at leisure on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday turned out to be a very pleasant day here at New Fractal Central, with a blue sky filled with puffy white clouds, and a cat-pleasing temperature of 68F 20C. True, the wind got a little gusty at times, but the warm sun soon erased any chill. My day was average. The next FOTD will be posted in 24 hours. Until then, take care, and be at peace. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ValleyOf_TheShadow { ; time=0:33:24.39-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip center-mag=-74.99016340175787/+1.587649774464434/\ 1.608924e+010/1/30/0 params=11/100 float=y maxiter=25000 inside=0 symmetry=none periodicity=10 colors=000mqslqplpmlojlmhklekkckiakhZjgXjeUjdSgaLi\ bOjcQldSmeUofWpfZrg`shbuidvjfzpqznnzlkwjhtheqfcnd`\ kbYh`VeZSeWPbXQ`XQYYQWYQTYQRZQOZRM_RJ_RH_RE`RC`RA`\ RCZPDXOEVNFTLGRKHPJHNHHLGGLGGKHIMGKPFMSENVDP_CRdBV\ g8Uh9Th9SiAvmlvjgvfaubWu_RuWLuSFuPAl_RcifVsvSpoQnh\ OlaMiVKgOIeHDd7GcBJbEMaHP`KS`NV_RYZU`YXcX_fXbiWflV\ ioUlrTozJyxOutTrpXomalieiejffUXfs`dpbbnc`ldZieXggV\ ehTbiR`jPZlNWmLUnJSo9SrHQpOPnWOmbNkjMij_YmVaoQdqLh\ sGkuBowDryIuxOszUrzZqzbozanz_mzXkzUjzRizTgzWfzZex`\ cvcbtfath`oiWjjRhlPejNciL`hJZfHXeGUdESbCPaAO`8N`6M\ `6M_6L_7M`9NaBOaCPbEPbGQcHRcJSdLTdMTeOUeQVfRWfTXgV\ YpQXgWWZaVQg91qUHmzhexcgs_hmWjhSkcNmYJnTFpF0pI3qL7\ qOBqRFqTKqWOqZSqaRqbRqbRpbQobQn`PpaOkbNkcMkdQkeVke\ Zjfcjggjhljipjevngvlhukitjksilrhmpgoofpneqmdspdrlc\ qhbqdbpaaoYaoU`nQ_mN_mJZlFZkBYj3Vk8YkD_kHakMdlQflV\ hl_klcmmhomlrmqtmrvmrxmqw } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 10-05-09 (Innate Troubles [6])
by Jim Muth 10 May '09

10 May '09

FOTD -- May 10, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today's FOTD is late; the color of yesterday's FOTD is terrible. Yes, I know all this. I posted the wrong parameter file for yesterday's image, and FL suffered another antiquing attack Saturday morning. (We found another new rug.) It's too late to post the right parameter file for yesterday's image, (though I have attached it at the end of today's FOTD), and when I finally got back to the fractal computer Saturday evening, it was too late to find a proper fractal in time for the usual mid-evening- of-the-day-before post time of today's FOTD. But it is now bright and early Sunday afternoon, FL is in the garden, and things have settled down. I have included the right colors for yesterday's image (for those who noticed the original sickly green pallor) and written a short discussion for today's image. Today's image shows another order-11 minibrot, this one located in the valley leading to a period-9 bud on the northeast shore line of the parent, which is an oversized Mandelbrot set. I named the image "Innate Troubles", which is not as bad as it sounds. I rated it at a 6, which is not quite up to FOTD average. The calculation time of 4-3/4 minutes may be dispensed with by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the finished image there. But because of the unusual time of this posting, give Paul a bit of time to calculate and post the image. Considerable clouds kept the temperature of 79F 26C from reaching its full potential here at Fractal Central on Saturday. The fractal cats had no complaints when we returned around 8pm, but they carefully checked the new rug before permitting it to be spread on the hallway floor. My day was . . . well . . . interesting. More philosophy is still brewing however, so stay in touch for new ideas. (The number-one sign that an idea has merit is when you know it is absurd and wonder how anyone could be so stupid as to believe it.) The next FOTD will be posted in 12 hours or so. Until then, take care, and be with the progressive thinkers. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Innate_Troubles { ; time=0:04:44.26-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip inside=0 center-mag=+32.40589564828817/+40.39158171013307/\ 6.227322e+011/1.0011 params=11/100 float=y maxiter=3200 periodicity=10 mathtolerance=0.05/1 colors=000ZOZUNUUORUSOUXZU`iUdtPgmNigRlaWnW`qPdsJi\ vDmx7kv9jtAirChpDfnFelGdjIchJ`iLbfKccKe`KfYKgWJiTJ\ jQJlNJmLInIIpFIqCIrAIt9Hu9Hw9Hx9Hz9Hz9Hz9Hz9Hz9Hz9\ Hz9Hz9Hz9Hz9HzAPuAWlAbdAi`DhYGhVIhSLhPOgMQgJTgGWgC\ alDYgEVbFSYGPTGMOHJJIGEJD9JA5L96M97N97P88Q88R89T7A\ U7AV7BX6BY6CZ6D`5Da5Ed0Gb5E`ADZFCXKBWPAUU9SY8Qb7Pg\ 6Nl5Lq4Jv3Iz2QxCYvMXrOXnPWjQWfRVbTVZUUVVURWTNYTJZS\ F_SB`Q7bS8aU8`W8_X8ZY8YZ8X_8W`8W`8W`C_`Gc_KgZPkYTo\ XXsV`wUdzQfyNhyJjxGlxImsKnoLojNofPpbQqYSrUTrQQxJ_q\ FijCsc9zT4zV5zX6zY7x_8va9tbArdBpeCogCmiDkjEilFgmGe\ oHcqIarJ_tK_xMZvLZuKZtJZrJvSWwTUxTSzUQzUOzUMzVKzVI\ zUIzVHzWHzWHwXHsYHpYHmZHj_Hg_Hc`G``GYaGVbGSbGOcGLd\ GIdGFeGCeGDdHDcIDbJEbKEaLE`LF_MF_NFZOGYPGYPGXQHWRH\ VSHVTIUUITUISVJSWJRXJQYIRVJQXJQYKQZKQ_LQ`LPaMPbMPc\ MPeNPfNOgOOhOOiPOjPOkWMvPOlyGWzLoyMrvMvsMwoMwlMwkN\ wlNzmNznNzoNvpOrmOmhOhcOc } Right_Color_May_09 { ; time=0:10:14.53-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=-178.5721094725071/-0.0000781075421812/\ 8.837183e+010/1/-62.4/0 params=11/100 float=y maxiter=3200 inside=0 logmap=550 periodicity=10 mathtolerance=0.05/1 colors=000_AR_AR_BR_BR_BR_BR_AR_AR_AR_9R_7R_5R_4M_\ 2H`0Db0Bb1Eb4Hb7LbAOcDSdGVeJZfNagQdgThgWkgZogargdv\ ggyITeFTeBSe7Se3Rd9TdBUbDVaGW_IYYGYWDYUAYS7XQFWSNV\ UVUWbTYjS_sQasT_rWXqZVpaSodQogNnjLmmIlpGksDa`CSIBI\ 0AJ0FK0LL0QM0WN1aO1fP2lQ2qR3wT4zT8zTCvTGrTLoTPkTTg\ SYcTaZVeTXiNZmH`qB`qD_qF_pHZpJYoLYoOXnQWnSWmUVmWUl\ ZIlb6kf6he6ec7ba7__8XY8TW8QU9NS9KQAHOAEMBAKDCMGEPJ\ GSMIUPLXSN_UPaXRd_UgbWieUlhQokMrnJnmCjk0fk0ik0gk1d\ j2bj3_j4Yi5Vi6Ti7Qh8Oh9LhAJgCGgIOYOLOUJD`GJTPPLYVC\ f`4of0xc0u`2rY6oVAkSEhPIeMLaJPZGTWDXSA`P7dM3hIAWMI\ JQQ6UY0ZZ0Z_0Za0Yb0Yd0Xe4WfFVgQjh`jitogroepmcnkaki\ _igYgeWdcUaaS__QYYOVWMSTKQQIONHMMGKIGGNGANO5PRAUUH\ YaPjpzznlmkTliLkfDjd5ia0ga3fa8daDbaH``JZ`LX`NW`PU_\ RS_TQ_VO_XMZYKWZKS_JPXJLaIIbHEeHEgGKiFPkFUmEZoDcqE\ hsGmuIrwKvyMzzOzzPzzRzzTzzVzzXzzZzz`zz`zz`zz`zzazz\ azzazzazzbzzbzzbzzbzzczzc } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 09-05-09 (Prime-Cut Fractal [7])
by Jim Muth 08 May '09

08 May '09

FOTD -- May 09, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows a Z^11+C minibrot gone crazy. The parent fractal is a grossly inflated Mandelbrot set that is quadratic only on the surface. Once we dive any depth into it, the M-set takes on Z^11 characteristics. Today's image is located in the East Valley area of a tiny minibrot just beyond the spike of the large minibrot on the main spike of the parent almost-Mandelbrot set. I chose the image to be FOTD for May 9 because it is one of the most decorative higher-order minibrots I have ever stumbled upon. The name "Prime-Cut Fractal" means little beyond its sound. The rating of a 7 is just about FOTD average. The calcu- lation time of 10-1/4 minutes is slower than FOTD average, but may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> In yesterday's discussion I told of a book-club offering of a book about the imminent collapse of civilization due to climate change (AKA global warming). Since then I have checked more of the books being offered. I found one about 'the myth of the self'. According to the author of this book, there is no such thing as 'the self'. What we perceive as the conscious 'self' is the content of a sophisticated model of reality generated by our brains. Whenever our brains successfully pursue the strategy of creating a unified and dynamic inner portrait of reality, we become conscious. In a sense, conscious experience is a form of virtual reality, a real-time world-model that can be viewed as a permanent simulation. (A lot of fancy words indeed!) It's probably an interesting book, but I'll not order it. The author has apparently not bridged the gap between neurons and consciousness. I wonder what the non-existent but always-the- same thing is supposed to be, which he claims appears from nowhere to become our illusory selves when our brains begin 'creating a unified and dynamic inner portrait of reality', whatever that means. Also, if conscious experience is a form of virtual reality and the world we appear to experience around us is a permanent simu- lation, as the author apparently supposes, then the brain that he claims creates the simulation must itself be a part of the simulation. I see circular reasoning once again taking the place of true critical thinking. One of these years someone might actually bridge the gap between brain and mind, if one actually exists, but it will not be in the year 2009. I have been reading books attempting to explain self-awareness for many years, and in that time I have seen the explanations grow ever more preposterous and unconvincing. The only thing I have become convinced of is that our science is missing some- thing of monumental importance, most likely non-physical, though not necessarily the teachings of any one religion. A mixture of clouds and sun here at Fractal Central on Friday, and a temperature of 77F 25C were enough to keep the fractal cats' crankiness under control. Light rain in the evening caused no problems, while less work than expected kept me under control. If all stays under control, the next FOTD will be posted in 24 hours. Until then, take care, and after all these years, our greatest thinkers can't even tell us what we are. It's almost unbelievable Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Prime-Cut_Fractal { ; time=0:10:14.53-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=-178.5721094725071/-0.0000781075421812/\ 8.837183e+010/1/-62.4/0 params=11/100 float=y maxiter=3200 inside=0 logmap=550 periodicity=10 mathtolerance=0.05/1 colors=000hHKhHKhIKhIKhIKhIKhHKhHKhHKhGKhEKhCKhBFh\ 9Ai76k54k87kBAkEEkHHkKLkNOkQSkUVkXYk_akbdkehkhkkko\ knrM_ZJ_ZFZZBZZ7YYD_YF`WHaVKbTMdRKdPHdNEdLBcJJbLRa\ NZ`Pf_RnZTwXVw_TvbQueOthLskJsnGrqEqtBpw9oz6eg5WP4M\ 53N58O6EP6JQ7PR8VS8_T9eU9jVApXBvXFsXJoXNkXShXWdX_`\ WdXXhSZlM`pGbtAdx4dx6cx8cwAbwCavEavH`uJ_uL_tNZtPYs\ SMsWAr_AoZAlXBiVBfTCcRC_PCXNDULDRJEOHELFFHDHJFKLIN\ NLQPNTSQWUTYWV`YYc``fbbi`elXhoTkrQgqJco5_o6bo7`o8Y\ n9WnATnBRmCOmDMmEJlFHlGElHCkJ9kPHaVES`CHg9N_ITSRZJ\ _dBhj2qg5nd9kaDhZHdWLaTPZQSVNWSK_PHcLEgIBkF7oBEbFM\ QJUDNa0Sb0Sc0Se0Rf0Rh1QiBPjMOkXclgcmrckpcinagl_eiY\ cgWaeU_cSY`QWZOUXMSVKQSIOQGMOELMEKJDKGKKCLS8NY40YM\ ReUctzgrlfo_emSdjKchCbe3`eA_eFYeKWeOUdQSdSQdUPdWNc\ YLc_JcaHccFbdD_eDWfCTcCPhBMiAIjAFk9Bl8Fm8Kn7Po6Up7\ Xq9_rBbsDetFhuHkvInwKqxMtyOwzQzzSzzUzzUzzUzzUzzVzz\ VzzVzzVzzWzzWzzWzzWzzXzzX } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 08-05-09 (Window in the Sky [7.5])
by Jim Muth 07 May '09

07 May '09

FOTD -- May 08, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: The following was written to the Fractint list a few days ago in reference to the curious rectangle in a Julia set of the Z^2.003 Mandeloid: >The name "Mystical Rectangle" refers to the mystery of trying >to determine the true four-dimensional shape of the object that >is rectangular in only two of its four dimensions. Well, if >the 4th dimension is time, I don't see what is meant here. Actually I should have written "rectangular in only two of its four *spatial* dimensions". If time is included as a dimension, then the mysterious rectangle thing is actually 5-dimensional. >The flu appears to be a flop. Yep! . . . a predictable flop. >Don't worry about climate change or cholesterol either -- all >these things are manufactured by the puppet masters to keep the >little people with little minds from daring to contemplate the >real things that matter and actually try thinking for >themselves. If it wasn't so true, it would be a dark comedy. In the mail this morning I received the latest offering from one of the puppet masters, the Scientific American Book Club. This month's selection is a book about the coming climate change dis- aster. In the promotional magazine, I see that global heating may all but eliminate people from the earth. The blurb goes on to forecast a disastrous rise in sea levels, leading to the de- struction of major cities and the failure of food supplies. The resulting flood of refugees from uninhabitable areas will lead to a climate war, which will throw the survivors back to a stone- age existence. I'm not buying the book, but it likely calls for lots of political action of the liberal kind A.S.A.P. Now I need a couple minutes to stop worrying! . . . . . . OK, Now I've calmed down! . . . . . . Some of the things that are always safe are fractals, which emit no deadly radiation or cancer-causing chemicals. Today's image is quite a nice example of a perfectly safe fractal. It shows a variation of that mysterious Z^2.003 rectan- gle, which has been slightly distorted by changing the exponent to Z^2.0032. With careful coloring I have made the rectangle into a view of a Rene Magritte-ish window in the night sky. I named the image "Window in the Sky" and rated it at a 7-1/2, which includes the usual 1/2 point for the coloring. The calculation time of 56 seconds could hardly be faster. The finishe dimage has also been posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather stayed dry here at Fractal Central on Thursday, and the temperature reached a pleasant 72F 22C, but the sun was actually shining for only 15 minutes, which was far too short a time to satisfy the fractal cats, who spent a good part of the afternoon sulking in the most prominent places they could find. Nicholas chose the doorway between the living room and the hall- way, while Cassie chose my TV chair. It took an extra treat of tuna and sharp cheddar cheese to pull them out of their funks. Otherwise, my day was about average, and FL managed an hour or so in her garden, which is about average. The next FOTD will be posted in 24 hours, which is even more average. Until then, take care, and relax, all is well. Cell phones are as safe as the tobacco companies once told us cigarettes are. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Window_in_the_Sky { ; time=0:00:56.74-SF5 on P4-2000 reset=2004 type=julzpower passes=1 center-mag=+0.00020598/+0.07933985/357.9201 params=-1.742/0/2.0032/0 float=y maxiter=750 inside=255 logmap=110 periodicity=10 colors=000000WMAWNAVOAVPAVQBURBUTBUUBTVCTWCTXCSYCS\ ZDS_Dzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzznzzozzpz\ zqzzrzMszztzzuzKwzzvzLuzMuzztzMszNszNrzzqzzqzzpzzo\ zPozPnzQnzQmzQmzRmzRmzSmzSmzSmzTmzTmzTmzUmzUmzVmzV\ mzVmzWmzWmzWmzXmzXmzYmzYmzYmzZmzZmzZmz_mz_mz`mz`zz\ `zzazzazzazzbzzbzzczzczzczzdzzdzzdzzezzezzfzzfzzfz\ zgzzgzzgzzhzzhzzizzizzizzjzzjzzlzzjzzizzhzzgzzfzze\ zzdzzczzbzz`zz_zzZzzYzzXzzWzzVzzUzzTzzSzzQhbPjcOkc\ NmdMneLpfKrfJsgIuhGwoHvkHvhHvdIvaIvZIuVIzSJzPJzLJz\ IJzFMzJOzMQzPSzTUzWWzZYzb_zeazhczlezogzrhzshzshzsi\ zsizsizsiztjztjztjztjztkztkzukzukzulzulzulzumzvmzv\ mzvmzvnzvnzvnzwnzwozwozwozwozwnzvnzvnzunzunztnztmz\ smzsmzrmzrmzqmzqmzplzplzolzolznlznlzmlzmkzlkzlkzlk\ zkkzkkzjkzjjzijzijzhjzhjzgjzgjzfizfizeizeizdizdizc\ izchzbhzbhzahzahzahz`hz`gz_gz_gzZgzZgzYgzYgzXfzXfz\ WfzWfzVfzVfzUfzUezTezTezS } END PARAMETER FILE=========================================

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Re: [Fractint] AOTD 05-06-09
by JackOfTradeZ＠comcast.net 07 May '09

07 May '09

. Fractal Animation visionaries and enthusiasts: I have long been intrigued by the Julia Rectangle. Is there something magical about the 2.003 exponent or will other numbers work? It seems to be a self-repeating pattern just like the minibrots you see when diving into the Mandelbrot. So backing out from the (FOTD -- April 29, 2009) we see an oval shape thing for start, then diving in we pass thru the original (FOTD -- April 29, 2009), then on to the (FOTD -- April 30, 2009) image, and finally arriving at another rectangle at E+13. I see fractal train tracks - but no fractal trains. Why is that? And why does it get so "blocky" at the end (I have seen this before zooming in to complex fractals). Is it real or some software "artifact"? Looks a bit like a CPU chip under a microscope ... The calculation time (even if you knew how to do it) of 5 days, while quite short by animation standards, would try the patience of all but the most dedicated fractal explorers. It can be avoided by downloading the completed animation directly from the UFVP website: http://www.fractal-animation.net/vid/jsqr.zip Like the original author of this fractal, I love mysteries and riddles too; I also hate them - when I can't figure them out. But death is hardly a mystery at all - like everything else in the fractal universe, it is all relative. Life isn't short, as they say - you just gotta be dead for so freakin' long it only seems that way! A more immediate concern is how to rate today's fractal animation. As fractal beauty is in the eyes and mind of the beholder, I will not, only to give it 2 diamonds on my site, roughly corresponding to a 6-7 on the Muth scale. Originally said: The name "Mystical Rectangle" refers to the mystery of trying to determine the true four-dimensional shape of the object that is rectangular in only two of its four dimensions. Well, if the 4th dimension is time, I don't see what is meant here. However, as you approach the Julia "square" objects during the zoom in, note that they appear to have a 3D appearance - of depth. I am reminded of that scene in the original "The Shining" where the viewer stares down into that shrub maze ... The flu appears to be a flop. Don't worry about it. Don't worry about climate change or cholesterol either - all these things are manufactured by the puppet masters to keep the little people with little minds from daring to contemplate the real things that matter and actually try thinking for themselves. Right now, worry about the Obamocrats, and how things have degenerated to such a point in this country that a creature like Al Franken can get elected to Senate. And don't never blame The Big Guy up in the sky for anything! Humanity digs it's own holes for itself and jumps in. (Job-5) The next AOTD will be posted in ?? hours. Until then, take care, and consider that eternity is the wrong thing to be wrong about... .

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FOTD 07-05-09 (Interest in Infinity [7.5])
by Jim Muth 06 May '09

06 May '09

FOTD -- May 07, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: ALERT! -- NEW FORMULA RENAMED! The name I gave yesterday's new formula -- DivideBrot5a -- is a repeat, so I took the DivideBrot5a formula and renamed it "NewDivideBrot", which is actually a misnomer, since the iterated part now multiplies Z^2 by recip(z^(a)+b) instead of dividing it by (z^(a)+b). The change not only makes the formula run about 10-percent faster, it also adds flexibility. Today's image lies in a quasi-seahorse tail in the rudimentary Seahorse Valley of the parent fractal, which resembles an over- sized and rapidly developing Mandelbrot set with a few added attractions scattered about in the interiors of the bays and buds. I named the image "Interest in Infinity". Almost all mathemati- cal fractals are infinite in one way or another. I rated it at a 7-1/2, which includes 1/2 point for the modicum of effort I put into the coloring. The image is a rather pleasant and decorative cubic minibrot. And the spiral effect actually helps the scene along. The calculation time of 4-1/4 minutes may be cut to almost nothing by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and peacefully viewing the finished image there. Heavy clouds kept the fractal cats of Fractal Central suppressed once again on Wednesday. The work slowed somewhat, though not as much as I had expected. The next FOTD will be posted in 24 hours. Until then, take care, and wait for the new world with eager enthusiasm. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= InterestInInfinity { ; time=0:04:14.00-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=NewDivideBrot function=recip passes=1 center-mag=-2.055475186118577/+0.3545724568315621/\ 1.564961e+010/1/57.5/0 params=3/2.66 float=y maxiter=2400 inside=0 logmap=408 periodicity=10 colors=000oQekObhM_dKWVIPVGQWARY9RZ8V`7Za6bc5ee4if\ 3mh2qj1uk3xg6sd9n`CiYFeXI`VMWQPSKRNITIGVEEXQCaUAdY\ 8h`9qdAyg9xe9wd9vc9va9u`8t_8tY8sX8rW8rU7qT7pS7pQ7o\ P7nO7nNGaXPQeYEnf2wg9qgFlhLfhRahXWibRihLinGciKZeOU\ `RPXVJSZEOa9Je4FhCLfKQeRWdZ`cffbmkanicogdoeepdfpbg\ q`hrZirYksWlsUmrSnqUooWpmYmk_hiacgcZeeUcgPaiKbkJcm\ OdoUeqZfpdgoihnohmqflseluclwblx`ly_lzZlzXlzWlzUlzT\ lzRlzQlzPlzOkzNkzMjzLjzKizJizJizIhzIhzIgzHgzHfzHfz\ GfzGezGezFdzFdzFdzKfzPgzThzYizbjvfkrkimmcmhemdYhbV\ c`TZZQUXOPWMKXLFXKCYJCYICZHDZGD_FD_ED`DE`CEaBEaAEb\ 9Fb8Fc7Fc7FdBDeEBeIAfL8gP6gS5hW3iZ1ia0i`3i_6iZ8iZB\ iYEiXGiWJiWMiVOiURiUTPGX42`55Y68W7BU8ES9HQAKOBNMCQ\ KDUIEZGFcEGhCGmAMrCSwEXwGbwIgwJezNcrRamV`hZacgbZoc\ UwcWjaXg`Xe_XcZYaXY_WYYVZWU`USbSReQQhOPkMOnKOqVOtd\ OwoOzyWztbzoizjpzfmzarzXwzTzzXzz`zzdzzhzzmzzqzzizz\ bzzazzazzQzzUzzYzzazzezzi } frm:NewDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 06-05-09 (The Mighty Cubic [7])
by Jim Muth 06 May '09

06 May '09

FOTD -- May 06, 2009 (Rating 7) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's image uses a new formula, the DivideBrot5a. When the 'recip' function is used, this formula does the same things as the old DivideBrot5 formula, but does them about 10-percent faster. In addition, the changeable function adds much more flexibility. Unfortunately, the continuing busy period here at Fractal Central has kept me from exploring the things that happen when the function is changed, but the rush is near an end, and I expect some interesting images from this new formula in the near future. Today's image is a scene in the Seahorse Valley area of its parent fractal, which is a distorted Mandelbrot set, with cubic features just beneath the surface. The circular features in the background of the image were created by rendering it with the inside set to 'fmod' and a proximity of 0.007. I gave the image a rather side-show sounding name -- "The Mighty Cubic" And then I rated it at a 7, which is just about FOTD average. The calculation time of 7-1/2 minutes is slow, but not unbearably so, and the finished image is posted, as always, for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was dry Tuesday here at Fractal Central, but the heavy clouds that hung overhead all day and the temperature of 57F 14C kept the fractal cats in a sullen mood. Nicholas got so out of sorts that he cussed me with the 'hiss' word when I tried to comfort him. Cassie simply found a soft cushion, curled up and slept for most of the day. My day was busy, though not as bad as Monday, and with FL unable to do garden work, I got a bit of help. The next FOTD will be posted, if all goes well, in 24 hours. Until then, take care, and where is Hilbert space? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Mighty_Cubic { ; time=0:07:31.94-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5a function=recip passes=1 center-mag=-1.790989550773074/+0.4048960468128376/\ 7.68e+008/1/-22/0 params=3/2.5 float=y maxiter=1500 inside=fmod proximity=0.007 periodicity=10 colors=000qmy__dIDKw_LhRFUIAF95U80K50A20Lm2AP1TasJ\ P`9CINLDHF9BA65531ke9fs6S`3EIU5dF2KyzX2Nm6_2ruG_aA\ IJ5pgnZTYHEH2E2171fJxmYoPHQWAlqgp_TZIEH2j21N1suyLc\ nFUaAKP5AC00r0ozOezIVhCLa6AAjLFKA7zfDgT9TJ6E936HM4\ BE257K`2FR1AI1590oPSbILQCEDzzVziAFV7BN57F237Dig6NM\ ojzYVeHFLCJm8CX46G1Do09b06Q03Dblk22MYcuHKThw_bqpQ_\ ZDIHEqOAcIcSQcJRcASWEUPIWILYOM_UNa_OcdPeSIlFCr26x6\ UcApJ8_D6J7431I2BW1Kh1TK3SM0E2ns1ae1PS0CEScMIQE9D7\ FLDL8bA4JgQySt_aaJSSEJJ9994CAk65ObxaThSJUJ9F91QXcE\ dK7KuVkIpzDbj9QV4DFFLkBF_7AO35CuNFfHBTB7E53`GBOA7C\ 53RhfDMLmzC`j9PV6CF3RrxI_c9IK3EePLoGEY87HHpXCbO8QG\ 4D8z93e62L31LhFEUA7F5ZW_HGIgGUXCMM8FB47a3WP2LC1AyR\ kcoXQYMDHBjWLNGApiJQN9QND8g04M0EWC7G6CUx6FUPdBGR78\ D3e5UV3ML2FA17PpRGZI8H9VilKUWAFGKR9DI6693LWxFOhAGU\ 58FPUzEkHbmsQX`DGIAoKYkpHOQ0hZ0MH6Zs4Qe3HS18EO8iC4\ NjFGN78nOePCLREbKATD7J639 } frm:DivideBrot5a { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z^2*fn1(z^(a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 05-05-09 (All Cracked Up [No Rating])
by Jim Muth 04 May '09

04 May '09

FOTD -- May 05, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image is a very hasty one because I spent all day Monday reworking one of last week's rush jobs. When it became apparent that all mankind was not going to die of the 'swine' flu, one of our customers decided to totally re-do his job to remove the possible impression that he expected an imminent repeat of 1918. It should have been obvious to him from the start that this flu scare was just another media-created big-news event designed to keep viewers worried and glued to the news channels. I barely finished today's re-do job in time to scrape up a below-average fractal. I avoid giving unusually low ratings to the FOTD images by not rating the ones that fall too far short. Today's image falls pretty far short, and therefore gets no rating at all. The scene is located near the negative X-axis of the Z^(3.003)+C Mandeloid, in an area that is rapidly fragmenting. There is nothing very new in the scene. I have posted similar images several times before. The name "All Cracked Up" describes my first impression of the image. The calculation time of 6-1/3 minutes is too much to spend on such a mediocre image. I strongly recommend saving the time by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A steady all-day rain and temperature of 54F 12C kept the fractal cats suppressed here at Fractal Central on Monday. The rain also kept FL suppressed. The un-necessary work kept me suppressed. The next FOTD, hopefully not suppressed, will be posted in 24 hours. Until then, take care, and I heard on TV that if you die as a result of taking a certain drug, you should call a lawyer to see if you have legal rights. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= All_Cracked_Up { ; time=0:06:48.68-SF5 on P4-2000 reset=2004 type=manzpower center-mag=-0.3858562468\ 4106250/-0.00183676829694136/2.589491e+008/1/10/0 params=0/0/3.003/0 float=y maxiter=10000 inside=0 colors=050dbVcdXafY_iZZk_Xm`VobUrcStdQvePxfOugNsgM\ phLnhKkiJiiIfjHdjGafG_cGX`FVXFSUFQRENNELKFLCEJHEIL\ DHQDGUDFYCEbCDf87iCCjFGjIKjLOjOSjRWjU_kXck_gkbkkeo\ khskkwkluhmsenqboo_pmXqkUriRsgOteLucIvaFw_CxY9xX6w\ UAwSEwQIwOMwMQwKUwIYwGawEewCiwAmw8qw6uw4xU5Y0572B8\ 3H94N95TA6ZA7dB3j68iBChFGhJKgNOgRTfVXeZ`ebddforbhd\ jaSrVFzUGwTGuSHsRHpQInQIlPJjOJgNKeMKcNFcMKaMO`LS_J\ VYLWZNW_OX`QXaRYaTYbUZcWZdY_eZ_e``fa`gcahpUidahUhh\ JohHfiFYi9OmEQiJSfNTbSV_WWW`YTdZPi`MmaJoYMpVOqRQsO\ TtKVuHXwDevEZvETvENyCIvEHsGHpHHmJHjKHgMHdNHaPGZQGW\ SGTTGQVGNWGKYGHZGWWIiTKv0mwQLsRNpSOmSPiTQfTScUT`UU\ XVVUWWRWYNXZKX_HY`EYaFXcGXdGWeHWfIWgIVhJViKUjKUkLU\ lMTmMTnNSoOSpQQtOSqMUnKWkIYhG_eEabCc_AeX9gVBdTCaRE\ ZQFWOHTMIQLKNJLKHNHGOEEOBEPCDPDCQEBQFAQG9RH8RI7RJ6\ SK5SL4SM3TN2TO1TP0ST6RXCQaIOePNjVMn`KsgTedbR`dYege\ jjlomtuTsa7rHkURiWShYTf`U } END PARAMETER FILE=========================================

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FOTD 04-05-09 (Buds in Springtime [8])
by Jim Muth 03 May '09

03 May '09

FOTD -- May 04, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image lies rather deep in the Seahorse Valley area of its parent fractal, which is the same parent that has given us the past two day's images. At this depth, the features have shifted almost completely from quadratic to cubic, though they remain far richer than those found in the pure cubic Mandel- brot set. I named the image "Buds in Springtime" because spring is really blossoming here at FC in central Pennsylvania, and also because FL's enthusiasm for her garden has me thinking of flowers. I rated the image at an 8 because I kind of like it. Unfortu- nately, the calculation time of over 15 minutes is longer than I would have preferred, but then, good things sometimes take quite a while to prepare and cook. Those who would rather pop a frozen dinner into the oven may see the finished image instantly on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Overcast skies, light but steady rain, and a temperature of 57F 14C, made Sunday less than ideal here at Fractal Central. The fractal cats turned sulky, but FL says this kind of weather is ideal for the new transplants in her garden. I guess we'll call the day undecided. My day was about average, with the philosophy brewing fast. The next FOTD will be posted in 24 hours. Until then, take care, and search for the cause of the effect. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Buds_in_Springtime { ; time=0:15:13.97-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 center-mag=-2.159\ 326422489538/+0.01879378114752815/1.545387e+009/1/\ 76.25/0 params=3/3 float=y maxiter=32767 inside=0 periodicity=10 colors=000nKemKdmKcnJanI_oIZoHXpHWphUqcSqZRrUPrPOr\ KMoDLlCJiCHfBGcBE`ADYABW99U98c86k85s73x72t94pB6lD8\ hFAdGB`IDXKFTMHPOJLPKHRMDTO9VQ5XS2XT1YT6VWATZERaJO\ dNMgRKjTKpVIlSHiPFfMEcJD`IEaIEbHFcHFdGGeGGfGGgFHhF\ HiEIjEIkDJlDJmDJnCKoCKpBLqBLr6LvBLsGLqKLoPLmULjYLh\ bLfkKefLdaMdXNcSOcOOcOTYOXTOaOOeIOjDOn8Rs2Or3Mq3Jq\ 3Hp4Eo4Co49n47m54m52l50l59k7Ik9RjB_jDhiFqiGmiHjiIg\ iJciK`iKYiLUiMRiNOiOKiOHiPEiQAiR7iS2lS4iS5gS7eS8bS\ 9`SBZSCWSEUSFSSGQSINSJLSLJSMGSNESPCSQ9SS7ST5SR1UU3\ SX4R_6Qb7Pd9OgANjCMmDLoFKrGJuIIxJHzKGvLIsMKpMMlNOi\ NQfOSbPU_PWXQYUQ_QRaNScKSeGTgDTiAUk8Tq7Um7Vi6Ve6Wa\ 5XZ5XV4YR4ZN3ZJ3_G2`C2`81a40c01a11_22Z22X33V33U44S\ 44Q55P55N66L66K77I77G88F88D99B99AAA8AA6BA6BA8FAAJA\ CNAEQAGUAIYAK`AMdAOhAQkESiIUhMWgPYeT_gXai`ckcemgho\ kkqonsrqurtwzzzzzzzzzzzzznzmZVrVSvSOzOLzLHzMEwPArU\ 7mZ3hc0ee3dc6c_9bUFfPPjKZ } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 03-05-09 (Etaoin Shrdlu [5i])
by Jim Muth 02 May '09

02 May '09

FOTD -- May 03, 2009 (Rating 5i) Fractal visionaries and enthusiasts: The name of today's image, "Etaoin_Shrdlu", is not nonsense. Old-time typesetters, if any remain, will know at once what it means. Anagram fans will also know. I gave today's image this name when I was caught in a spate of nostalgia for the good old days, (which seem so good only now that they're long gone). The rating of an imaginary 5 indicates that most of the image's worth is in its mathematical aspect. The parent fractal is a somewhat distorted and oversized Mandelbrot set. Today's scene lies in a tiny clump of debris floating in the center of the main bay of the parent. On its surface, the image is near total chaos. I call it sand. This sandy effect is the first impression one gets of the area. But just beneath the surface some strange things are happening. The shadowy outline of a quadratic Mandelbrot set is the most obvious feature, but look in the upper left corner. Yes, that is the edge of a cubic bud showing. Other cubic minibrots are scattered throughout the image. Perhaps the most curious things are the holes in the sandy layer where it lies over the outline of the M-set. These holes are shaped like the julia sets of the particular part of the M-set that they lie over. Some of the holes in the Seahorse Valley area are most unusual, with totally unexpected lobes and spirals. I might explore these holes in more detail in a future FOTD. The calculation time of 6 minutes will pass in a slow flash. But since the result might not be all that impressive, it could be a good idea to hop out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished GIF image there. Saturday featured lots of clouds here at Fractal Central, but enough sun filtered through to satisfy the requirements of the fractal cats. The temperature of 66F 19C was near perfect for the start of May. My day was fair enough. The next FOTD will be posted in 24 hours. Until then, take care, and help save the earth by living sensibly and ignoring all the commercial 'green' hype. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Etaoin_Shrdlu { ; time=0:06:03.69-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 center-mag=-0.330\ 6614681/+0.0152126363/9191.458/1/12.5/0 params=3/3 float=y maxiter=2500 inside=253 periodicity=10 colors=000YYfYYeYYeYYeYXeYXeXXeXXdXXdXXdXXdXWdXWcX\ WcWWcWWcWWczYKyWKxTKwRKvOKuMKtJKsHKrEKqCKpAKo8Kn6K\ m4KUU`UU`UT`UT`UT_UT_UT_UT_TT_TS_TSZTSZTSZTSZTSZTS\ YSSYSRYSRYSRYSRYSRXSRXSRXSQXRQXRQXRQWRQWRQWRQWRPWR\ PVQPVQPVQPVQPVQPVQPUQOUQOUPOUPOUPOUPOTPOTPNTPNTPNT\ PNTONSONSONSOMSOMSOMROMROMRNMRNMRNLRNLQNLQNLQNLQNL\ QMLQMLPMKPMKPMKPMKPMKOMKOLKOLJOLJOLJOLJNLJNLJNLJNL\ INKINKIMKIMKIMKIMKIMKILKHLJHLJHLJHLJHLJHKJHKJGKJGK\ IGKIGKIGJIGJIGJIFJIFJIFIHFIHFIHFIHFIHEIHEHHEHHEHHE\ HGEHGEHGEGGDGGDGGDGGDGGDFFDFFDFFCFFCFFCFFCEFCEFCEE\ CEEBEEBEEBDEBDEBDEBDEBDDACEBDEBDEBDEBDFBEFBEFCEFCE\ GCEGCFGCFGCFHDFHDFHDGHDGH0GIDGIEHIEHIEHJEHJEHJEIJF\ IKFIKFIKFIKFJLFJLGJLGJLGKLGKMGKMGKMHKMHLNHLNHLNHLN\ HLOHMOIMOIMOIMOINPINPINPJNPJNQJOQJOQJOQJORKORKPRKP\ RKPSKPSKQSLQSLQSLQTLQTLRTLRTMRUMRUMRUMSUMSVMSVNSVN\ TVNTVNTWNTWNTWNUmzzI`Ntmz } END PARAMETER FILE=========================================

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I'd Like to Share A Gigapan...
by Guy Marson 02 May '09

02 May '09

Dear fractinters, Hey, take a look at the following URL to see a really interesting Gigapan! The URL is: http://share.gigapan.org/viewGigapan.php?id=21222 let´s make a fractal "contest" at gigapan.org :). Cheers, Guy

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Re: [Fractint] gigapanz
by Guy Marson 02 May '09

02 May '09

Hi Jack, At 00:46 02.05.2009 +0000, you wrote: >. > > >what is the big deal with gigapans (very large images) and what does it >have to do with fractals, or am I missing something? You missed nothing :). I like this way to explore fractals like gigapans. > > > :( > > > >. Cheers, Guy

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I'd Like to Share A Gigapan...
by Guy Marson 02 May '09

02 May '09

Hey, take a look at the following URL to see a really interesting Gigapan! The URL is: http://share.gigapan.org/viewGigapan.php?id=2159

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Re: [Fractint] gigapanz
by JackOfTradeZ＠comcast.net 02 May '09

02 May '09

. what is the big deal with gigapans (very large images) and what does it have to do with fractals, or am I missing something? also, you CAN easily make multimegapixel images with fractint, I made default mandelbrots at 24000 x 18000 for 12 Meg size; I was hoping to print out a 4x6 foot poster but noone can do it :( .

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FOTD 02-05-09 (Fanciful Cubical [7.5])
by Jim Muth 01 May '09

01 May '09

FOTD -- May 02, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Friday began with the discovery via e-mail that an unknown relative had died in England and left me over 2-million pounds. All I need to do is send a check for 725 dollars to the lawyer holding the money, and he will forward the 2-million pounds to me. The money I am to send will cover the legal work and trans- fer fees. I replied, telling the lawyer to deduct the transfer fees from my 2-million pounds and send the remainder to me. I expect to be a millionaire within 2 weeks! But just in case something goes wrong, I have not yet given up my regular income, nor have I given up finding fractals. The parent fractal of today's image is not a cubic Mandeloid, it is a pretty much normal, though oversized, traditional Mandel- brot set. There is nothing normal about the large minibrot on the negative spike however. Its main bay has split into at least 3 sections, and its East Valley has split into 2 East Valleys. Today's scene is located very deep in a looping filament in the northern East Valley. At the extreme magnitude of over 7*(10^11), all traces of the quadratic parent have long since vanished. The image is purely cubic. Actually, it's a rather interesting cubic scene, with areas of mass chaos contrasting with areas of boring flatness. I named the image "Fanciful Cubical" because I feel the cubic Mandeloids are under-appreciated. After all, they are the runner-ups to the champion of all fractals, the Mandelbrot set. I rated the image at a 7-1/2, which includes 1/2 point for the coloring. The calculation time of just over 7 minutes may be cut to zero by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the completed image there. Cloudy skies and light rain did not dampen the spirits of the fractal cats here at Fractal Central on Friday. The temperature of 68F 20C was just about the middle of their comfort zone. With the health-care rush out of the way, and the flu panic showing signs of subsiding, my day was average. The next FOTD will be posted in 24 hours. Until then, take care, and anyone who thinks I'm going to get 2-million dollars should send me 2-thousand dollars and I'll give him half the 2-million. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fanciful_Cubical { ; time=0:07:07.02-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 center-mag=-5.041034711270663/+0.02399223935214779\ /7.538396e+011/1/-78.5/0 params=3/3 float=y maxiter=4800 inside=0 logmap=786 symmetry=none periodicity=10 sound=off mathtolerance=0.05/1 colors=0009BoABrAEtBFvBGxBHyBJy9Ly9Ry9ay9lyBryIlvP\ boUMhZ9df8frKjyUqyqxyzyyzyy_ryzyyz9yzYyF9000814P9K\ 00074D`65TQ4`TBoS8jUGhZWR5CV5HZ7ObLW9zGJsOYdYyN9yQ\ 9tSEmYTrM8mM7jZFymXyvHyzjyzy9zybihdfdyuhtnkDd6I`5Q\ YFXXTvrAmgR9zy9zyIrtXfh8At9ByPEoF21LYtT_m_ahbadyaq\ tbkyj9710rg8mb7j`Gh`WyS9tWLyqttAto9lmAhhOem9ryBiyB\ hrNeWsA6h6rz9nuGhgUf_612DezDhuLfjSfe`N6`2AIyvuyooo\ gi1CAOPO45RA9VQMZQo7Sh6WbF`_Uwz9ojGOAxUAoaLfyX9xZD\ vz9ouGjhUyQ9IVODByUIvyzyyvvrlm1B1C4Mdzyyz9ojBo98jE\ EhPS000FBDyivvfnG3KM8PTGT`SZyBrJ9dPGbWMb`U`9RyAUyM\ Xr_`hHBySEy`OmyBQyIWxPZoXc9z98uBEjKW`WyUytXtyay000\ IJKPf_Z`ZEPVWXZyu9mkEhcUT85`OO23GA4OPGV9zK9zROhXyz\ jOud`fcyzY9uXRf_9Ax8DrIKjVTdmughjffhftUOoYXj`a3P38\ R7JRHTVT`654FX5KZEOZWX`yByyR9yVHxZRoe`Nh6Us8`zHgzX\ lz9kzFyzyyzydzylzsyzrxzpuzn9zJ9zwMzrazmizflzjXz9wz\ 9azylzytzxyzxyzrHzy9zk9zM } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 01-05-09 (Yhrow-Away [3i])
by Jim Muth 30 Apr '09

30 Apr '09

FOTD -- May 01, 2009 (Rating 3i) Fractal visionaries and enthusiasts: I actually avoided getting dragged into a futile discussion on Thursday when FL uttered something about fighting climate change and I kept my opinion to myself. Finding a proper fractal was a more immediate if not quite as important task. Today's fractal image rates an imaginary 3. I have no idea how this rating fits into the usual rating scale, it must be off to the side somewhere, but after all the trouble the image gave me, I had to give it this rating. The clam-shell effect helped none at all. The problem was in the coloring. The scene looked promising when I found it, but nothing I tried produced colors that worked. I ended up rendering the scene with the outside set to 'summ', but even then the colors never approached anything near satisfactory. In frustration, I finally settled on today's too-blue-and-too- red color palette that is not helped by adding green. The name "Throw Away" refers to how I felt about the image when all my efforts at coloring failed. The calculation is thankfully fast, almost as fast as viewing the image, already calculated, on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Spring doesn't seem able to make up its mind. The temperature of 59F 15C and thick clouds kept the fractal cats close to the heat, which came on again here at Fractal Central on Thursday. My day was unusually busy. If it doesn't get even busier, the next FOTD will be posted in 24 hours. Until then, take care, and for those concerned, my opinion about climate change is that it is 50-percent politics, 49-percent commercial advertising and 1-percent real, and of this 1-percent-real part only 1-percent is man-made. To make matters worse, there is little we are able and truly willing to do about the 1/100 of 1-percent that is both real and man-made. But if it makes us feel good to imagine that we are actually doing something about climate change when we buy the products of the 'green' companies, all the better for both us and the companies. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Throw-Away { ; time=0:00:28.36-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 center-mag=+0.863\ 3692599764913/+0.08290534486951669/4.106888e+009 params=-12/16/1e-007/0 float=y maxiter=1500 inside=0 outside=summ periodicity=10 colors=000KUCLWENXFPZHQ_ISaKTcLVdNXfPYgQ_iT_iV`jXb\ l_bl`dnbepeepggqjhskhsmjtpkvrkvspywszxwzzzzzzzzzzz\ uzzpyzptzppxpjrp_mkRbfFTaHUKHZ0Jc0JhUKmcPrhUvmYxKJ\ 0KNPMOYFPeIRbNVgS_eXdj_igzzzzzzzzzzzzzzzzzzzzzzzzF\ tN5qI0nE0i50jA0lF0lK0nN0nS2pX5p_9qdEshHzkKzpNzuQzx\ TzzXzz`zzzzzYzzXzzzzwVzrTzmzzhQzdPz_zzVNzQzzLzzHIz\ Czz7QzAzzEbzHzzKpzNzzQzzNzzSwzVzzYhz`bzdzzgPzjIzmC\ zpzzXzzVzzTzzSzzQzzPzzNzzLzzKzzIzzLzzNzzPzzQzzSzzV\ zzXzzYzz_zz`zzdzzezzgzzhzzkzzjzzjzzhzzhzzhzzgzzgzz\ gzzezzezzdzzdzzdzzbzzbzy_zzbzzezzhzzkwzoszrozskzwg\ zzbzz_zzVzzSzzPzzLzzIzsFzoEzjAzd7z_4zT2zP0zK0zE0z9\ 0z10z40z54z7CzAIyCPtEXpHbjIhfKpaNwXPzMPzTQxXQsaQof\ SjjSepS`tTXyTSzTNzVIzVEzV9zX4zX0zXgzs0zX1zN5zF7nA7\ P7CUEHXKKaPPdVTg_Xle`pjdtphwumzzpzzuzzzzzxzzrzzjzz\ dzzXzzQzzIzz9zzCzzFpzIUzFZzCaz9dz5gzLzm`zNY_mVWpSR\ sQKwNGzKBzIAz0z42zEFzLSzT } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 30-04-09 (In the Rectangle [6.5])
by Jim Muth 29 Apr '09

29 Apr '09

FOTD -- April 30, 2009 (Rating 6.5) Fractal visionaries and enthusiasts: I must have seen the mysterious Z^(2.003) rectangle over 100 times in my 20 or so years of fractal adventures, yet I have never gone very deep into it. Well, today we correct that oversight. Today's image lies deep within the same view of the rectangle that appeared in yesterday's image. Today's image shows a curious little thing, kind of like an alien being with a head on both ends, waving his arms, with smaller arms on his arms. BTW and not surprisingly, more mysterious rectangles lie where the smaller arms branch from the larger arms. I named the image "In the Rectangle". That's where it is. Then I rated it at a 6.5, which is adequate and reflects a 1/2-point bonus for coloring. The calculation time of 2-1/2 minutes means no one will be annoyed because they spent too much time calculat- ing a disappoining image. Of course, the easiest way, as always, to see the completed image is to view it in its full glory on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Hazy sun and a temperature of 70F 20C made for a pleasant day here at Fractal Central on Wednesday. The fractal cats, who on Tuesday had complained about the heat, complained instead about the lack of food in their dishes. I complained about the health- care job, which the customer is still making changes on and which he insists we deliver by Friday. FL complained about my cavalier attitude toward life and death. She said that some- times I 'upset' her when I talk about stuff like that. The next FOTD will be posted in 24 hours. Until then, take care, and how can it be bad news to talk about going to eternal happiness? (Then again, maybe we're not quite so certain that it's actually there.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_the_Rectangle { ; time=0:02:28.78-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=JulibrotZpwr passes=1 center-mag=+0.0029274462303777/+0.0748848963434437\ /3.809697e+007/1/21.5/0 params=2.003/0/-1.7435/\ 0.0003/-0.0015/0.0005 float=y maxiter=3000 inside=fmod proximity=12 periodicity=10 colors=000UQdDjk9tk9uk8vk7wk7wk8vj9uiAtiAshBrgCqgC\ pfDofzzezzdzzdzzczzczzbzzazzazz`zz`zz_zzZzzZzzYzzY\ zzXOZWPYWQXVgSei0PQWVRYTS_RTaPUcNVeLWgJXiHYkFZmD_o\ B`z9`z8az9az9az9az9azAazAbzAbzAbzAbzBbzBbzBczBczCz\ zmmzCczCczCczDdzDdzDdzDdzEdzEdzEezEezEezFezFezFepF\ hsEepFcmGakH_hIYeIWcJU`KSYLQWLNTMLQNJOOHLPFIPDGQBD\ R9AS66T78S8AR9CRAEQAGQBIPCKPDMOEOOEQNFSNGUMHWMIYL8\ SUIZLVcBTdCSdCRdDQdDPeDOeENeEMeELfFKfFIfFHfGGgGFgG\ EgHDgHChHBhIAhI9hIBgLDgOFgRHfUJfXLf_MfbOeeQehSekUd\ nWdqYdt_exZdwZcwYbwYawY`wXAwXCwXEwWGwWKwVMvVOvVQvU\ RvUSvUTvTUvTVvSWvSVvSUvRTuRSsRQqQOoQMmPKkPIiPGgOEe\ OCcLAaN7_O4YP3WR0US0ST5QVAOWFMXKKZPK_UK`ZRbcWzrTzu\ RzzOzxPzvPzsPzpPzlPhjPihPjfPjdPkbPk`PlZPmXPmVQnTQo\ RQoPQpNQpLQqJQrHQrFQsDQtBQt9Qu7Qx1Pu5Qr8RoBSlFSiIT\ fLUcPU`SVYVWVZWSaXPdYMhYJkZGn_Dq_HrzLrzPszTszWzz_t\ zFzzEzzDnzDozCpzBqzBrjAsj } frm:JulibrotZpwr {; Jim Muth ; Draws oblique slices of order n Julibrot Figure ; P1 defines power of Z, P2 sets center of slice ; P3 sets angle of slice z=pixel, c=p2+(pixel*p3): z=z^p1+c, |z| <= 100 } END PARAMETER FILE=========================================

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FOTD 29-04-09 (Mystical Rectangle [?])
by Jim Muth 28 Apr '09

28 Apr '09

FOTD -- April 29, 2009 (Rating ?) Fractal visionaries and enthusiasts: Tuesday was interesting here at Fractal Central. FL and I were at breakfast with the TV playing softly in the background, when FL suddenly asked, "are we going to die?" Without much thought, I answered, "Of course," and FL exclaimed something like 'oh my God!' I was reading the paper, and did not realize that the quarter-hourly swine-flu scare was being hyped on the TV morning news show and she was referring to the flu scare. When I realized what she was talking about, I assured her that the whole doomsday atmosphere was created to get people to worry so that they would spend more time watching the news channels and thereby enable the stations to charge more for their adver- tising. But the whole thing really started my philosophical juices flowing. I love mysteries, and next to the fourth dimen- sion, death must be the biggest mystery of all, so expect some morbid musings in the not too distant future. A more immediate concern is how to rate today's fractal. After at least 2 minutes of contemplation, I realized that I would never be able to honestly rate the latest appearance of my old friend, the rectangle in the Z^(2.003) Julibrot, so I rated it as a question mark. The name "Mystical Rectangle" refers to the mystery of trying to determine the true four-dimensional shape of the object that is rectangular in only two of its four dimensions. Today's orientation is very close to the Julia direction, just far enough removed to make the scene interesting. I'm not sure what slices the JulibrotZpwr formula cuts in Julibrot, but I have never found similar slices with any of the other four-dimen- sional formulas. The calculation time of 1-1/4 minutes is very fast. Equally fast is the trip to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The April heat wave continued here at Fractal Central on Tues- day. The fractal cats made the most of things by avoiding the hot sun and temperature of 90F 32C. The humidity remained low however, so the cats were reasonably happy. My day started slow, but turned busy when an unexpected job arrived around 10am. Crises notwithstanding, the next FOTD fractal will be posted in 24 hours. Until then, take care, and why worry about the flu, when the disease that will kill everyone is already out there. It is not yet fully defined, but it is 100-percent fatal and everyone is certain to contract it and die of it. Its name is 'something'. (Don't blame me for mentioning the unpleasant and inescapable truth! I didn't make things this way. The Big Guy up in the sky did it, so blame Him.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mystical_Rectangle { ; time=0:01:14.64-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=JulibrotZpwr passes=1 periodicity=10 center-mag=-0.000545676/+0.07365904/101.6427/1/19/0 params=2.003/0/-1.7435/0.0003/-0.0015/0.0005 float=y maxiter=2800 inside=255 logmap=56 colors=000A0NA0NA0NA0PA2PA4PA6P48R0AR0CR0ER0GP0HR0\ JT0LV0NX0PZ0R`0Tb2Td6Ve8XgAZiC`iEbkGdmHeoJeqNgsPiu\ RkvTmxVozXqzZszbvzkszuquzokzkbziRzOHz58zE0zM0zP0zS\ 0zV6ucCkcHkcNkJRUHXUGbUEgUCmUAsU2mU8cUEcUHcUNcuTzz\ Xzzdzzkzzqzzvzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ vzuuzkszbozZmzXkzTizRgzPgzNgzLgzJzzHzzGzzEzzCzzAzz\ 8zz6zz4zz2zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0iz2ez8bzCXzHzzLzxRzuVzq`EodAki6im8zoAzoAzo\ CzqCzqEzqEzsGzsGzsHzuHzuJzuJzuLzvLzvNzvNzxPzxPzxRz\ zRzzTzzLzzTzz`zugzmmzguzbzzVzzPzzRzzJzeEzg6qk0io0z\ i0bq00x00v00u00s00s00q00o04o06m0Ak0zi0zi0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0zz0uz2qz0mZ0id0ei0bo0Zu0Vz\ 0Rz0Nz0Hz0zz0zz0zz0zz0zz0zz4zz6zzNzsdzdszeuzguziuz\ kuzmuzouzou0qu2su2uu4vu6xu8zuAzuCzuEzuGzuHzuJzuNzx\ JzuHzsGzoEzmCzk8zg6ze4xb2v`0uZ0sV0zT0zR0zN0zLozPqz\ NuzLzzJvzLszLozLkzLezNJAJ } frm:JulibrotZpwr {; Jim Muth ; Draws oblique slices of order n Julibrot Figure ; P1 defines power of Z, P2 sets center of slice ; P3 sets angle of slice z=pixel, c=p2+(pixel*p3): z=z^p1+c, |z| <= 100 } END PARAMETER FILE=========================================

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FOTD 28-04-09 (Stripes in Sight [4.5])
by Jim Muth 27 Apr '09

27 Apr '09

FOTD -- April 28, 2009 (Rating 4.5) Fractal visionaries and enthusiasts: Even with its half-point bonus for the coloring, today's image is nothing to write home about. The parent fractal resembles a Julia set with a grossly enlarged Mandelbrot bud in the back- ground. In the southeast corner of the parent lies a prominent spiral. Today's image shows that spiral with stripes added, plus one of the smaller but much-enlarged Mandelbrot ghost buds lurking in the background. I posted the image after trying for almost an hour to bring it to life, with very little success. I named the image "Stripes in Sight". One look at the image will explain the name. I have done many images of this type over the years, and most of them are notably better than today's. The maxiter of 32,767 is barely adequate for the ghost-bud effect. A maxiter of some- thing like 200,000 would improve the definition, but it would also almost double the calculation time. Oh, what the heck. I think I'll go ahead and raise the maxiter to 200,000. The calculation time has now been raised from 10 minutes to just under 17 minutes, which is far too slow for an image of such questionable quality. I strongly recommend sufing to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Too much of a good thing prevailed here at Fractal Central on Monday. The temperature of 93F 34C combined with an unbroken hot sun made for heat that sent the fractal cats searching for the coolest place they could find. With the cool air vents in the living room not yet producing cool air, the cats chose to lie on the cool tile of the bathroom floor. My day was very close to average. Most likely, tomorrow will be the same. The next FOTD, a much-improved one without doubt, will be posted in 24 hours. Until then, take care, and be at peace with your iterations. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Stripes_in_Sight { ; time=0:16:58.04-SF5 on P4-2000 reset=1960 type=formula formulafile=jim.frm formulaname=ObliqueManPlus passes=1 center-mag=+1.0191258/-0.42280024/75.0584/1/-8.75/0 params=0/0/-0.5/0.527/0.018756/0.024873 float=y maxiter=200000 inside=0 logmap=488 periodicity=10 colors=000rIPNILrIPNIUwIYNI_yIcNIgzIlNIpzJtNJyzJzN\ LzzLzNLzzNzNNzzNzNNzzLzNLzzJzNJzzIzNIzzIzNIzzIzNIz\ zIzNIzzIzNIzzIyNIwzItNIrzIpNInzIlNIjzIgNIezIcNIazI\ _NIYzIWNIUzISNIPzINNIPzIPNIPzIPNISzISNISzISNIUzIUN\ IUzIUNIWzIWNIWzIWNIYzIYNIYzIYNI_zI_NI_zI_NIazIaNJa\ zJaNLczLcNNcyNcNPewPeNRerReNTgpTgNVgpTlNVjnVjNVjnV\ gNVgnVgNVgnVeNVelVeNVelVcWVchVcNVchVaYVagVaaV_gV_e\ V_gV_fV_dVYeUYgTYhSYhRWgQWgQWgQWgQUgQUgQUgQUgQUgQW\ gSYgS_gUZgWaeYce_ec_gc_ja_la_n__p__r__tY`wY`yWazWa\ zUbzUbzSczSczPczPdzPdzNdzNdzLdzLdzJdzJdzHdzHdzFdzH\ dzJdzJdzLdzNdzNdzPdzPdzSdzUdzUdzWdzWdzYdz_dz_dzadz\ adzcdzedzedzgfzgizjkzlmzloznqznszpuzrwzryztzzpzzrz\ zrzztzztzztzzwzzwzzyzzyzzyzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:ObliqueManPlus {;Jim Muth z=p1+pixel, c=p2+(p3*pixel): z=sqr(z)+c, |z| <=100 } END PARAMETER FILE=========================================

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I'd Like to Share A Gigapan...
by Guy Marson 27 Apr '09

27 Apr '09

Hey, take a look at the following URL to see a really interesting Gigapan! The URL is: http://share.gigapan.org/viewGigapan.php?id=21150

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Re: [Fractint] Fractint Digest, Vol 74, Issue 8
by JackOfTradeZ＠comcast.net 26 Apr '09

26 Apr '09

. PNL say: ""WOW !!! Is that running a PC 24x7, or just part of a week?? And when did you start the project?? I assume it will be a really lengthy video (or maybe a full-length movie)."" The "universe #6" posted on my site goes to E+87. It was originally targeted to a minibrot at E+112 but I gave up on it at first cause I thought it impractical. However, after purchasing 2 new P3-933 systems to add to my render farm, and recalculating the sequence, it looks like it can be done by years end. The images so far look astounding - it is interesting how things keep getting more intricate and complicated the deeper in you go, nevertheless they still "look the same" due to self-similarity. It will be a full 6 minutes long. Patience ...patience.... If fractaleers have nothing else it has to be patience ....... .

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FOTD 27-04-09 (Half Asleep [6])
by Jim Muth 26 Apr '09

26 Apr '09

FOTD -- April 27, 2009 (Rating 6) Fractal visionaries and enthusiasts: The Saturday trip to Old Fractal Central, where Thomas, the one remaining old fractal cat still lives, went well enough, but I didn't get back to new F.C. until almost midnight, and this is my excuse for having a very lazy day on Sunday. Today's image, which I found effortlessly with the Fractint evolver feature, is another of those MandNewt things that are a total puzzle to me. But whatever the image is, it rates a 6, and is relatively easy on the eye. A large part of the image consists of 'inside' stuff brought to life by the 'bof60' inside fill. Some interesting scenes might lie deeper inside the image, but I was too lazy to check. The name "Half Asleep" refers not only to the appearance of the fractal but to the awareness level of the fractalist as well. The calculation time of 3-1/4 minutes will bring joy to the hearts of every fractal fan, as will a trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for immediate viewing followed by absolute bliss. The bright sun on Sunday here at Fractal Central looked promis- ing at first, but when the air temperature reached 91F 33C, the sun no longer brought comfort. The fractal cats tried lying in the sun for a couple minutes, then stretched beneath the cool air vent. Needless to say, April is too early to turn on the cool air, so the cats complained and cooled down on their own. After the trip to Old Fractal Central on Saturday, I spent Sunday doing little or nothing. FL spent the day working in her garden, while I checked her progress every hour or so to give the impression I would be ready to help . . . if she needed it. Luckily, she never did. The next FOTD will be posted in 24 hours. Until then, take care, and I just saw a Higgs particle fly past the window. And it stopped long enough to look in. I guess this makes me world famous. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Half_Asleep { ; time=0:03:14.60-SF5 on P4-2000 reset=2001 type=formula formulafile=mandnewt.frm formulaname=MandNewt11 passes=1 center-mag=0.08566\ /0/1.8/1/-90/0 params=-1.38/-0.99/-1.98/0.47/-0.48\ /3.46 float=y maxiter=250 inside=bof60 logmap=yes periodicity=0 colors=000zzzzzzzzzzzzzzyzzxzzwzzvzzuzztzzszzrzzqz\ zpzzozzozyoyxoxwowvovuoutotsosrorqoqpopnoolonjomho\ lfoldojboj`ohZohXofWofUoeTodSocRobQoaPo`OmZNlYMkWM\ jWMhULgUKeSJdSIaQH_OGYOFWMEWMDUKCSKBSIAQI9OG8OE7ME\ 6KD5KD4IB3GB2G91E90D80D80B609509508306306205203103\ 10200100100000000000000000000000000000000000001002\ 00300400500600700800900A00B00B00B00B00B00B10B20B30\ B50B60B80B90BB0BD0BG0BI0BK0BM0BO0BQ0BS0BU0BW0BY0BW\ 0BU0BU0BS1BS1BQ2BQ3BO5BO6BM6BM8BK9BKBBIDBIDBGEBEGB\ EIBDKBDKBBMBBOB9QB9SB8UB8UB6WB6YB5_B5aB3aB2dB2fB1h\ B1jB0jC0lE0oG0qI0sK0sM0uO0xQ0zS0zU0zZ0zZ0zB0xB0uB0\ sB1qB2oB5lB6jB8fBBdBDaBG_CIYDMWDOUESSGUQGWQJUQKSQM\ OQOMQPKQTIQVGQXDQZBQ`9Qd8Qf5Qh3Qj2Ql1Qq0Qs0Qu0Qw0Q\ z0Ww0_u0fs1jq3oo5ul8zjBzhEzfIzdKzhQzjUzoYzqaxufuwj\ szoozslzxhzzfzzdzz_zzYzzUzzSzzQzzMzzKzzIzzEzzDzzBz\ z9zz6wz5sz3oz2jz0fz0bz0Zz } frm:MandNewt11 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-b)*z-f j=c*z^d+g z=z-e*h/j, .0000000000000000000000000000005 <= |h| } END PARAMETER FILE=========================================

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FOTD 25-04-09 (Fully Discharged [7])
by Jim Muth 24 Apr '09

24 Apr '09

FOTD -- April 25, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image came into existence when I added 0.3 part of Z^(-7.4) to 1.5 parts of Z^(-1.1) and then added (1/C). The resulting parent fractal is immense. In fact, it is so large that part of it lies beyond the bounds of Fractint visibility. But the important part consists of 2 large bays resembling a figure-8, with a sinuous filament extending east from the east branch of the valley connecting them. Today's image lies in the detail surrounding this filament. Like I did with yesterday's image, I set the maxiter of today's scene a little higher than necessary to give the impression of a fractal floating in the eternal emptiness of higher-dimensional space. I named the image "Fully Discharged" when it reminded me of one of those coronal discharge globes sometimes seen in trendy stores. The rating of a 7 indicates that the image is good enough, but nothing to get excited about. The calculation time of 53 seconds is superb however, and can only be equalled by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Spring was in the air here at Fractal Central on Friday. The total sunshine and temperature of 77F 25C made the fractal cats of F.C. as well as the non-fractal cats in the area quite happy. My day was average, while FL worked herself to exhaustion in the FC garden. I'll be making a short trip back to Old Fractal Central on Satur- day, so the next FOTD fractal will probably not be posted until the 27th. Until then, take care, and those who have faith in reason can apply that reason to their faith. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fully_Discharged { ; time=0:00:53.79-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=t center-mag=84.7641/1.51626/30.7169/1/-143.5/0 params=1.5/-1.1/0.3/-7.4/0/0/0/0 float=y maxiter=1100 inside=0 logmap=106 periodicity=10 colors=000000_caaaYc`VeZRgYOiWKjUHkSGlQFmOEnMDoWCp\ cBqhAzr9zv8zz7zzBzzEuKHuKKuKNuKQuKTvKWvKZvKavKdvNg\ mKjvImlHkoGjgFhiEgbDccCgZBZYAbU9XR8KO7KL6KI5KF4KC3\ A920F30K30P30V4K_4Ud4cj5ko5nt5qqUrnUrzzzzzzzzzzzzz\ zzzzzzmzzmzzmzzmzzmzPMnSFhV8bY2Y`JVbZSdXRfVQhTQjRP\ lPOnNUpLcrJo0mz0mz0cz0cz3FX4EX4DX5CX5BX5AX69X68X67\ X76X75X74X83X82X81XA3WC5WE7VG9VIBVKDUMFUOHUQJTSLTU\ NSWPSYRS_TRaVRcWReMRgCRh2Rg3Pf4Ne5Ld6Jc7Hb8Fa9DaAB\ ZCFWEJUGNRIQOKUMMYJN`GPdERhBTl8Vo6Xs3Zw1_zHaXXz3Wz\ 4Vz5Uz6Uz7Tz8Sz8Rf9RfAQgBPgCPgCNhFLiIJjLHkOFlRDmUB\ nX9o_7pb5qe3rh1sk3gn4Wq6Kt79wHEnQIfZMZhRRqVJzZBu_E\ p_Hk_Kf_Nb_QY_TT_WO_ZK_aF_dA_g5_j1_l4Xm7VmATmDRmGP\ mJNmMLmPJmSHmVFmYDm`Bmb9mfIpjQsnZvqfxrbvs_tsXrtUpu\ RnuOlvLjvIhwKfwMewOcwQbwRaxT_xVZxXXxZWx_VyaTycSyeQ\ ygPyhOvgNtgMqgLofKmfJjfIheHeeGceFadEZdDXdCUcBScAQc\ 9Ne8Kg7Hj6El5Bn48q35s22u2 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 24-04-09 (Caught in the Fact [6.5])
by Jim Muth 23 Apr '09

23 Apr '09

FOTD -- April 24, 2009 (Rating 6.5) Fractal visionaries and enthusiasts: Today's image came about when I subtracted Z^(1.1) from Z^(-1.1) and added straight C. I chose these values because exponents between Z^(2) and Z^(-2) make the most interesting fractals when mixed together in the iteration soup. The effect of surrounding blackness filled with star-like dots and tendrils was created by rendering the image with the logmap intentionally set to too high a value. The fancy scalloped shapes surrounding the central minibrot are a natural bit of the fractal however. The parent fractal consists of a large Mandeloid facing south- east, with a main bud as large as its main bay, and a second Mandeloid a bit to the northwest, connected to the larger Mandeloid and slightly cut off by a discontinuity. Today's scene lies in a train of scattered debris leading from the smaller Mandeloid toward the larger one, but being cut off by the discontinuity before reaching it. The name "Caught in the Fact" leaves open the question of what fact. God only knows, and He isn't telling. The rating of a 6-1/2 means that I like the image just enough to grant it FOTD status even though my coloring was responsible for the extra 1/2 point of the rating. The calculation time of 1-2/3 minutes will bring smiles to the faces of the time challenged. A trip to the awesome FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the completed image there will bring a smile to the faces of everyone. Partly cloudy skies brought off-and-on happiness to the fractal cats of Fractal Central on Thursday, while the gusty winds and temperature of 54F 12C made it feel like mid-March rather than late April. My day was fair enough. The next FOTD will be posted in 24 hours. Until then, take care, and when I get to heaven I'm going to tell God to take sensitivity training, learn anger management and start obeying His own commandments. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Caught_in_the_Fact { ; time=0:01:41.46-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.728552855008/-1.644842873009/3271978\ /1/152.5/0 params=1/-1.1/-1/1.1/0/0/0/0 float=y maxiter=800 inside=0 logmap=125 periodicity=10 colors=000000zzzzzFanDboBcd9c_8mc6mZ4mU2mP1mK4mG6r\ D9vDBzDDzCGzCIUCKZOPcZUhjZlucerd_odTmdNUdGUdAUd4cd\ BffIzhPzjVzlaznzzznzrpoeqlUriIsg6kk8dnAYqCRtEKmGDz\ IHmNLzROtVSz_VpcZnzalk`jz_i`ZhzYgzXfMWeHWdCGgK1jSs\ hXkecdbiY_oRYuVadZeO`gRaiTbkWcmYeo_fqbgsdhufzk`faV\ zTPdJJz9Db07M7I6DSzGPEJMIMJMPHQSEUVBYY8`_6_Y7ZX7YV\ 8XU8WT8XP7XL6XH5XD4X93X63SObrw7cgzmnOfhQ`cSUZTOUVI\ PWHWQGbKGiFQbDZXChRAqL9c18_OUWioSgiOfdKdZGcUCbP8`J\ 4_E1Z94a86d88g8Aj8Cm8Ep8Gs8Iv8Fw7Cw79x77x7DrDImJNg\ PSbUXY_aSefNkkIpkGkkFfkDakCXkASk9Nk8Jd9TZ9bTAlNAuK\ FtHKtEPsBUs8Zr5cr3gr8jiDmaIpUNsMRuECQV9OO7NI4LCGMJ\ TNWeOhaMdYK`UIXQGTMEPICLNLJSUHXaGajEerD`mKWiRRdYM`\ dIQbEF`A4_EHXIUVMfTPsREucKveQvgVvh`vjfwlkwmqwovwpm\ xgdy_WzSNzJEzB5z3Gz76zX4zM2zBzzdzzUzzKzzAzz4zzjzzr\ zzRzzuzzzzz7zz5zz3zz1zzozzdzzUzzKzzAzz0zz0zz0zzjzz\ VzzFzz0zz0Ez07z0izrNzRnz6 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 23-04-09 (Natural Reality [5])
by Jim Muth 22 Apr '09

22 Apr '09

FOTD -- April 23, 2009 (Rating 5) Fractal visionaries and enthusiasts: I named today's image "Natural Reality" because no one seems able to agree on exactly what 'reality' is, and at the same time it's nearly as hard to decide what a fractal is. The parent fractal was created by mixing 1 part of Z^(1.5) with 1/2 part of Z^(3) and adding C. This parent consists of two Mandeloids lying north and south of the origin, with a broad band connecting them. This broad band has a kind of East Valley on its east side, and today's image is located very near the X-axis, slightly inland of the valley. The image has nothing special about it. What you see is what you get, nothing more, nothing less. After careful study I rated the scene at an adequate 5. The calculation time of 5 minutes is bearable, but downloading the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will make it more bearable. Heavy clouds, blustery winds, occasional sprinkles and a temperature of 55F 23C made Wednesday unpleasant for the fractal cats of Fractal Central. For me, both the day and FOTD fractal were average. The next FOTD fractal will be posted in 24 hours. Until then, take care and where is science leading us? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Natural_Reality { ; time=0:05:02.10-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+0.1753695852258426/+0.0000394671963969\ 2/5.024515e+012/1/-120/0 params=1/1.5/0.5/3/0/0/0/0 float=y maxiter=2400 inside=0 logmap=366 periodicity=10 mathtolerance=0.05/1 colors=000X_Kj`WleQPcuTekWbbZhTY11Ly0Rs7XnEl_HmHhj\ PagWWdbQYTifVgd__bdS9IdJSYT`ROsN5hEMiHBk4PjCyClcFK\ bNKbVKaSKcIEGLLMSKRYKXcKDz_MtUUnPGCbR0VKX`QaVWeP7N\ CfbRgsC877IKCSXGz7QsHOmRNg`LNENRMMVULosK80HDitP6xU\ KjYXXCTmJYePaZWeRHRp8_sIcgSfWc1tbOaqLL10W1VOKbM4M2\ GU8RhEBO8KWCTbG3HqLW`peWkgSfhOZCH`TJbVJaZKabKafKDO\ gQZWkaSfeOhCwfLmdTcbaUUkGYjInuYjrUgoRdlNbyuashanWR\ KHON44jrGifRiVCWWJ_TPbQWfN9qgHoaOmWVkQdXwbccXzd_qU\ en3dl8ckCbjGGCDMLFRTHXaJcGUbORbVPabMJo_sI2nP7jWBeb\ GVkqXjhZj``iS5L5GUARaFZLW_US`aOs3uVYCZYBbYAeY9iY8m\ Y7pY6tY5wY4t_BncDifFdiG_lIVpKrsLLvNzyOHsTHnXwh`Icd\ IYiITmJNqJIuJDyVCsfBmrAgnHekOdhVcd`aag`Zn_WtZSq`On\ aLkbHicDfeAcf6`g3Zh4Tk4Nn4HpljDaWARI8G46FGCERHDaND\ lSCiUCfVBcWB`XXQKKcSTfOYnh6pmHzzSzzjzznzzizzezzezz\ dzzczzbzzzz2zzBzzXzzQzzWzzQzz_zzWzzSzzOzz0zzAzz7zz\ lzzbzzTzzuzS2zV8zbEzFMzQL } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Re: [Fractint] Deep and Slow
by JackOfTradeZ＠comcast.net 22 Apr '09

22 Apr '09

. PNL say: This title would make a good slogan for a bumper sticker: Fractalists do it Deep and Slow :-) :-D ;-) I know the feeling .... My current project to E+112 is figuring to take to end of year (if all goes well). Most people wouldn't know what a fractalist is, but you can design and print your own bumper stickers online at: http://www.makestickers.com/ I have several done already (political). I have some ideas for Obambam, but I'll wait a while and give him a chance first. .

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FOTD 22-04-09 (Deep and Slow [8.5])
by Jim Muth 22 Apr '09

22 Apr '09

FOTD -- April 22, 2009 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image is an extremely deep scene on the northeast shore line of the main bud of the Mandelbrot set. I think it is the second deepest FOTD so far in FOTD history. At this depth the patterns around the minibrots settle into a series of concentric circles, which are very obvious in today's image. I named the image "Deep and Slow". Actually, the calculation time is not as slow as might be expected at the extreme magni- tude of almost 10^55. The rating of an 8-1/2 includes the traditional 1/2 point bonus for the coloring, which I think is worth it. The image calculates in 1-1/2 hours for those who like to do it the haed way. The much easier way is to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A cloudy morning gave way to a sunny afternoon here at Fractal Central, while the temperature reached 63F 17C, but at 6pm a thunder-shower moved in to end the day on a wet note. The fractal cats enjoyed the sun while it was shining, and ignored the clouds and rain. The next FOTD will be posted in 24 hours. Until then, take care, and search ever deeper. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep_and_Slow { ; time=1:31:15.13-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.8258\ 15776368296644495089770635123369097730630839395359\ 626344/0.18537815042145875449626178497852303287572\ 8204898436494525953/9.647924e+054/1/-148/0 inside=0 params=0/0 float=y maxiter=10000 bailout=100 logmap=2122 periodicity=10 mathtolerance=0.05/0 colors=000ULdRLbPL_NLYKLVILTGLQDLNBLL9MILMGPNDRPBS\ RAUU9XX8_`7bd6eh5hl4kp3nt2qw2tx4wx5zx7zx8zx9zxBzxC\ zyDzyFzyGzyIzyKzyMzyOzwQzuSzsUzqWzoYzm_zkazibzhgzi\ eWidUicSibQiaPi`Si_WiZZiYbiXeiWiiVliUpiTsiSqcToYUn\ SalMbjGbiAbg9Yf9Ue9Qd9Mb9Ha9E`9B_98Z95`B7bD9dEAfHC\ hJEjMFlOHnRJpTKrUMsUNqUOpTOoSOmROlROkRPjRPhRPgRPfR\ PeRQcRQbRQaRQ`RQbTRcUSdWTeXTfYUg_Vh`VibWjcXkdXlfYm\ gZnhZmhXmhVlhTceI`aJYYKVULSQMPMNMIOJEPGAQiLagNbeQc\ r`kcSdQJZCATZ9Vt9XpKVlVUheSezzcqmajX`h_ZfbYdeWagV_\ jTYmSWpQUsOTzPSuQSpRSk_dWYdUMZdBUn9N`8GOEJKJLHONET\ PAYR7bT4gV1kY3o`4sb5we6zn7tzEzzKzzQcvWZyaSjbMXbFJc\ 95cUMMma5lY4kV4kR3jO3jL3hQ4fV5dZ5bc6`h7Zl7Xq8Wu8Rj\ 6M`5IR4HOBGMIGKOEJNCINAHN8GN6FN4EN2DN1CN7KPDRRIYTO\ dVTkXVmH`oKeqMjsOouQtwSyxUkzTYzTKzS7zSmziYzUJzFGzE\ DzDAzDPzMbzVZzKVz9SzAwzjuzgszdqzblzUgzMUzEGz73z0Hz\ GVzWSz`PzdNzhKzlgzadz_bzY } END PARAMETER FILE=========================================

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<Paul> FW: re: FOTD 18-04-09 (Cheshire Elephants [6])
by Hal Lane 21 Apr '09

21 Apr '09

Paul, You said: -------------------------- > Too bad the FOTD web page image could not easily be made to draw the > image in an animated way just as it was rendered. Once upon a time (quite a few years ago) I ran across a 'compute server' on the web that you could submit a fractal to. They would render it (probably on a really large computer for the time) and then display your fractal in your browser. This would allow "...draw[ing] the image in an animated way..." I haven't looked for anything like this for a while. btw, I try many of Jim's FoTDs in Richard's Fractint for Windows beta 5. I have found that Richard's version of Fractint doesn't like to do fractals that use the MandelbrotBC3 -- this one included. - Hal Lane ######################### # hallane(a)earthlink.net <mailto:hallane@earthlink.net> # ######################### > -----Original Message----- > From: fractint-bounces+hallane=earthlink.net(a)mailman.xmission.com > [mailto:fractint-bounces+hallane=earthlink.net@mailman.xmission.com]On > Behalf Of Paul N. Lee > Sent: Sunday, April 19, 2009 3:49 PM > To: fractint(a)mailman.xmission.com > Subject: Re: [Fractint] FOTD 18-04-09 (Cheshire Elephants [6]) > > > Jim Muth wrote: > > > > After all, how impressive can a couple > > disembodied elephant trunks sitting over > > some half-squashed buds be? > > > > START PARAMETER FILE======================================= > > > > Cheshire_Elephants { ; time=0:01:50.06-SF5 on P4-2000 > > reset=2004 type=formula formulafile=basic.frm > > formulaname=MandelbrotBC3 passes=b > > > > I have always enjoyed watching the drawing method of "Boundary Tracing" > (using the passes=b option). And this particular image had that extra > little "flare" towards the end of the rendering process, which one does > not always see in your FOTD images that use this setting. (I understand > why it happened to draw that way, it just is not seen that often.) > > Too bad the FOTD web page image could not easily be made to draw the > image in an animated way just as it was rendered. I think many people > who do not use FractInt would get an extra trill viewing. :-) > > > Sincerely, > P.N.L. > ------------------------------------------------- > http://home.att.net/~Paul.N.Lee/PNL_Fractals.html > http://www.Nahee.com/Fractals/ > > _______________________________________________ > Fractint mailing list > Fractint(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint

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FOTD 21-04-09 (Filler Thriller [5])
by Jim Muth 20 Apr '09

20 Apr '09

FOTD -- April 21, 2009 (Rating 5) Fractal visionaries and enthusiasts: With a heavy day Monday, I had too little time to work up a proper fractal, but I did find one that rates an everyday 5, which is average and leaves it to the viewer to decide how to define an average fractal. The parent came into existence when I combined 2.5 parts of Z^(-1.7) with 0.25 part of Z^(-6.6) and added (1/C) to make a fractal that resembles a 3-leaf clover with curious decorations around the leaf edges. Today's scene is located in an area of debris near an occluded bay on the southwest shore line of the largest clover leaf. To raise the image from the grave, I needed to render the scene with the outside set to 'tdis'. And even then I could rate it no more than average. The name "Filler Thriller" implies that the image is merely a filler to take the place of the fractal with a rating of 9 that I might have found but did not find today. The good news is that today's image calculates in about 1/1800 the time of yesterday's monumental calculation job. But still, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds, frequent showers, a blustery east wind and a chilly temperature of 45F 7C made things quite unpleasant for the fractal cats here at Fractal Central on Monday. More work than expected made it rather unpleasant for me also. The next FOTD will be posted in 24 hours. Until then, take care, and live life to the limit. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Filler-Thriller { ; time=0:00:55.79-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.3881294045/-0.8705987174/36639/1/\ 122.5/0 params=2.5/-1.7/0.25/-6.6/0/0/0/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=10 colors=000nIIoHJoHJpGKvGGpGKjGOdGRZGVTGYNGaHGdBGh5\ Gkabibajdakealfalg`mh`ni`oj`omWqoRrrMstHuwCvy8wvAu\ sCtqDsnFrlHqiIpfKodMnaNm_PlXQkUSjSUiPVhNXgKZfH_eFa\ dCccAdb7fa5g`8ebAdcDcdFafI`gK_hMZiPXkRWlUVmWToZSp`\ RqbQr`TlZWgYZaWaXVdRTgMTlISjHRhHRgHQeGPcGPbGO`FNZF\ NYFMWFLUELTEKREJPDJODIMDHKDHJCGHCFFCFEBECBDABC75D9\ BDBGEDMEFRFHWFJaGLfGNlHPqGQxHRvHStHTrHUpHVnHWlHXjH\ YhHZfH_dH`bHa`HbZHcXHdVKfRHeUFeXDe_Bea9dd7dj5em4ep\ 3em3dl3dk3ci3bg3ae3`c3_a3Z_3YY3XW3WU3VS3UQ3TO3SM3R\ K3QI3PG3OE3NC3MA3L88M6CP4HU6LZ8QcAUhCUm4YpD`mLdjTg\ g`jdhkajlZkmZln_noaopcpqeqrfsshttjusnwtkvtiutgtues\ ucsuarv_qvYpvWpwUowSnwQmxOmxMlxKkyIjyGjyEizChzAgz8\ gxAhwChvEhuFhtHhsJhrLhqMhpOhoQhnShlTikVijXiiZih_ig\ aifcieeidfichibji`mlakiajfaidahaaf_beXbdUbcSbaPb`N\ b_KcZHcXFcWCcVAcU7cT5dS6eR7eR7fQ8fQ9gP9gPAhOBiNBiN\ CjMDjMDkLEkLFlKFmJGmJHnIH } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 20-04-09 (Elephants are Slow [Indeterminate])
by Jim Muth 19 Apr '09

19 Apr '09

FOTD -- April 20, 2009 (Rating Indeterminate) Fractal visionaries and enthusiasts: For two reasons I strongly recommend viewing today's image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The first reason is that the image requires the type=DivideBrot5 formula that is hard coded only in version 20.04.9 of Fractint or a later version. The second reason is that even with the latest version of the program and a SOTA computer that doesn't choke on DOS programs, the image will take 28 hours to complete. A few days ago I posted an image of an anti-bifurcation minibrot that lies on the west side of its Mandelbrot-set-like parent. Today's image lies on the east side of the same parent, not too far from East Valley, affectionately known as Elephant Valley. Instead of the hairline filaments of the earlier image, in today's image we have nascent elephant trunks seemingly sprout- ing from nowhere and repeating over and over as we approach the central cubic minibrot. The number of elements around the minibrot seems to obey no rule at all. It begins at 12, and as we approach the minibrot the series continues 24, 9, 18, 9, 18... The iteration count also appears to repeat in some kind of cycle, though slowly growing larger. It's too bad that the arbitrary math routine is so slow with all but the Mandel and Julia formulas. Things could get rather interesting deeper down. The name "Elephants are Slow" refers not to the ponderous pachy- derms themselves, but to the time required to calculate today's image, which lies near Elephant Valley, -- four hours longer than one full day. I left the rating indeterminate. The image itself is worth about a 7, but the slow calculation time spoils most of the fun. As I said at the beginning, by far the best way to see the image is to view it on the web site. A hazy sky dimmed the sun here at Fractal Central on Sunday, but the temperature of 68F 20C was quite warm enough for the fractal cats, who alternated between their window shelf and the floor. My day was quite slow, due in large part to FL, who complained of all-over soreness from the garden work she did on Saturday, and wanted us to take it easy today. The next FOTD, certain to be a faster one, will be posted in 24 hours. Until then, take care, and watch for the signs and wonders. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Elephants_are_Slow { ; time=28:14:24.1-SF5 on P4-2000 reset=2004 type=DivideBrot5 center-mag=9.633645938\ 02534282/2.73965185203579343/6.691063e+013 params=3/25 float=y maxiter=1500 bailout=1000000000 inside=0 periodicity=10 mathtolerance=0.05/0 colors=204Et8Et8Ht8Ht8Wt8ht8dtGbtMaqS_iXWbbUWgSNmQ\ FrN8wL0zJ0zH0zE0zot8mtGmtOmtWltblsilpqjlwjizjfzhbz\ h_zhWzhSzbWz__zWbzQfzNizJkzCnz8qz6tz6tz6ty6tv6tr6t\ o6tk6ti6qeApbCn`HlXJkUNgSOfOSdKUbIY`E_Y9bW8dU8hS8j\ Q8fN8bJ8_H8GA8IC8KE9MGCOIEQKGSMIUOKWQKYSM_UMaWOcYO\ e_QgaQicQkdSmeSofUqgUshWuiWwjWykXzlXzmZzoZzqZxsatq\ `ql_mgZjbYeYW`SUXNSSHQABOA6MA0KA0IzFZzBZzHSzLMzPGz\ S9zW8zbCziIzpOztUzwqzzzzvlzsWzlUzgUzdSz`Qx_QsWOoUO\ lSMhPKdNKaJIYHIUDGQBEN8EJ6CE1CA09809z0zt0wb0QN08Q0\ 8U08Y08_08f08x0gz0gz0gz0zz0zz0gz0gz0gz0Xz0Zz1bz1dz\ 4gz4iz6gz6gz6gz6ez6ez6ez6dz6dz6dz6bz6bz6bz6`z6`z6`\ z6Zz6Zz6ZzAXzDWzHWzJUzNUzQSzSSzWQz_Qz`OzdOygMyiMxl\ KvpKvqIttIstGstGttEvtCxs9yq8zp8zn8zl8zk8zi8zg8zf8z\ d8zg8zi8zk8zl8znCzpGzqKztOztSztWztXzt`ztdztgztkzto\ ztrztvztyztzztzztzztzztzztzztzztzztzzpzzlzzgzzdzz_\ zzWzzQzyNzxHzvDzs8zq4zCt8 } END PARAMETER FILE=========================================

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FOTD 18-04-09 (Cheshire Elephants [6])
by Jim Muth 19 Apr '09

19 Apr '09

FOTD -- April 18, 2009 (Rating 6) Fractal visionaries and enthusiasts: Those familiar with the Alice in Wonderland stories know that one of the abilities of the Cheshire Cat is to show its smile without showing the rest of itself. I named today's image "Cheshire Elephants" because it shows elephant trunks without the rest of the elephants. The parent fractal is the Z^(1.5)+C Mandeloid as it appears 1.64159265 levels down the logarithmic hyperspiral. (The number is 1.5 minus PI) Today's scene is located in the East Valley of the parent, an unusually well defined East Valley for a Mandeloid of such a low order. I rated the image at a not-too-impressive 6. After all, how impressive can a couple disembodied elephant trunks sitting over some half-squashed buds be? The calculation time of 110 seconds is not at all bad. Viewing the finished on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is even better. Friday was the best day so far this spring here at Fractal Central in central Pennsylvania, with total sunshine and a temperature of 72F 22C. The fractal cats made the most of things. In fact, they made too much of things when they got into a tussle over their catnip rat. I guess we'll have to get a second catnip rat to keep them both happy at the same time. My day was average enough to keep everyone but the cats happy. And if all goes well, tomorrow will be another average day and the FOTD will be posted on schedule in 24 hours. Until then, take care, and where does one's lap go when he stands up? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cheshire_Elephants { ; time=0:01:50.06-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 passes=b function=floor center-mag=+0.166550673876/-0.00577360745223/\ 1014.208/1/30/0 params=1.5/0/-1.64159265/0 float=y maxiter=6400 inside=255 logmap=33 periodicity=10 colors=000aZV__WY`XWaYUbZSc_Qd`OeaMfbKgcIhd9ie0jf2\ kg4jh6ie8fbAc_B`XDYUFVRHSOJPLKMIMJFOHCQF9S46T03W55\ Z96aD7dH8gLAiPBlTCoXDr`FudGxhHzlIvlJrlJnlJklJglJcl\ J`lJXlJTlKQlKMlKIlKFlKBlK7lK4lKFnPPpUZrYgobclc_edU\ `bSZ_R_YZ_UgdQohMlcHiZDfU9dQ5aPD_OKYORYMOYLMYKKYJI\ YIGYHEYGCWJCTMCROCPRCMUCKWBHZBFaBDcBAfB8iB6kBBjDFi\ EJhFOgGSfIWeJ`eKddLhcNmbOqaPu`Qy`RtZPoXNkVLfUJbSIY\ QGTPEPNCKLAGK9FJCFJEFJGFJJFJLFJNEIQEISEIUEIXEIZEI`\ OHmJNoFSqAYs6bt5ds5er4fq4gp4io3jn3km3lm4il4gk5dj5b\ i5`h6Yg6Wf6Ue7Rd7Pc7Nb8Ka8I`8G_AHeCIjEJpGKuILzPIeW\ FMbD2`EAZEHXEPVEWTEcREjPErOEyNHxMKxMMwLPwLSwKUvKXv\ JZuJauIduIftHitHmtImqJmnJmkKmhKmeLmbLm_MmXNmUNmROm\ OOmLPmIPmFRmGSmGTmHUmHWmIXmIYmJzmJzmOzmSznWzo`zpdz\ rhzsmzuqzvuzxyzz9zzEzzIzzNzzRzzWzz_zzazzbzzdzzezzf\ zzhzzizzkzzlzzmzzozzpzzqzznzzkzzhzzfzzczz`zzZzz_zz\ _zz_zz_zzpzzpzzozzozznR0K } 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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FOTD 19-04-09 (Biomorph At large [7])
by Jim Muth 18 Apr '09

18 Apr '09

FOTD -- April 19, 2009 (Rating 7) Fractal visionaries and enthusiasts: Help! There's a biomorph on the loose! Now, what the <bleep> is a biomorph? A biomorph, IMO, is a coloring method related to binary decompo- sition, (What the <bleep> is that?), which produces coloring effects that sometimes resemble one-celled life forms. (Now I think it's a blob on the loose.) I use this option only rarely, but in today's image it creates an effect that raises the rating of the image from a lowly 5 to an acceptable 7. The calculation time of 1-1/2 minutes means relief for the time- pressed. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> means more fun for everyone. Spring was in full bloom here at Fractal Central on Saturday. The temperature reached a balmy 77F 25C and the blue sky was streaked with only the thinnest angel-hair cirrus. It was warm enough indoors that the fractal cats were happy even without basking in the sun on their shelf. Meanwhile, FL was severely bitten by the gardening bug and spent the entire day working in what I hear will be the best garden of all time. With the regular work caught up, my day was spent in the tradi- tional awe and wonder. The next FOTD will be posted in 24 hours. Until then, take care, and don't be overcome by that awe and wonder, or you'll soon be wondering what all the awe and wonder is about. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Biomorph_At_Large { ; time=0:01:31.83-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+2.795092906612666/+0.6474369169982751/\ 2.848578e+011/1/50/0 params=1/-1.1/-1/-2.8/0/0/0/0 float=y maxiter=800 inside=0 logmap=107 biomorph=120 periodicity=10 mathtolerance=0.05/1 colors=0200zz0ez06z52zzzzzozzazxKzm2za2z0yj0TW000z\ ezvovpvjkzWgzIaz0Xz0Qz0Mz0dz3vznzzzzzzzzxzzjzzWzzG\ zz0zz0zz0zz0zz0vz0kz0mz0pz0srGva_xEnx2zzEPzT0zg0zr\ 0zz0zz0zz0zz0zz0zz0zz0pz3ZzIJz_0zn0zx0zz0zz0zz0zz0\ zz0zzDzzQozaTzm2zvEzzPzzYzzezzkzzozzkzzgzzezzazzYz\ zYzxozszzmzzkzzdzzZzzXzzazzgzzmzvszaxzCzz0zz0zP0z2\ 3z2Im2WZ2dJ2p0Pz0az0kz0vz0zz0zz0zzDzzQzzazzmzzzzgz\ y8zY0zE0z20z20zz0zzIzzszzzzzzzzzzzzzynzYMz20zk0zz0\ dz0vz0zz0zz0zz3zzGzzWzzjzrxzazzKzz2zz2zz2z9PM0KM0K\ M0EM0EM06M06M5YCTk0my0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0vz0sz0pz3mzIQ2zkzTgzddznavxZgz\ XYzTKzQ2zM2zJ2zF2zmz0Xzp0Kz06z02z02z02z02z02z02z02\ z02z52z92zD2jD2zD2zD2zD2zDzzDezD6zD2zz2zz2zz2zz2zz\ 2zz2zz2zz2zz2zv2zp2zg2za2zX2zQ2zJ2zsy0mo0kg0gaCdTT\ aEgZ2sT2zQ2zM2zJ2zF2zzzzzzzzzzzzzzzzzzzzzzzzzzyzvg\ zmTzd2zX2zM2z0z00z30zP0zj } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 17-04-09 (Peak of Destruction [8])
by Jim Muth 17 Apr '09

17 Apr '09

FOTD -- April 17, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a scene in the fractal that results when the formula Z^(1.3)+C is calculated at a level of 1 minus PI on the logarithmic hyper-ladder. A jagged minibrot lies at the center of the image, though it is rather obscured in the glare of a fractal nuclear explosion. I named the image "Peak of Destruction", which is kind of what it looks like. The rating of an 8 includes a mighty 2 points for the coloring. Without the special coloring effects, the image is rather boring and worth no more than a 6. I used the passes=b option because I like to see it working. The outside=tdis option is necessary for the explosive effect. The calculation wait of 1-1/4 quick minutes may be avoided by viewing the already-calculated image on the FOTD web site at. <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Total sun and a temperature of 66F 19C here at Fractal Central on Thursday gave the fractal cats their best day so far this spring. If my day had not been so busy, it might have been my best day of the spring also. FL had a very good but rather hard day starting her garden work for the season. The next FOTD will be posted in 24 hours. Until then, take care, and look for the ultimate fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Peak_of_Destrution { ; time=0:01:16.04-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 function=floor passes=b center-mag=-1.919725495606011/+1.976500603464784/\ 3.008302e+011/1/-97.5/0 params=1.3/0/-2.1415926535\ 8979/0 float=y maxiter=2000 inside=255 outside=tdis logmap=117 periodicity=10 colors=000zzzzzzzzzbJkgVflebjadiYehUffQgeNhdJjbFka\ Bl`7m_4nV9mQEmLImGNlBRl6Wl2_lBajKciTeg`ffihdrjczkb\ ymZxoWwqSvsPuuLuwIqsHmoGilFehEadDYaCUYCQUBMRAIN9EJ\ 8AG76C6296485585685875975A75C65D65E65G55H55I55MA6P\ E6TJ6WN6_S7bW7f`7id7mi8pm8tr8wv8tsAqpBomCljDjgEgdG\ daHb_I_XJYUKVRMSONQLONIPLGQJEOIDMHCKGBJFAHE9FD8EB6\ CA5A948837725613502_SY`PZaNZcLZdJ_eG_gE_hC`iA`j8`i\ 7ai7bh7ch7cg6dg6ef6ef6ff6ge5ge5hd5id5jc4jc4kc4lb4l\ b4ma3na3n`3o`3p`3p_6o_8n_AmZCmZFlZHkZJkYLjYOiYQiYS\ hXUgXWgXZfW`eWbeWddWgcVicVkbVmaVoaSlZPjWMgUJeRGbPD\ `MAYJ7WH4TE2RC3QD4PD4OD5ND6ND6MD7LD7KD8JD9JD9IDAHD\ AGDBGDCFDCEDDDDDCDECDFBDFADG9DG9DJACLACNABQABSAAUA\ AXAAZA9`A9cA8eA8gA8iFDkKHmPLoUPqUKsUUuYWwYXxcYyXZz\ c_zf`zgazhbziczjdzkezlfymgynhzoizpjzqkzrlzsmztmzum\ zvmzwmzxmzymzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzzmzzmzzz } 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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FOTD 16-04-09 (Split Fractality [8.5])
by Jim Muth 15 Apr '09

15 Apr '09

FOTD -- April 16, 2009 (Rating 8.5) Fractal visionaries and enthusiasts: Today's image came about when I added 0.5 part of Z^(-12.6) to 5 parts of Z^(-1.26) and added (1/C) to create a fractal consist- ing of a disembodied filament with a ring at its end, surrounded by a cloud of other smaller rings. Today's scene is located in an even smaller ring in one of these smaller rings. The scene is semi-evaporated, with the circumference of the evap- orated area bisecting the image from upper left to lower right and cutting exactly through the center minibrot. The extremely critical imag(p3) parameter defines the escape radius and there- fore the position of the evaporation circumference. The upper right half of the image, which is partially evapora- ted, consists of a mixture of outside and inside stuff, with the inside stuff made visible by the 'zmag' fill, while the lower left half is all outside stuff rendered in the usual 'equal-iter- ation-band' manner. The difference is quite apparent. I named the image "Split Fractality", which sounds a bit like 'split personality'. Then I rated it at an 8.5, which includes 1/4 point for the mathematical interest and 1/4 point for the coloring. The calculation time of 2-1/2 minutes is about average. The image may be seen faster by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and meditating on the finished product. Wednesday began with heavy rain here at Fractal Central, but by noon the rain ended and by 3pm the sun appeared, giving the fractal cats just enough time in the sun on their shelf to keep them happy. The temperature of 45F 7C did not worry them. My day was average. The taxes were out of the way weeks ago, so we had no last minute tax surprises. The next FOTD will be posted in 24 hours. Until then, take care, and how can you be sure that no invisible fractal is lurking in that corner over there? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Split_Fractality { ; time=0:02:32.32-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+7.379862680725198/+0.3887433179391824/\ 6.696877e+007/1/-115/0 params=5/-1.26/0.5/-12.6/0/\ 1.9405265505e+021/0/0 float=y maxiter=750 inside=zmag periodicity=10 colors=000egbMaM2W56MKACYBjVAmz8`h7Wo6RvHWjS`ZaeO`\ `M_XK_SIZOGZJEYFCYAAX68X27Z69_ABaECbIEjMFjQHtUJhXK\ i`MjdNlhPmlRosStwUzzVozZnvbmueluijtlitphssgswfsz`l\ wWetR_qMTnHNlFQkESjCViBXh9Zg8ag6cf5ee3hd2jc1lc8jaE\ i`KhZQgYWfWaeVgdTmcSsbQyaPx`Ow`Ow_Ov_OvZOuZOuYOtYO\ sXOsXOrWOrWOqVOqVOuNOsRQrUSqXUp`WncXmfZlj`kmbjpcfl\ XbiQZeJVbCTeDRgEPjFNlGLnHToS`obhpmppwlquhrtdrs`srY\ tpUtoQunMvmIvlFwjBxi7xh3yg0yf5tc9p`DlYIhVMdSQ`PVXM\ ZTJbPGfLEWUGLbIAkK0tMAsQKrUUqXcp`mpcio`fnZcmX`lVYk\ TVjQSiOPhMMgKJfIGeGFbJF`LEZNEXPEURDSTDQVDOXCLZCJ`B\ HbBFdBCfAAhA8jA6lneejbdg`ddZd`WdYUcVScRPcONcLLcSJg\ YHkdFokDsqBvnGulLtiQsgVrd_qbdqeZmhUjkPgnKcqF`sAYn8\ Vi7Td5Q_4OV2LQ1JM0H4RhDMgMHfUDePFZLHTGJNCKHFbSItbO\ veUwg_yidzkXrbPjUHbL9VD9XF0u70x70zT0zo0zz0xz0vz0mz\ 1iz3cz3_z4Tz6vz6Jy7Fx7Ax6Fr4Jm4vi3Sd3X`1`X0000iO0l\ P7gLDcQuJFrOJoSNmWRj_VgcZ } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 15-04-09 (Planetary Nebula [8.75])
by Jim Muth 14 Apr '09

14 Apr '09

FOTD -- April 15, 2009 (Rating 8.75) Fractal visionaries and enthusiasts: Today's image shows an apparently cubic minibrot caught in the act of anti-iterating, a phenomenon that I recently discovered, or more accurately heard about. I named it "Planetary Nebula" because it rather looks like one. Anti-iteration is when the number of elements is repeatedly cut in half as we approach a point of attraction, rather than constantly doubling, as is the case with normal minibrots. (A planetary nebula is formed when a normal-sized star runs out of nuclear fuel late in its life and puffs off its outer layers in a gaseous shell until it finally collapses into a white dwarf.) On the surface, the parent fractal of today's image resembles a grossly oversized Mandelbrot set, but deep in its depths every- thing turns cubic. Today's scene is located on a filament exten- ding southeast from the main bay of the third largest minibrot on the main stem of the Mandelbrot-like parent, at a depth where everything has become almost but not quite cubic. The rating of an 8-3/4 includes 1/2 point for mathematical interest and 1/4 point for the coloring. The calculation time of an incredibly fast 43 seconds will pass in an instant when the top part of the image first appears. Those with a high- speed connection to the internet may download the finished image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> in even less time. Those with a dial-up connection may need to wait a few seconds longer. Clouds, rain and drizzle kept the fractal cats in a sour mood all day Tuesday here at Fractal Central. The temperature of 48F 9C cheered them none at all. Only a combination of tuna, turkey and cheese made the duo bearable. My day was a bit improved however -- the day's work went better than expected. If the luck holds, the next FOTD, which will be posted in 24 hours, will also be better than expected. Until then, take care, and if the government gave everyone a tax refund of one million dollars, all our economic problems would instantly be solved as they went out and spent the money. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Planetary_Nebula { ; time=0:00:43.63-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 center-mag=-40.49524913009\ 69/-0.1710667530665/1.65e+009/1/-122.5/0 inside=255 params=3/25 float=y maxiter=1500 periodicity=10 colors=000PFpPCqPArP8rQApRBnSClTEjUFhVGgWIeXJcYKaZ\ L__NY`OXaPVbRTcSRdTPeUNfWMgXKhYIi_Gj`EkaClbBkaCkaD\ k`Dk`Ek_Ek_FkZFkZGjZGjYHjYHjXIjXIjWJjWJjWKiVLiVLiU\ MiUMiTNiTNiSOiSOhSPhRPhRQhQQhQRhPRhPShPSiSRiUQiWPi\ YPj_OjaNjcMjeMkgLkiKkkJkmJlkKliKlhLlfLldMlcMlaNl_N\ lZOlXOtM4lWOjcWdefZgpUhzTgyTfxTfxTewTevTdvTduTctTc\ tTbsTbsTarTaqT`q000555AAAEBEFBFFCHGDJGEKHFMHGNIHPI\ IRJJSIKUILWHLXHLZGL_FLaFLcELdELfDLhDLiCLkCLlBLnBLp\ ALqALs9Lu9Lv8Lx6Jz8LyANyBPyDRyETyGVxHXxJZxK`xMbxNd\ wPfwQhwSjw_lwcnvjyzuyvzzzzzzzzzzzzvvvbrrmmmbwzbqzb\ kzbhzbfzbezccudauf_ugYuhXuiVujTukRulPumOumMunKuoIu\ nGuo8tnFujLuaRuTXuLbuJapH`lF`hD_dB__9ZWzzSzzO2zzzz\ z4zz5zzzzTzzW7_Z8`a9`dAagAajBbmCbpDcs6rzDcvJPrPBnO\ EmOGmOIlOKlNMkNOkNQjNSjMUiMWiMYhM_hLahLcgLegLgfKif\ KkeKmeKodJqdJscJucJwcKtdKreKofLmfLkgLhhLfhMdiMajM_\ jMYkNVlNTlNQmOOnOMnOJozzz } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 14-04-09 (Chrysanthemum [fast and slow] [7.5])
by Jim Muth 14 Apr '09

14 Apr '09

FOTD -- April 14, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image lies on the border between the magnitude range of arbitrary precision math and conventional math. I have included two parameter files -- a slow version done with arbitrary preci- sion math, which takes about 10 minutes to finish, and a fast version done with conventional math, which draws the image in only a few seconds. The slow version has a somewhat better resolution than the fast version, but it is up to the individual viewer to decide whether slightly better resolution is worth a calculation time about 200 times as long. Perhaps the most unusual thing about the image is its anti- bifurcation. The outer ring around the minibrot consists of 16 lobes, while the next inner ring has reverted back to 8 lobes, from where it again begins normal bifurcation. This is a sign that the minibrot lies within the attraction basin of a larger minibrot. The image lies deep in the East Valley of the largest minibrot on the filament network extending from the period-4 bud on the northeast shore line of the main bay of the Mandelbrot set. I named it "Chrysanthemum" because that's what it reminds me of. (This might not be the first time I have used this name.) I rated the image at a 7.5, which includes a self-awarded bonus of 1/2 point for the coloring. The coloring probably makes 3/4 of the image. As I said earlier, a decision must be made between top quality and saved time. But this decision may be avoided by surfing out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for total bliss. I leave it to Paul to decide whether to calculate and post the fast or slow version. The Monday morning sun at Fractal Central faded fast as midday approached, and by afternoon was totally gone. The fractal cats, looking forward to a pleasant afternoon on their sun- shelf, were much disappointed. A short burst of artificial heat and a minor treat of tuna restored their good moods however. My day was semi-busy; tomorrow will likely be the same. Until then, take care, and when we have faith, must we turn off our faculty of reason and our knowledge of science? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Chrysanthemum-fast { ; time=0:00:03.88-SF5 on P4-2000 reset=2004 type=mandel center-mag=0.36010379625664\ 01851/0.6412655477927573511/6.016702e+013/1/132/0 params=0/0 float=y maxiter=2500 bailout=16 inside=0 logmap=-570 periodicity=10 mathtolerance=0.05/1 colors=000XePXePXePXePXePXePXePXePXePXePXeOYeNZeM_\ eL`dK_dLYeLXeMVeNUfNSfOQfPPgPNgQMgRKhRJhSHhTGhTKjU\ OlVTmWYoXbpYgrZls_pu`tvaxxbzyczr`zkZzeWYZUSSRMMPGF\ MA8K42I37K3BL3FM3KN3OO3SS3XV3`X3dZ3hZ6bZ9YZCTZFOPK\ JGOEEV9CbG8eM5cO8`QBYREVTGSVJQWMOYPM_RK`UIbXHcZKaX\ N_WQYVTWUWUTYSSkZVzdYzj`zpczvfzzhzoazbWbRQdQNePKfO\ HhNEiMBjL8kL5lIAlFFmCKm9Pn6Un3Zj9VfESbJOZOLzWjobfc\ hbebYgXThSOjMJkHEmB9n65p5Kq5Zs4mt4zGdrFchFb_EbREaI\ Ea9zNfuQgmTgeWgYZgQagS`fT_fU_eVZeWYdXYdWb_WgWVlSVq\ OVvKcrRknYsjdzgjzZgzRezJbzB`z3Zm9V`FSOLPBRMETRGVVI\ XZLZbN`fPbjRdnTimVmmXqmZumbvifvejwamwYAvzCrzEnuGjp\ IfkKbfM_bJafHciFelIZjKTiMNhOHgQBfS5eQEiOMlMUoLasJi\ vHqyGyzIzuKzoMzhOzbUza_zaez`jz`gzzezzbzz`zz_zz_zzZ\ zzZzzZzz`zzbzzdzzfzzhzzizzczzZzzUzzOzzJzzEzz9zz8zz\ 8zz8zzVzzpzzgzzZzzQzzHzz8zzDzzIzzNzzSzzVzzYzz`zzcz\ zfzzhzzjzzlzzmzzozzuzzrzz } Chrysanthemum-slow { ; time=0:09:27.18-SF5 on P4-2000 reset=2004 type=mandel center-mag=0.36010379625664\ 01851/0.6412655477927573511/6.016702e+013/1/132/0 params=0/0 float=y maxiter=2500 bailout=16 inside=0 logmap=-570 periodicity=10 mathtolerance=0.05/0 colors=000XePXePXePXePXePXePXePXePXePXePXeOYeNZeM_\ eL`dK_dLYeLXeMVeNUfNSfOQfPPgPNgQMgRKhRJhSHhTGhTKjU\ OlVTmWYoXbpYgrZls_pu`tvaxxbzyczr`zkZzeWYZUSSRMMPGF\ MA8K42I37K3BL3FM3KN3OO3SS3XV3`X3dZ3hZ6bZ9YZCTZFOPK\ JGOEEV9CbG8eM5cO8`QBYREVTGSVJQWMOYPM_RK`UIbXHcZKaX\ N_WQYVTWUWUTYSSkZVzdYzj`zpczvfzzhzoazbWbRQdQNePKfO\ HhNEiMBjL8kL5lIAlFFmCKm9Pn6Un3Zj9VfESbJOZOLzWjobfc\ hbebYgXThSOjMJkHEmB9n65p5Kq5Zs4mt4zGdrFchFb_EbREaI\ Ea9zNfuQgmTgeWgYZgQagS`fT_fU_eVZeWYdXYdWb_WgWVlSVq\ OVvKcrRknYsjdzgjzZgzRezJbzB`z3Zm9V`FSOLPBRMETRGVVI\ XZLZbN`fPbjRdnTimVmmXqmZumbvifvejwamwYAvzCrzEnuGjp\ IfkKbfM_bJafHciFelIZjKTiMNhOHgQBfS5eQEiOMlMUoLasJi\ vHqyGyzIzuKzoMzhOzbUza_zaez`jz`gzzezzbzz`zz_zz_zzZ\ zzZzzZzz`zzbzzdzzfzzhzzizzczzZzzUzzOzzJzzEzz9zz8zz\ 8zz8zzVzzpzzgzzZzzQzzHzz8zzDzzIzzNzzSzzVzzYzz`zzcz\ zfzzhzzjzzlzzmzzozzuzzrzz } END PARAMETER FILE=========================================

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FOTD 13-04-09 (Cranberry Salad [Rating--Repeat])
by Jim Muth 12 Apr '09

12 Apr '09

FOTD -- April 13, 2009 (Rating Repeat) Fractal visionaries and enthusiasts: Due to 'unavoidable' Easter Activities here at Fractal Central on Sunday, I was forced to go into the FOTD archives for today's image. The image I found originally appeared on March 22, 2006, when it was named "Aqualung", with a rating of an exceptional 9. To create today's image I zoomed slightly toward the central minibrot of that older image and slightly intensified the colors. I named the result "Cranberry Salad" after a special treat FL cooked up for the 'unavoidable' Easter activities, and which tasted much better than it sounds. I first rated the image at an 8, but this troubled me. After all, it is a virtual repeat, so I hedged a bit by re-rating it as a 'repeat'. Actually, I think it is worth about an 8-1/2. The parent fractal of today's image came about when I added 0.135 part of Z^(3) to 1 part of Z^(1.5) and added straight C. This parent consists of two widely separated Mandelbrot sets connected by an open highway. Today's image is located on the eastern shoulder of the highway, very near the X-axis. The calculation time of 1 minute is very fast. But equally fast is the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to see the already-calculated image there. The temperature was a chilly 48F 9C here at Fractal Central on Easter Sunday, and the wind was blustery, but there was not a single cloud in the sky over the entire state of Pennsylvania, and the brilliant sunlight that covered the scratching post all afternoon gave the fractal cats one of the best days ever. My day was average. The next FOTD will appear not by magic in 24 hours or so. Until that moment arrives, take care, and Easter comes but once a year. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cranberry_Salad { ; time=0:00:42.03-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=b center-mag=+0.259179523/-0.024608674/18835.44/1/\ -147.5/0 params=1/1.5/0.135/3/0/0 float=y maxiter=750 inside=255 logmap=60 periodicity=10 colors=0000PN0QQ0RT0SW0TZ0Uc0Vh0Wm0Xr0Yw0Zw0_w0`w0\ aw0bw0cw0dwdqUit_nyeszlxzszzzxyqtxjquenr_jnUgiQdeK\ a`FZXBWS6TM1QG0NI0KP0HU0OZ0We0an6inDoqLxtUzvazoZzi\ XybWxXUvRTtLRsGQsCObGLOKKBOJ0TH1WC4Z76a48d0Bg0Ad28\ a87_G6XN6UW5Tb4Ql2Nt2LzZHxzFtzGjzGbzGWzGOzGHzGByG5\ yG0sH1nH4iH5dH7_HAWHBRHDNHGJHHFHKBHN7HO6LQ5OR4RT2U\ U1ZU0aW0dX0gZ0jZ0iao0ed7ZWGTLQLD_GCXNBUUBTaAQiAOq8\ Nj7Ld7KZ6JU6HO5GJ5GF4FA4D52C12B01A01A01B01B01B01B4\ 1B71BB1CF1CJ1CN1CR1CW1C_BGXLKWXNTiRRvUQgWZUWgHXo6X\ y0Xz0ay1dq4gi6jb8nWBqODtHGxCHyFJzHKzKLzNNzQOzTQzWR\ zZRz_NzWKzRHzNFzJBzF8zB6z74z40z00z00z00z00z00z50zA\ 0zF0zK0zP0zU1zZ1zc2zh4zm5zr5zvBzzHzzNzzOzzQzzQzzRz\ zTzzTzzUzzWzzWzzXzzZzzZzz_zzazzazzbzzbzzdzzezzgzzi\ zzizzdzz_zzWzzTzzOzzKzzPzzUzzZzzczzhzzmzzrzzvzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzz000 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 11-04-09 (The Magic Rectangle [7])
by Jim Muth 12 Apr '09

12 Apr '09

At 04:44 PM 4/11/09 -0500, you wrote: >Jim Muth wrote: >> >> ..... float=y maxiter=15000 inside=253 >> logmap=32 periodicity=10 sound=off >> > >I have always wondered why some of the .PAR files that you have posted >contain the SOUND= parameter specified, and as far as I can remember, >they seem to always be set to OFF. > >I can only assume that at those times when this parameter is used, then >there must be one or more other individuals around when you do your >searching. And that you do not want them to hear the small "beep" after >the image has been rendered. > > >Curious as Always, >P.N.L. Paul: Your guess is pretty much right. Both FL and I find the constant beeps annoying. I have a sound=off entry in my sstools.ini file, which causes the sound=off to be included in my parameter files. I usually edit the sound=off entry out of the parameter files before I post them, but occasionally one slips through un-edited. Jim

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FOTD 12-04-09 (Lest We Re-Iterate [6.5])
by Jim Muth 12 Apr '09

12 Apr '09

FOTD -- April 12, 2009 (Rating 6.5) Fractal visionaries and enthusiasts: The very deep parts of the Mandelbrot set have barely been touched. In fact, every time a new scene such as today's is discovered, another infinity of undiscovered scenes opens up. Today's image shows a minibrot deep in the East Valley area of another minibrot. This larger minibrot lies on a side filament extending from the period-6 bud on the northeast shore line of the main bay of the Mandelbrot set. I named the image "Lest We Re-Iterate". Due to a mental lapse, I exited the program without saving the finished image, and had to retrieve the partially finished version that had automatical- ly been saved earlier and resume the calculation from there. The showness of the image made the oversight even worse, and I decided to memorialize my mistake by naming the image after it. The rating of a 6-1/2 includes 1/2 point bonus for my coloring. I leave it to the viewer to decide whether the coloring is worth it. The calculation time of almost 45 minutes may be avoided by going electronically to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Saturday started dull, dreary and wet here at Fractal Central, with a temperature of 46F 8C. It looked like another bad day coming up for the fractal cats, but the clouds suddenly broke at 1:00pm, just in time to flood the cats' shelf with sunlight and raise the outside temperature to 55F 13C. The rest of the after- noon was near perfect. My day was uneventful. The next FOTD will be posted in 24 hours. Until then, take care, and be confident that all is well. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Lest_We_Re-Iterate { ; time=0:44:55.32-SF5 on P4-2000 reset=2004 type=mandel center-mag=0.39831350911220\ 687656243421901548446/0.19160183288161261498353550\ 958724032/2.600878e+029/1/145/0 params=0/0 float=y maxiter=12500 bailout=25 inside=0 logmap=1770 periodicity=10 colors=000GdfHdfHcgHchIciIbjJbjJbkKalKamL`mL`nM`oM\ _pM_qN_qNZrOZsOYtPYtPYuQXvQXwQXwRWvRVuRUuSTtSTsSSs\ TRrTQqTPqUPpUOoUNoVMnVLmVLmWKlWJkWIkWIjXHiXGiXFhYE\ gYEgYDfZCeZBeZAd_Ac_9c_8b`7a`6a`6`a5_a4_a3Za3Zc5Wd\ 7Ue8SgAPhA4hBNiDLjEJlGGmIEnJCpL9qM7rO5iWfjVckVakUZ\ lUXlTVmTSnTQnSOoSLoRJpRHqREqQCrQArP7sP5pS0mR1kR1iP\ 1gO1eN1cM1bL1aK1cJ2hI2mH2rG2vF2zE2zC2zB2zA3zczzc3z\ czzc3zczzc3zczBC4CD3DD3ED3FE3GE3HE3IE3JF3KF3LF3MG3\ NG3OG3PG3QH3RH3SH3TH3UI3VI3WI3XJ3YJ3ZJ3_J3`K3aK3bK\ 3cL3dL3eL3fL3gM3hM3iM3jM3kN3lN3mN3nO3oO3pO3qO3qP3r\ P3sP3zzXyqRygQycPx_OxUNxUMw0LwgcwfcwdIvcHvbGvaEu`D\ uZCuYBuXAtW9mP8zT7zZ6zc5zc4za8z`7z_7zZ7zZ6zY6zU6mz\ 6zz5zz5zz5zz4zCzzDzzEzzFzzGzzHzzIzzIzzJzlKzHLzEMzC\ Nz9Oz7Oz8Qz8Rz8Sz8Tz8Uz8Vz8Wz8Xz8Yz8Zz8_z8`z8wz8wz\ 8wz8wz8wz8wz8wz8wz8wz8wz8wz9wz9wzAwzAwzBwzBwzCwzCw\ zDwzDwzDwzEwzEwzFwzFwzGwz } END PARAMETER FILE=========================================

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FOTD 11-04-09 (The Magic Rectangle [7])
by Jim Muth 11 Apr '09

11 Apr '09

FOTD -- April 11, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows one of the strange rectangles that exist in a Julia set of the Z^(2.003)+C Mandeloid. (To see one of the actual rectangles check the Z^(2.003)+C Julia set with a C-value of -1.7435+0.0i at the Z coordinates of 0.00019+0.07388i, with the magnitude set to 100. It's not a perfect rectangle, but it's close enough to be quite surprising.) When we check today's image however, we wonder what has happened to the rectangle. The rectangle, or at least one slice of it, actually is in the image. It appears as the dark bluish area in the lower right corner, with the narrow white line across its center. The rectangle has been reduced to a single narrow line because today's image is not a Julia set. It is what I call an Oblate set, a slice through the four-dimensional Julibrot figure that is defined by the imaginary C-axis and the real Z-axis. It is actually a fractal hybrid -- half Julia, half Mandelbrot. Even though no full rectangle appears in the image, I named it "The Magic Rectangle". The missing rectangle is made up for by the image's unusually strong impression of a three dimensional scene. I have no idea what the quite solid looking things might represent however. I rated the image at a 7, which means I consider it to be an average FOTD image. The calculation time of 1-1/4 minutes is unusually fast, which will be good news for those who prefer more than a single slice of their rectangles. Another way of viewing the image is to surf out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view it in completed form there. Totally miserable conditions prevailed both with the weather and the fractal cats here at Fractal Central in central Pennsylvania on Friday. The spitting rain and temperature of 46F 8C kept the cat duo glued to the warmest radiator, glaring at the outdoors in full sulk. My problem was not the weather -- I had no time to worry about that -- but with the rush that won't go away. I still managed to find time for the fractal however. And I would not be sur- prised in the least if another fractal were to show up in about 24 hours. Until next time, take care, and never question the fractal truth. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_MagicRectangle { ; time=0:01:14.91-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=OblateN passes=1 center-mag=-0.0106678\ 7037571017/+0.00398419476438538/231.7069/0.202/\ 4.105/63.193 params=2.003/0/0.000185/0.0739678/\ -1.7434/0 float=y maxiter=15000 inside=253 logmap=32 periodicity=10 sound=off colors=030mzzmyzmxzmxzmxzmxzmxzmxzmxzlwzkwzjwzivzh\ vzgvzftzetzdrzcrycrxcqwcqvcqucntcntclsclsclrcirciq\ ciocgocfmcemcelcejccjcbhcbfc`fc`ec_ecZccZacWacW_cW\ YbUYaUX`SX_SVZSSYQSXQRWQPVOPUONTMNSMLRLJQJJOIIMJGK\ GGIGEGHCFHEEIGDHICGJBGLBHNAGPAFR9FS9FV8FX8DX7DY7D_\ 6Da5Bc4Bd3Be2Bg19h09j09k09j07l07n07n05o05o05o05n03\ n03n03n03n01n01n01n01n01n01n00n00n00n00n00n00n00n0\ 1n13n33n55n77n97nB9nDBnFBnHDnJFnLFnNHnNJnPJoQLoSNp\ UNpWPqYQqZQraSrcUsdUsfWshYsjYrjZqlaqmaoocmqdmsdltf\ lvhjxhhyjhzlfzlezmezoczsazqczoczoezmezmfylfxlhvjhv\ hjthjsflqflodmmdmlcojcojaqhZqfZrdYrcYsaWsZWsYUsWWs\ YUsZUsZUsaUsaUscUsdUsdUsfUsfUshUsjUsjUslUslUsmUsoU\ soUsqUsqUssUstUstUsvUsvUsxUsyUsyUszUszUszUszUszUsz\ UszUszUszUszUszUszUszSszQszQszPszNszNszLszJszJszHs\ zFszFszDszBszBsz9sz7sz7sz5sz3sy3sy1sy1sx0sx0sx0sv0\ sv0sv0st0st0sv0szzzzzszzs } frm:OblateN {; Jim Muth b=p1, z=real(pixel)+p2, c=flip(imag(pixel))+p3: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 10-04-09 (Mandelbrot Ringlet [7])
by Jim Muth 09 Apr '09

09 Apr '09

FOTD -- April 10, 2009 (Rating 7) Fractal visionaries and enthusiasts: After all these years, an occasional trip back to that king of all fractals, the Mandelbrot set, always seems to yield a sur- prise or two. Today's scene lies far out on a filament in the interior of the north branch of Seahorse Valley of the large minibrot on the main spike of the Mandelbrot set, and after all this description, it's no wonder there's a little surprise in it. What I find surprising in today's image is the thin ring of debris surrounding the central minibrot. Normally, the Mandelbrot debris fields are much broader. There is not much more to be said about the image, but one thing virtually certain is that if this universe is limited and if it is the only one that exists, then this particular minibrot has never before appeared on the screen of a computer. By contrast, if this universe is infinite or if an infinity of similar para- llel limited universes exist, then this minibrot has appeared on an infinity of computer screens. Bombastic speculation aside, after not-too-careful considera- tion, I rated the image at a 7. Then I noticed the narrow ring of chaos surrounding the minibrot, and named it "Mandelbrot Ringlet". Despite being well beyond the range of conventional math, the image calculates in a not-too-slow time of 3-3/4 minutes. An even faster way to enjoy the image is to hop like the Easter Bunny out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and gaze in awe and wonder at the already calculated image there. Thursday here at Fractal Central was much improved. Partly cloudy skies and a temperature of 61F 16C are hardly ideal, but the periods of sun came at just the right time, and the fractal cats had a very pleasant day. With a customer who was unhappy when we gave him what he asked for and he saw that it did not work, my day was not so pleasant. But that's how it goes sometimes. Tomorrow however should be better, permitting more time for a better FOTD. Until next time, take care, and though the commandment says 'thou shalt not steal' I also hear that God helps those who help themselves. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot_Ringlet { ; time=0:03:44.66-SF5 on P4-2000 reset=2004 type=mandel passes=t center-mag=-1.7693\ 815837260665074818/0.00428779035481775236759/1.434\ 916e+017/1/-122.5/0 params=0/0 float=y maxiter=1200 bailout=25 inside=0 logmap=189 colors=0009Cb8Ee7Fh7GkEHnKIqQJtWKw_NzZQu`Vr_Yng`ki\ egjhdcP2fYEheQkmaWFl`Qmd`mikmmumhlfdc__VTWMMRDFKAX\ L8RM7LM6FN59EDAUU8UU6UU4UU3SVBUTCVRCXPDYOD_MD`KEbI\ Ef85iKElQNsZWAzzDzzGfzIYzLPK7jmH70NGBSPMXYXafgkmwf\ oqaplXrgSsbNuYJvTRjUZZUFoFGmIHkLIiOJhQKfTLdWMbZN`a\ O_cNefMjiMplLuoLzrNyjzzbzzVizNczFUz7lQVnRUoRUqRUrR\ UtSTuSTwSTxSTtRWpQZlPaiOdeNgaMjZMlXOlVPlUQlSRlQSlP\ UlNVlLWlKXlIYlHZlJWgLTcNQZPNVRLRSHOTELUBIV7FW4CW1A\ X5JY9SZC`_Gi`Kr`NzRSwIWt9_q0cnIRd_EVq1Mn6PlBSjGVhK\ XeP_cUbaZe_bgXgjVlmTqpRurUsqWrqYqq`opbnpdmpbnpaop`\ pp_qpZrpYspXtpVupUvpTwpSxpRypQzpPzpQwqRtrRqrSosTls\ TitUgtUduVauW_vWXvXUwXSwZTu`TtbTscTreUqgUohUnjUmlV\ lmVkoViqVhrWgtWfvWewWdhZgUajGdmHejIfhIgfJhdJibKi`L\ jYLkWMlUMmSNnQNnOJoYGpfJqgkrQMshztezubzv`zwYzxWzyT\ zzDzzIzzMzzRzzuzznzzgzz`zzVzzTzzGzzKzzOzzSzzWzz_Hz\ qGziFzbEzVDzOCzGoz_Bz9AzA } END PARAMETER FILE=========================================

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FOTD 09-04-09 (Fine-Tooth Fractal [7])
by Jim Muth 08 Apr '09

08 Apr '09

FOTD -- April 09, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image is another scene in the same oversized parent fractal that held yesterday's image. And as far as I know, tomorrow's might be the third. Most of the action appeared when I rendered the image with the outside set to 'summ'. The name "Fine-Tooth Fractal" came about when I noticed the comb- like elements filling the scene. The rating of a 7 indicates that I consider the image adequate for FOTD status, but not unusually exciting. The calculation time of 3-1/4 minutes is long enough to give time for fun, but not so long that boredom might arise. The finished image is or soon will be posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and the web site is definitely not boring. Too many clouds, too little sun and too low a temperature (48F 9C) kept the fractal cats in too cranky a mood here at Fractal Central on Wednesday. The extra treat of tuna and cheddar made them somewhat cheerier. My day was busier than I consider ideal. The next FOTD will be posted in 24 hours regardless. Until then, take care, and wait for the sun with bated breath. (I never knew there was a sun with bated breath.) Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Fine-Tooth_Fractal { ; time=0:03:13.91-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.3789554866286804/+0.8798264972975226\ /4.726508e+012/1/175.5/0 params=14.55/0.6/-14.55/\ 0.666/0/1000/0/0 float=y maxiter=1600 inside=0 outside=summ periodicity=10 mathtolerance=0.05/1 colors=000WW4ZZ4``4bb4dd4cd6bd8adA`dB_dDZdFYdGXdIW\ dKVdLVdNUdPTdQSdSRdUQdVPdXOdZNd_MdaLdcLddRb`WaY``V\ e_SjYOoXLtWIyVFZ5M_8O`BP`ERaHSbKUbNVcQWdTYdWZeZ`fa\ afdcggdormgie``YUSQMILNKJOMIPOHQQGRSFSUETWDUYCV_BV\ aAWc9Xe8Yg7Zi6_k5`m4ao3bq2bs1dd1eR1918fD1eF3eH5eJ7\ eL9eNBePDeRFeTHeVJeXLeZNe`PpqfebQc`Rb_RaYR_XRZWSYU\ SWTSVSSUQTSPTRNTQMTOLUNJUMIULHUKP_JXeIdkHlqFwyGtvH\ rtIorHlrJmpLnoNnnPomRplTpkVqjXriZrh_sfasectdeucgub\ ivakw`mw_oxZpxYqvXqtXqrXqpXqnXqlXqjXrhXrfXrdXrbXr`\ WrZWrXWrVWsTWsRWsPWsNWsLWsJWsHWsGWgY_XncXneXnfYngY\ niZnjZnlZnm_no_np_nq`mn`lkakhajebibbh_bhYKamJboIcq\ IdsHduGewFfyFfzEctE`oEZjEWdET_DRVDOQDLKDJFDGADE5EF\ 8FGBFHEGIHGJKHJMHKPILSJMVJNYKN_KObLPeLQhMRkMRmUSma\ TmiUmqVmnShkPdhM_eKWbHR_ENXBIU9ER69O35L11SJ4Y`6ZYA\ ZWDZTGZRJZPM_MP_KS_IV_FY_D`_BcaCXbCRdCKeCEgC7hC1eB\ 8cBFaBMII3LL4NN4PP4SS4UU4 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 08-04-09 (Silver Barrels [8])
by Jim Muth 07 Apr '09

07 Apr '09

FOTD -- April 08, 2009 (Rating 8) Fractal visionaries and enthusiasts: The parent fractal of today's image came about when I subtracted an unlikely 14.55 parts of Z^(0.666) from an equally unlikely 14.55 parts of Z^(0.6) and added straight C, which created a grossly oversized thing that is better seen than described. Today's scene is located on the northern seacoast of a bud in a bud on the negative X-axis of this oversized parent. I named the image "Silver Barrels" for no reason except that the name sounds a bit 'alternative' and there is a lot of silver in the image. The rating of an 8 shows that I consider the image rather good, but also that I put too little coloring effort into the image to award myself a 1/2 point coloring bonus. The curious parent fractal seems very interesting. It may be the source of several more FOTD images in the near future. The calculation time of 3 minutes will pass like lightning for the fanatical fractal fan. It will pass like a space shuttle in orbit for the everyday fractal fan. For the casually interested, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But don't look at too many fractals there. The next thing you know you'll be an everyday fractal fan, and then, without warning, you'll be a fanatical fan. It happened to me! With a temperature of 41F 5C, blustery winds and lumpy gray clouds, Tuesday was anything but spring-like here at Fractal Central. The fractal cats stopped waiting for the sun when a half-hour passed with no sun. They spent the next hour asking for and finally getting an extra treat. My day was once again average. The next FOTD is due in 24 hours. Odds are that it will appear on schedule. Until then, take care, and what is everyone so concerned about nowadays? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Silver_Barrels { ; time=0:03:03.18-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident center-mag=+19.62066736201389/+3.489640752547452/\ 2.24442e+007/1/17.5/0 params=14.55/0.6/-14.55/\ 0.666/0/1000/0/0 float=y maxiter=1400 inside=0 logmap=232 periodicity=10 colors=000UPTOHOQJQRLRTNRVOTWQVWRWYTWZVY`WZbY`cZ`e\ `bebcfceheejffkhhmjjnkjnmkonmqonrqntroutqvurvvrxxt\ yyuzzvzzvzzxzzyxDVyGWyHWyJYyJYyLZyNZyO`yO`yQbzRbzT\ bQvYOtYOrWNoWNnWNkVLjVLfVJeTJbTJ`TYjNkrGxyAzrGzmJz\ fNz`RzVVzOYzH`z8cz0fr0hq0jq0jo4jo8jnBjnGjmJjmNjkQj\ kTjjWjjZjzrrzquzovznxzmyzmzykzxjzvhzuhztfzrezqczoc\ z0jL0oV4ubDyjLzrTzyZzzezz`zxYzjTyVQtDNn0Ok4QjDRhNT\ eTVc`WbhYZnZYu`WzbVzmGtv0fz0TeTJAzA6o64c20R00D00OL\ 0Ye0fv0kx0oy0tz4xz8zzBzzGzzJzzLzzRzzYzzbzzhzznzzrz\ zrzzrzzrzzoyxnvukrrjoohmmehjcefbbcZY`YVZWRWTNTRJQQ\ GNNAJL6GJ2BG08D04B02D04G06G06H08zzyJ0AJ0AL0BL2DN4D\ O6GO6GQ8HQAJRBJTDLTGNVGNVHOWJOYLQYNRZNR`OT`QVbRVbT\ WcTWeVYeWZfYZfZ`h`bj`bjbckcckeemffnffnhhojjqkjqmkr\ mkrnmtonuqnurovtqvtqxuryvryxtzyuzyuzzvzzxzzxzzyzz0\ zz4zz8zzBzzGzzJzzNzzRzzVzzYzz`zzczzfzzkzznzzqzztzz\ vzzBzzDzzGzzHzzHzzJzzLzzN } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 04-04-09 (Sideways in Time [5.5])
by Jim Muth 07 Apr '09

07 Apr '09

FOTD -- April 04, 2009 (Rating 5.5) Fractal visionaries and enthusiasts: There's nothing quite like a scene in a perturbed Mandelbrot set when rendered with Fractint's little-used 'ranges' and 'stripes' features in effect. Today's super-quick image located on the north shore of East Valley is a typical example of a perturbed Mandelbrot forest. The effect of seeing a brilliant distant scene through a deep dark fractal forest in the foreground is typical of perturbed M-sets, and can be quite striking. This effect was one of the first I found when I began exploring fractals. Unfortunately, by now this effect is quite old to me. It dates from about 1989, so I could rate the image no higher than a 5.5. One-half point of this rating is a reward for my coloring. I had forgotten how the 'ranges' and 'stripes' features work, and it took a bit of research to track it down. The name "Sideways in Time" refers to the fact that to find today's scene we needed to go sideways in the Julibrot in the fourth dimension, and time can be considered a fourth dimension. Calculating in only 5 seconds, today's image is so fast it is almost instantaneous. Those with Fractint-challenged machines that panic at the sight of a DOS program will find the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Friday began with heavy rain showers here at Fractal Central. The sun made a brief appearance just after noon, but within an hour the clouds re-built and the showers returned, spoiling the fractal cats' afternoon in the sun. The duo didn't even notice the pleasant temperature of 64F 18C. My day was about average. The next FOTD is due in 24 hours, but with another of FL's week- end antiquing trips looming on Saturday, it might not appear until 36 hours have passed. Until whenever, take care, and like today's image, virtual particles may also move sideways in time. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sideways_in_Time { ; time=0:00:05.59-SF5 on P4-2000 reset=2004 type=mandel center-mag=+0.339238739/\ +0.050991211/4387.093/1/-42.5/0 params=0/1 float=y maxiter=32767 bailout=25 inside=253 periodicity=10 ranges=0/-1/300/315/340/400/500/700/999/\ 1400/2000/3000/32767 colors=000YQMK00JPiOUpSWyUauUevUizamzipzluzzzz000<\ 233>000<4>0000FS000000 } END PARAMETER FILE=========================================

4 4

FOTD 07-04-09 (Stellar Nursery [8])
by Jim Muth 06 Apr '09

06 Apr '09

FOTD -- April 07, 2009 (Rating 8) Fractal visionaries and enthusiasts: For the curious, the 'Great Mandelbrot Set' image of April 5, 2009 originally appeared in a slightly different form as the FOTD for September 5, 1999, when it was named "Mandelbrot Vision". Paul Lee almost had it tracked down. Today's image is another slightly modified old one, this one from March 12, 1999, when it was named "Edge-On Galaxy". I'm re-using old images because of a heavy work load which leaves too little free time for a proper fractal search. I tweaked the colors a bit and turned the image almost upside-down, but the overall effect of stars scattered among streaks of interstellar dust is much the same. In keeping with the same theme, I named today's image "Stellar Nursery". The rating of an 8 is perhaps a bit high for a re-used fractal, but I think it is worth the rating, especially since I had not yet started rating the images when I posted the first version. The calculation time of 35 seconds means no one will waste much time doing the calculation. And as always, the finished image is or soon will be posted for immediate and total gratification on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds and occasional rain made the fractal cats unhappy on Monday here at Fractal Central. With a lack of sun, the near-normal temperature of 55F 13C gave no comfort. My day was near average. The next FOTD will be posted in 24 hours. Until then, take care, and it will all work out, re- gardless of what 'it' may be. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Stellar_Nursery { ; time=0:00:35.07-SF5 on P4-2000 reset=1960 type=formula formulafile=basic.frm formulaname=multimin-XZ-YW-new passes=1 center-mag=+0.06912407603522651/+0.000287532042665\ 15/203.8073/0.04155/0.206674009974176315/64.560649\ 9155611289 params=90/-10/3.5/0/0.03907/-0.28621/\ 0.8042/0 float=y maxiter=1200 bailout=25 inside=255 logmap=16 periodicity=10 colors=000`KWZKVZKUYJTWISUHRSGQRFQPEPODOMCNLBMJBLI\ BKHBJFAJDAJAAI7CI5CI2CG0CG0CG0CE0CE0CD0CE0CE0CE0CG\ 0CG0CG0CI0CI0CI0CJ0CJ0CJ0CJ0CL0CL0CL0CL0CN0CN0CN1D\ O1EO1FO1GO2HQ2HQ2HQ4HR4IR4IR6IT6IT6JT6KT8LV8MV8NV9\ NX9MX9MX9MXBMYBMYBMYDM_DM_DM_DM_EKaEKaEKaGKbGKbGKb\ IKdIKdIKdIKdJKfJKfJKfLKgLKgLKgLKgNKiNKiNKiOKkOKkOK\ kOKnQKqQKtQKwRKzRKzRKzTKzTKzTKzTKzVKwVKuVKsXKsXKsX\ KsYKtYKtYKtYKt_Kw_Kw_KwYOt_Kw_JxaHzaFzaCzbBzbBzaBz\ aBzbBzbBzbBzdBzdBzdBzdBzdBzfCzfCzfDzfDzfDzgFzgFzgF\ zgHziHziJziJziJziKzkKzkMzkMzkOzkOzlPzlPzlPzlRxnRxn\ RxnTxnTxnUxpUxpUxpWwpWwpYwpYwqZwqZwqZws`ws`ts`tsat\ sattcttcttettetteswgswgswhswhsxhsxjsxjsxlqxlqzlqzm\ qzmqzoqzoqzoqzqpzqpzrpzrpzrpztpztpzvpzvnzwnzwpzwrz\ ytzyvzzxzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:multimin-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=(-z)^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

1 0

FOTD 06-04-09 (Just Testing [No Rating])
by Jim Muth 05 Apr '09

05 Apr '09

FOTD -- April 06, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image lies in the pathetic fractal that is created when 6.6 parts of Z^(0.08) are combined with 0.6 part of Z^(1.9) and plain C is added. The discussion is short because I'm pressed for time. I gave the image no rating because I can't decide what I think of it. The name "Just Testing" confirms my indecision. The calculation time of 9 minutes is rather slow, so I recommend enjoying the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunny skies and a temperature of 66F 19C made Sunday near per- fect here at Fractal Central. The fractal cats agreed. My day was pleasant enough, and with any luck tomorrow will be the same. The next FOTD is scheduled to be posted in 12 hours, but in the FOTD world, schedules are not always followed. Until the next time, take care, and think deep thoughts. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Just_Testing { ; time=0:09:05.01-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 maxiter=3750 center-mag=-8.033545031345833/+0.0021\ 598878272083/4.155029e+010/1/-127.5/0 params=6.6/\ 0.08/0.6/1.9/0/0/0/0 float=y logmap=680 inside=0 periodicity=10 colors=000N8KN9LN9MNAMNBNNBNNCONCPNDPMDQMERMERMFSM\ FSMGTMGUMHUMHVMIVMIWLJXLKXLKYLLYLLZLM_LM_LN`LN`LOa\ KObKPbKPcKQdKQdKReKSeKSfKTgKTgKUhJUhJViJVjJWjJWkJX\ kJXlJYmJYmJZnHYoIZnJZnKZnKZmLZmMZmNZmN_lO_lP_lQ_lQ\ _kR_kS_kT`kT`jU`jV`jW`jW`iX`iYaiYahZah_ah`ah`agaag\ bbgcbgcbfdbfebffbffbegcehceiceicdjcdkcdavgflekcdpU\ bwJbuLasMarOapPanR`mz`kz`jz`hz_fz_ez_cz_bz_zzZZzZz\ zZWzZzzYTzYzzYzzYzzXMzXzzXJzXzzYIzXzzXztWztWJzzzrz\ JzVzqzKzUzozKoTzzTLmzzmzLzSzkzMzRzjRMzzMhQNhQNgPNf\ PNePOeOOdOOcOOcNPbNPaMP`MP`MQ_LQZLQZLQYKRXKRWKRWJR\ VJSUISUISSISQHTOHTMHTKGTIGSGHTEGUCGUAGVAFVAFWAFXAE\ XAEYAEYADZAD_ADz0Cz0Cz0Cz0Bz0Bz0Bz0Az0Az0Az09z09z0\ Iz0Jz0Jz0Ko0in0in0jm0kl0lm0kl0llKlkUlkcljiljnljomi\ qmismhumhwmhxmgyngznfznfzneznzznzzozzozzozzozzozzn\ zzozzozzozzozzpzzpzzpzzpzzqzzqzzqzzyzzuzzqzznzzjzz\ gzzczzazzHzzHzzIzzIzzJzzL } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 05-04-09 (The Great Mandelbrot Set [N.A.])
by Jim Muth 05 Apr '09

05 Apr '09

FOTD -- April 05, 2009 (Rating N.A.) Fractal visionaries and enthusiasts: Today's image is a slightly redone FOTD from the past. (I leave it to the viewer to find the original version.) It's all I had time for after FL and I spent most of the day Saturday exploring an antique emporium near Chambersburg, PA. (The trip was not wasted. FL found an old carpet that she insisted we simply had to have.) Today's image shows "The Great Mandelbrot Set", floating in the sky above a world it has just created but to which it has not yet added the details. (Any resemblance to the assumed Deity of our universe is purely intentional.) The proportions of the Great Mandelbrot Set are slightly different than those we are used to, but there can be no mistaking that it is a Mandelbrot set. The nascent universe and its creator were created by subtracting some Z^(0.45) from about twice as much Z^(0.98) and adding straight C. Since basically the same image is being posted for the second time, I could give it no rating, but even so, I think it's a bit more striking than average. The calculation time will cause no impatience. At a godlike speed of 25 seconds, it will finish before boredom even thinks of arising. Those with over-challenged computers may view the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Gusty winds, thick clouds and a temperature of 48F 9C took all the fun out of life here at Fractal Central on Saturday. At least, that's what the fractal cats told us when we returned from the antiquing expedition around 9pm. A quick treat of tuna cheered the cat duo, though I had to go into my archives to find today's fast FOTD. The next FOTD is due in a mere 8 hours. But whether the FOTD actually appears on schedule is a matter of chance. Until next time, take care, and seek union with the great fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Great_Mand-Set { ; time=0:00:25.91-SF5 on P4-2000 reset=1960 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=t center-mag=+0.01248328825047417/0/557.041/1/-90/0 params=0.98/0.76/-0.23/0.45/1.00087/0/0/0 float=y maxiter=95 inside=bof61 logmap=yes periodicity=10 colors=0000000000000000000000000000000000000000000\ 00000zzgzHbzzXzQSzzNzZHzbCzzIzWNzzTzPZzLdzzjzFozzu\ z8zrCxnGwiKueOtaSrYWpT_oPcmQdjRegSfdTgbTh_UiXVjUWk\ RWbOWE_XFaYGcZHe_Ig`JiaKkbLmcModNqeOrfPrgQrhQqiSoi\ UihUhbUgcUhcUecUdcUccUbcUacU`cU_cUZcUYcUXcWWdYVg_c\ jacnccqectgcwiczkczmczmczmczmczmcmUwmKwmRwmUwmUwmU\ wmUwmUwmUwmUwmUwmUwmUwmUwmUwmUwmUwmUwmUwmUwAjZHhVO\ gSVeOk0IhAJfLKcVLFmpLkhRh`XfTRDSxmkrjdlhYffRbmqah`\ P9DWPHduQMExSNjXWYGgyxOKlXLJ0cQEXWSRYi3Zh8_fC`eHY4\ 7_HC`THORLTWLY`Lc_LbaLacLpgnDT6JWAQZEWaIPOvUUiY_X2\ KsBPjKVaT_T18DKPHORfSMkWTbZZUPQ9SUCWYFZaIjVrnWiiZ`\ eaTxLjpSahZTUTvp_MkaLfcLL2kPCdUMYYWRlATfQPHEHSSJkM\ dhR_fWVc`QFzDLtFRoHXiJYFaZMY_ST`ZPRequxRnqPgjNbyqa\ n`3YCagNafMaeL4QVGVRR_OkwAcS9m5wgNchd7VEiXLcZSX`ZR\ W_UY`SZbP`cNkPRQFUWSPbJYbPVaURa_ODinRlqVifZfWFPvNV\ iV_XFhSLgQRfOXeM_OCWIASC8 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

2 1

FOTD 03-04-09 (Squiggly Things [7.5])
by Jim Muth 02 Apr '09

02 Apr '09

FOTD -- April 03, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: When (1/Z) is subtracted from 0.001 negative part of Z^(25) and straight C is added, the resulting fractal is a circle with a ring of 26 dots just inside its perimeter and some interesting fractal stuff near the east and west edges. Today's scene lies at the edge of a valley in the stuff near the east edge of the ring. (Rendering the formula with the function set to 'recip' creates an even more interesting parent fractal, but that's a story for another day.) I named the image "Squiggly Things" because of all the S-shaped holes surrounding the central minibrot and filling the frame. Most of the coloring effect was achieved by rendering the image with the outside set to 'fmod'. The normal 'iter' rendering is rather dull. When all was finished, I rated the fractal at a 7-1/2, which includes the usual 1/2 point reward for my coloring efforts. The calculation time of 3-1/3 minutes is not as fast as I would have preferred, but this time may be saved by viewing the image already calculated on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Spring came in like a lion here at Fractal Central on Thursday, with sunny skies and a temperature of 68F 20C. The fractal cats actually got a bit too much sun on their shelf in the window, and decided to stretch out on the floor instead. My day was about average. The next FOTD will be posted in 24 hours. Until then, take care, and if God is an all powerful monarch, does this make the universe a dictatorship? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Squiggly_Things { ; time=0:03:27.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+1.984006758708603/-0.0181790017486502/\ 1.108e+008/1/-57.5/0 params=-0.001/25/-1/-1/0/0/0/0 float=y maxiter=1800 inside=0 proximity=0.9 outside=fmod periodicity=10 colors=000DAjB8k97m75n53p21s32r32q32p32o32n42m42l4\ 2k42k42j42i53h53g53f53e53d53d63c63b63a63`63_74Z74Y\ 74X74X74W74V84U84T84S84R84Q62O84Q95RB6SC8TE9UFAVHC\ WIDXKEYLGZNH_OI`QKaRLbTMcUNdWPeXQfZRg_ThaUibVjdXke\ YlgZmh`njaokbpnhrmeqlcqkaqjZqjXqiVqhTqgQqgOqfMqeJq\ dHqcFqcDqbAqa8q`6q_2p`3q`4q`5q`6q`6q`7qa8qa9qaAqaA\ qaBqaCqbDqbDqbEqbFqbGqbHqcHqcIqcJqcKrcLrcLrdMrdNrd\ OrdOrdPrdQreRreSreSreTreUreVrfWrfWrfXrfYrfZrhYqgZr\ fZrfZreZrdZrdZsc_sb_sb_sa_sa_t`_t__t_`tZ`tY`tY`uX`\ uX`uW`uVauVavUavTavTavSavTbwSavSavSauSauSauSatSatS\ asS`sS`sS`rR`rR`qR`qR`qR`pR`pR_oR_oR_oR_nR_nR_mQ_m\ Q_mQ_lQZlQZkUZkZZkcZjhZjmZirZivZizZYzVMzMMoMAhECZG\ DKJEBLFDOGFQHITJKVKMXLP_MRaNTdOWfQ_hUcjYglakneopit\ rmwtqywvyyyyyyxxzwwzvvzuuzutztrzspxrnvqmtplrplqokq\ nkqmjqlipkipkhpjhpigphgogfmfekecidagc_eaYc_WaYU_WS\ ZUQZSO_QM`OKbMIcKGeIEgGCh } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 02-04-09 (Eruption in Progress [8.5])
by Jim Muth 01 Apr '09

01 Apr '09

FOTD -- April 02, 2009 (Rating 8.5) Fractal visionaries and enthusiasts: Today we have a fractal created by the MandNewt05 formula, one of a group of 12 that I wrote about 10 years ago and soon filed and forgot. Don't ask what this series of formulas does; I have no idea. But whatever they do makes some interesting fractals. Most of the image consists of inside stuff brought to life by the 'bof60' inside fill, which colors the points according to how close they come to the origin. The name "Eruption in Progress" came about when I fancied a volcano on some abstract mathematical alien planet erupting strings of bubbles. The rating of an 8-1/2 includes the usual 1/2 point for the effort I put into tweaking the colors to get the smooth pastel effect. The calculation time of 1-1/4 minutes is quite fast, and will cause no one the least bit of impatience. The only ones in trouble could be those with new-fangled and over-qualified machines that have forgotten how to run old-fashioned DOS pro- grams. But even for these few, relief is at hand. The image has been already calculated and posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where one may view it at leisure and say 'aaaaahhh'. Heavy clouds and rain spoiled almost everything here at Fractal Central on Wednesday. The chilly un-springlike temperature of 48F 9C gave no consolation at all to the fractal cats, who gave up waiting for the sun early in the afternoon and spent the rest of the day getting into trouble in and around the book shelves in the F.C. hallway. My day was spent finishing up some work left over from Tuesday. The immediate future looks slow, but like the weather, this has a way of changing suddenly. The next FOTD will be posted by me in 24 hours. Until then, take care, and fight violently to bring about a world where all the ethnic, political and relig- ious groups live together in peace and harmony. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= EruptionInProgress { ; time=0:01:16.51-SF5 on P4-2000 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt05 function=atanh passes=1 center-mag=0.490891/0.11292/0.6210325/1/-25/0 params=0.9141/3.2639/-3.3039/-1.062/-0.3534/3.0686 float=y maxiter=180 inside=bof60 logmap=yes periodicity=10 colors=000zzJzyJzwIzuIzsIzrHzqHzpHzoHznGzmGzlGzkFz\ jFziFwhFtgFqfEneEkdEhcDebDbaD_`CX_CUYCRWBOUBLTBKSA\ KRAKRAII3H00mzzmzzmzzlzzkyziyzgyyeyxcxwaxu_xsYxqWw\ oUwmTwmSwlRwlQwlPvlOvlPulQulRtlSslTslUslVrlWrlXqlY\ qlZpl_ol`nlamlbllcklejlfilghlhglifljelkdllclmblnal\ o`lp_lqZlrYlrYlrYlrYlrYlrYlrYlrXlrXkrXkqXkpXkoXjnX\ jmXjlXjkXjjXiiXihXigXifXheXhdXhcXhbXgaXf`Xh_XgZXgY\ XgXXfWXfVXfUXfTXeSXeSXeRXeQXdPXdOXdNXdMXcLXcKXcJXc\ IXcHXbGXbFXbEXbDXaCXaCXaBXaAX`9X`CX`FX`IX_LX_OX_RX\ _UW`XW`_V`bVaeWahXakYbnZbq_bt`bv_bvYdwWcwTbtTarSao\ S`mR_jRYhRVgPVdPScNUaMQ`MOZLKXKIWJFUIESGDPDDMACJ08\ YLQXLPXKPWKOWKNVKNUJMUJLTJKTIKSIJeHIdHHdGHcGGcGFbF\ FaFEaFD`ED`EC_DC_DBZDAYCAYC9XC8XB8WB7VB6UC6VC6VC6W\ B6WB6XB6XB6YB6YA6ZA6ZA6_A6_A6`96`96a96b96b96c86c86\ d86d86e86e76f76f76g76g76h66h66i66jA7kA8lA9lA9lA9lA\ 9lA9lA9mAAmAAmAAmAAmAAmAA } frm:MandNewt05 {; Jim Muth z=c=fn1(pixel): a=z^2+(c-p1)*z-c b=p2*z^2+c-1 z=z-1*a/b p3 <= |a| } END PARAMETER FILE=========================================

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Fractals and Quantum Dynamics
by Lee H. Skinner 01 Apr '09

01 Apr '09

A fascinating article in New Scientist talks about resolving Quantum Theory with fractals is at http://is.gd/pFiD Lee Skinner

4 3

FOTD 01-04-09 (Textured Textures [7.5])
by Jim Muth 31 Mar '09

31 Mar '09

FOTD -- April 01, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Take away the texture and today's image is just another scene not very deep in East Valley of some Mini-Mandelbrot set. But today's image has texture -- this is why I named it "Textured Textures" -- and the textures make the image worthy of being rated a 7-1/2 and named FOTD for April 1 -- no fooling! The parent fractal was created by mixing 100 parts of Z^(-100) with plain Z and adding plain C. This parent is nothing more than a large circle with cogs around its edge and a small minibrot where the east side of the circle meets the X-axis. Today's scene is located on the south side of the East Valley of a tiny minibrot on the main stem of the small minibrot on the X-axis. The calculation time of 7-1/2 minutes is a little slower than average, but not slow enough for severe impatience to develop. And do not stop the calculation at the first pass. The main effect of the image does not become apparent until the final pass has finished. The image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Lots of sun and a temperature of 61F 16C kept the fractal cats of Fractal Central content on Tuesday. A reduction in the work kept me content. The appearance of daffodils, forsythia and the first spring growth on the fractal roses kept FL happy. Unless the world ends first, the next FOTD will be posted in 24 hours. Until the world turns 360 degrees, take care, and think about solving the measurement problem. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Textured_Textures { ; time=0:07:28.91-SF5 on P4-2000 reset=1960 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident float=y center-mag=-0.042314218591227/-0.0000021689096984/\ 1.77436e+010/1/-146.5/0 params=1/1/100/-100/0/0/0/0 maxiter=3750 inside=0 logmap=383 periodicity=10 colors=000zz2zz2zx2xu2vr2so2rm2oj2mg2jd2hb2e_2dX2a\ U2_S2XP2VM2SJ2QH2NE2KB2J92H83H85H86H68H68H69H6BH6D\ H5EG5GG5HG5HN5JG3KG3MG3NG3PQ3QG2QG2SG2UG2VX2XG1YG1\ _G1aE1aX1bE0dE0eE0gE0hX0eE0jE0lE0mE0oX0bE0rE0sE0sE\ 0uX0XD0xD0zD0zD0zU0sU0rD0zD0zD0zE0zG0zH0zH0zJ0zK1z\ M2zN3zP5zP5zQ6zS8zU9zVBzVBzXDvYEu_GraHpbJobJmdKmeM\ lgNlhPjhPhjQhlSgmUgoVepXepXdrYbs_buaavbavb_xdYzeYz\ gXzhXzjVzjVzlUzmSzoSzpQzpQzrPzsNzuNzzMzzMzzKzzKzxJ\ znJzzHzzHzsHzeHzoGzmGzlGzjGzhEz_EzdEzbDzaDzNDzYDsV\ BoUBoSBzQBlN9dM9dK9XJ9XH8XE8PD8lX6dH6lH6H56d35H25X\ 15005N03003N03002002001001001000000QH0UJ0YM0bN0gQ0\ gQ0eS0eS1eS2eU3dU5dV6dV8bV9bXBbXDbXEaYGaYHa_Ha_J__\ K_aM_aNYaPYbQYbSYbUXdVXdXXeYVe_VeaVgbVgdUgeUhgUhhS\ jjSjlSjmSloQlpQlrQmsPmuPmvPovPoxNpzNpzNpzNrzMrzMsz\ MuzKuzKxzKxzKxzJzzJzzJzzJzzJzzJzzJzzHzzHzzHzzHzzHz\ zHzzHzzHzzHzzHzzHzzHzzHzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 31-03-09 (Pentagram Pannikin [6])
by Jim Muth 30 Mar '09

30 Mar '09

FOTD -- March 31, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a harmless scene in the Z^5+C Mandeloid, which of course is its parent fractal. Z^5 is about as high as one can go and still expect variety. Beyond this point a boring flowery sameness creeps in, which continues, I suppose, all the way to infinity. Today's image clearly shows the progression of the series 5,25,125... as the four-lobed minibrot is approached. The image is located on the shore line of the northeast lobe of its parent. I named the image "Pentagram Pannikin" for reasons known only to myself. I think a pannikin is a small cup, though I would never bet anything on it. The rating of a 6 could be a bit liberal. After all, it's only a quintic minibrot. But to avoid bringing politics into fractals, let's call a rating of 6 a consensus. The calculation time of just over 2 minutes makes calculation a pleasure. Those who wish to avoid being overwhelmed by pleasure may view the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> There is no formula included in the parameter file because the image uses the type=manzpower formula hard-coded into Fractint. Too many clouds, too little sun and a temperature of only 46F 8C kept the fractal cats on the sullen side here at Fractal Central on Monday, while too much work and too little time kept me sullen. But in the end the fractals prevailed and today's image appeared almost from nowhere. With any luck, the same thing will happen again in 24 hours. Until then, take care, and beware of the cornflicker jumping caterpillar. It could devastate the corn crop. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Pentagram_Pannikin { ; time=0:02:09.23-SF5 on P4-2000 reset=1960 type=manzpower center-mag=+0.3553089574\ 873845/+0.6853393808366973/2.3e+013/1/-173.25/0 params=0/0/5/0 float=y maxiter=2000 inside=0 logmap=208 periodicity=10 mathtolerance=0.05/1 colors=000KClKDkKEjKFiKGhKHgKIfKJeKKdKLcKMbKNbKObK\ PbKQbbVXhXNnZEs`5t_9tZCtYFuYIuXLuWOvWRvVUvUXwU_wTb\ wSewShsRioRikRjhRjdRk`RkXRlURl`LYgFJn95mB7lD8kE9kG\ AjHBiJCiKDhMEgOFgPGfRHeSIeUJdVKcXLcYMe_NgaOibOkdPm\ ePngQpiRrjRtlSvmSxoTypTwlSuiSteRrbRqZRoWQnTQlPQjMP\ iIPgFPfBOd8Oc5OznnznlznlznlznizkgzgbzdazaYzYRzVRxQ\ QtNQqLQnJInJInIInIIsQRxYazfazn_zsgzzdzzqzzzzzzzzzz\ zzzzVzzVzzTwzTwzRwzRtzQtzQtzQszOszOszNszNqzNqzLqzL\ pzJpzJpzJpzInzInzGnzGlzElzElzDlzDkzDkzBkzBLFwRMvXT\ vb_uhfudgpagkZgfWgaTgXPhSMhNJhIGhDDh8Ah3Bi6Ci9DjCD\ jEEkHFkKFlNGlPHlSHmVImYJn_JnbKoeLohLojIhdGa_EWVBPQ\ 9IL7CGAGFDKFGNFJRFLUFOYFR`FUdEXhEZkEzozzrzzvzzyzzw\ zzuzzszQqbLohHmnGkkGiiGggGeeGcbGc`FcZFcXFcUFcSFcQF\ cOFcMIcKKcJMcHPcGRcETcDVbBYfAzj8zm7zp5zs4zv2zx1zz0\ zzBzzLzzVzzdzznzzkzzhzzfzzczz`zzZzzWzzTzzRzzOzzLzz\ JzzOzzSzzXzz`zzezzizznzzr } END PARAMETER FILE=========================================

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FOTD 30-03-09 (Star of Infinity [8])
by Jim Muth 29 Mar '09

29 Mar '09

FOTD -- March 30, 2009 (Rating 8) Fractal visionaries and enthusiasts: Space goes on forever, which is unimaginable, or it comes to an end, which is equally unimaginable. Or it might curve back on itself and close up like the surface of the earth, which is also unimaginable. And I hear that space might actually open up, so that there is more of it out there than we can imagine. What- ever might be the actual state of affairs, of one thing we can be sure -- the truth lies beyond our feeble powers of imagina- tion. So let's concentrate of something even less imaginable -- the totality of all possible fractals. Today's fractal image is but one of an infinity, though I'm not sure which infinity. Some infinities are infinitely greater than others. Actually, the image is a scene in the parent fractal that results when a tiny portion of Z is subtracted from an even tinier portion of Z^100. This parent fractal appears as a circle with a Mandeloid thing attached to its east perimeter and some flowery debris on its west side. Today's scene is located in the detail near the north shore of the Mandeloid thing. I named the image "Star of Infinity" and rated it at an 8. I see several nested 8-pointed stars in the scene. The calcula- tion time of 4-3/4 minutes is not quite as fast as I would like, but still plenty fast enough for a S.O.T.A. unit to handle before boredom arises. And as always, the finished image is or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> for immediate perusal and gratification. The mild weather on Sunday here at Fractal Central was compro- mised by heavy clouds and occasional showers of rain. With no sun, the outside temperature of 61F 16C gave little comfort to the fractal cats as they lay on their shelf by the window. But a bit of tuna lifted their spirits. My day was peaceful, which I guess is all one can ask for. The next FOTD, peaceful or not, will be posted in 24 hours. Until then, take care, and change is in the air, but who knows which way it might go. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Star_of_Infinity { ; time=0:04:44.05-SF5 on P4-2000 reset=1960 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+1.66407211213/+0.39288926327/3.6e+007/\ 1/44/0 params=0.01/100/-100/1/-0.9897/0/0/0 float=y maxiter=12000 inside=0 logmap=270 periodicity=10 colors=000DGNCHKBIKAILAIM9IN8IP7IQ7IR6IS6IT7IU7IV8\ IW8IZ9Ic9IhAHmAHrBHvBHzCUzCczCUzDHzDHvDHrEHmEHhFHd\ FGdFGdGGcGGcHGcHGcIGbIGbIFbJFbJFaKFaKFaPLeUQhZWlc`\ phfsmkwkjvjivhhugfueetddtbcsabs_arZ`qXZqWYpUXpTWoR\ VoQUnOTnNSmLQmKPlIOkHNkFMjGLjIKiKIiMHhOGhQFgSHhUJi\ WKkYMl_OmaQncSoeUpgVriXskZtmcuphztmzwrzzvzzzzzzzwv\ zrrzmmXahWadUacTacRcbQhbOmaNrfMvjKzjJviIriGmcFhcEc\ `CZXBUW9RU8PT7QR5RR4RT7PVAOWDNYFL_IK`LIaOHaRKbUPcW\ UdZZdacedhfgmgjrhlvhozirzjuzmtzoszqzzszztzzszzqzzo\ zzmvzkrzimzghvegrcgsaftafubevcewcdwccwzcwzbwzbwzaw\ zawz`wz`wz_wzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzz\ wzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwz\ zwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzVwzVwzVwzVwzVwzVw\ zVwzVwzVwzVwzVwzVwzVwzVwzVwzVwzVwzVwzVwzVwzVwzVwzV\ wzVwzVwzVwzVwzVwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwzUwz\ UwzUwzUwzUwzUwzUwzUwzUwzU } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

1 0

Fractal Diode
by sciwise 28 Mar '09

28 Mar '09

Dear FractInt members . The diode is a very basic electronic component that exhibits a non-linear behavior . When used in a circuit an iterative approach is necessary to find the varying currents and voltages . To model the diode , to a reasonable accuracy , the diode equation can be used : I = Is ( exp(Vd /(n Vt)) - 1 ) I is the diode current, IS is the reverse bias saturation current . VD is the voltage across the diode, VT is the thermal voltage, and n is the emission coefficient , also known as the ideality factor. The emission coefficient n varies from about 1 to 2 Refer Wiki Diode Equation . When placed in a circuit containing reactive components , inductor , capacitor and appropriate resistive values the parameters in the exponential function become complex , with the next value being dependent upon the last : I(n+1) = Is ( exp((Vd + r I(n) )/(n Vt)) - 1 ) Where r [ impedance ] and I(n) [ current ] might be complex . I(n) represents the previous current through the diode . An iterated map might therefore use the real and imaginary components of I(0) as (x.y) coordinates . The result might be compared with datasheets or spice modelling . Why attempt this ; because a better , more interesting insight might be obtained . Has anyone on this list delved into this ?

1 0

FOTD 29-03-09 (Poppy Fields of Oz [8.5])
by Jim Muth 28 Mar '09

28 Mar '09

FOTD -- March 29, 2009 (Rating 8.5) Fractal visionaries and enthusiasts: Today's parent fractal is little more than a series of horizon- tal stripes in the Rectangular orientation of the Z^(1.1)+C Julibrot. This parent looks like a scene to be discarded fast, but when stretched and skewed to a great degree, the stripes turn into a poppy field in the land of Oz. It must be OZ; the scene most certainly is not in Kansas (or Pennsylvania). Seeing the fractal poppies blowing in the invisible wind under an azure sky, I named the image "Poppy Fields of Oz". Then I gave it a rating of 8.5, which includes 1/2 point for my color- ing. Such a smooth color palette is quite difficult to achieve with only 256 colors available. The calculation time of 2-1/3 minutes is brief enough to avoid boredom. The image is also available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> All good things must come to an end, and so the good weather of Friday came to an end on Saturday as heavy clouds moved in and rain began. At the same time, the temperature of 57F 14C was a bit too chilly for the fractal cats, who spent the afternoon with sour looks on their faces when their anticipated sun failed to appear. A treat of tuna cheered them however. My day was slow -- a welcome change after a busy week. The next FOTD will be posted in 24 hours. Until then, take care, walk with confidence, and believe that change is coming. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Poppy_Fields_of_Oz { ; time=0:02:22.63-SF5 on P4-2000 reset=2000 type=formula formulafile=slices.frm formulaname=RectangularN passes=1 center-mag=-0.00255084527186440/+0.000015032024027\ 91/178233/0.001255/0.148/89.811 params=1.1/0/0/0/\ 0.041627863/-0.002064849 float=y maxiter=10000 inside=0 logmap=136 periodicity=10 colors=000YNzYOzYPzYQzYRzOdxPdxQdxRdxSdxTdxUdxVdxX\ dxYdxZdy_dzadzaezbfzbgzbhzcizdjzckzdlzdmzemzfnzfoz\ gozhpzipzipzjqzkqzkqzlqzmqznqznqzoqzpqzprzqrzrrzrr\ zsrztrwtrttrqsqmsqhsqcrqZrqUrqPrqKqqGqqFqqFqqFpqFp\ pEppEppEopEopEopDopDnpDnpDnpDnpCmpCmpCmoCmoBloBloB\ loBloBkoAkoAkoAkoAjoAjo9jn9jn9in9in8in8in8hn8hn8hn\ 7hn7gn7gn7gn7gm6fm6fm6fm6fm5em5em5em5em4em4em4dm4d\ m4cl5ck5bj5bj5ai5ai5`h5`h5_g5_f5Zf5Ze5Ye5Yd5Xc5_c5\ mb5cb5cc6zc6cm6Zm6cc6cc6vn6zb6zc6zc6zm6cV6`V6YU6VU\ 6ST6PS6NR7MQ7KQ7KQ7KQ7UQ7UPPUQ7KQ7KQ7IM7HL7HL7GK7G\ J7FJ7UI7UI7UH7DG7DG8CF8CE8BE8BD8UD8AC89B89B88A8UA8\ U98788688U78678U8978989A89AU9A99BAABUABAACBBCBBCCB\ DCBDDCDUCDECEEDEEDEFDFFEFGEFGEGHEGHFGHFHIFHIGHJGIJ\ GIKGIKHJKHJLHJLIKMIKMIKNIKNJLOJLOJLOKMPKMPKMQKNQLN\ RLNRLORMOSMOSMPTMPTNPUNQUNQUOQVORVORWPRWPRXPSXPSYQ\ SYQTYQTZRTZRU_RU_RU`SV`SV } frm:RectangularN {; Jim Muth b=p1, z=flip(real(pixel))+p2, c=flip(imag(pixel))+p3: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

2 1

FOTD 28-03-09 (Hypersphere Scene [8])
by Jim Muth 28 Mar '09

28 Mar '09

FOTD -- March 28, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image shows a series of four-dimensional hyperspheres caught in the act of passing through our three-dimensional space. (The additional networks of twisting filaments and flying clouds of fractal sand can be considered extra bonuses.) If a 4-D hypersphere were to pass through our space, we would see a tiny sphere appear, which would grow in size, reaching maximum size as the center of the 4-D hypersphere passed through our space, and then shrink at the same rate as it grew until it finally vanished. Today's image shows a series of hypersphere intersections from the first 3-D slice to the largest. Of course, I invented this analysis. The image is a pure abstraction that could represent almost anything one wanted to see in it. It is actually a scene in a fractal created by the MandNewt06 formula, a formula I wrote about 10 years ago and soon forgot about. I have a whole series of these formulas, which are equally as forgotten. Most of today's image consists of 'inside' stuff made visible by the 'bof60' inside fill, a fill that has a tendency to create 'bubbles'. The rating of an 8 might be a bit overblown, but I kind of like the image. The name is self-descriptive. The calculation time of 2-1/2 minutes is fast enough to prevent boredom and slow enough to give time to enjoy the rendering precess. The image is also available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The rain ended during Thursday night here at Fractal Central, leading to a foggy start on Friday. But the strong spring sun cleared away the fog by 10am, and the rest of the day was hazy and mild. The fractal cats found the afternoon sun on their shelf just warm enough for comfort. My day was peaceful but rather busy -- not a bad combination. The next FOTD will be posted in 24 hours. Until then, take care, and if you see it with your own eyes, it might or might not be real. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Hypersphere_Scene { ; time=0:02:28.62-SF5 on P4-2000 reset=2001 type=formula formulafile=basic.frm formulaname=MandNewt06 passes=1 float=y center-mag=0.274128/-1.06927/24.13934/1/-67.5/0 params=-2.37/2.17/-1.56/-1.05/3.29/-3.17 maxiter=254 inside=bof60 logmap=yes periodicity=0 colors=000pzznyxlxwjvuhtsfrqepodnmclkaji`ig_geZecY\ caXa_V`YUZWTXVSWTRUSQSQOQPNPNMNMLLKKJJJIIEEGGEGFCH\ EBID9JC7K94LA6MB7NC8OD9PEAQFBRGCSHDTIEUJFVKGVJHVKI\ VLJVLKVbLRdMSfNUhOVjPWlQYmRZoS_qTasUbuVcwWexXfxYgr\ ZdkZadZ_XZXQZVJZSAYRCZQDaNFeKGhHIlEInBJoCKoCKoCLoC\ LoCMoCMoCNoCNoDOoDOoDPoDQoDQoDRoDRoDSoESoEToEToEUo\ EUoEVoEWoEWoFXoFXoFYoFYoFZoFZoF_oF_oF`mG`lH`kIajIa\ hJagKafLbeLbdMbbNbaOc`Oc_PcYQcXRdWRdVSdUTdSUeRUeQV\ ePWdMYeOWeQVeRTeTSeUQeWPeXOeZMe_LeaJebIedHeeFegEeh\ CejBekAdj9dj9cj9cj8cj8bj8bi8bi7ai7ai7ai7`i6`i6`h6_\ h6_h5_h5Zh5ih4ih4ig4ig4ig3hg3gg3fg3fg2ef2ef2df2df1\ cf1cf1bf1be3ad4ad5`c6`c7_b8Zb9YaBXaCW`DV`EU_FT_GSZ\ HSZJSYKSYLRXMRXNRWORWPRVQRUSRUTRTURTVQSWQSXQRYQR_Q\ Q`QQaQPbQPcQOdPOePNgPNhPMiPMjPLkPLlPKmPKnRMmTNmUOm\ WQmXRlZSl`UlaVlcWkdYkfZkh_kiajkbjlcjnejpfiqgisiitj\ iukhvmhwnhxohyphzqhzrhzsh } frm:MandNewt06 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b 0.000000000000000000000000000001 <= |a| } END PARAMETER FILE=========================================

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FOTD 27-03-09 (Interwoven Threads [7])
by Jim Muth 27 Mar '09

27 Mar '09

FOTD -- March 27, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's FOTD combines Z with Z^(-4) and adds straight C. This combination produces a parent fractal consisting of a single large Mandel bay with strings of debris scattered well west of it. Today's image is located in a string of this debris near the point where the string emerges from behind a round-cornered blob in the foreground. According to my non-scientific and rather useless rating system, which I may soon abandon, the image rates a 7. I chose the name "Interwoven Threads" when I noticed the resemblance of the circ- ular area around the central minibrot to a doily under the lamp on the table in the hallway here at F.C. The best part of the image may be its calculation time of a minuscule 40 seconds, which means little time will be wasted waiting for fractal satisfaction. Equal or even greater satisfaction may be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted. Heavy clouds, steady rain and a temperature of 43F 6C kept things suppressed here at Fractal Central on Thursday. The fractal cats, perhaps the most suppressed of all, spent the day sulking by the heat, waiting in vain for the sun to appear. My day was spent waiting for the work to disappear, which, with some effort on my part, it finally did. The next FOTD is due to appear in 24 hours, and at this time I see no reason why it will not. Until then, take care, and one who knows he cannot do it, cannot do it, but one who knows he can do it, might do it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Interwoven_Threads { ; time=0:00:40.72-SF5 on P4-2000 reset=2000 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.809781992375213/+0.7438658124462563/\ 3.11042e+011/1/95/0 params=1/1/1/-4/0/0/0/0 float=y maxiter=300 inside=0 logmap=40 periodicity=10 mathtolerance=0.05/1 colors=000UPfURrUTz000000000000000000p4zlESnNSqXSs\ eTvoTxxTlrRalPQfNF`LGZJGYHGXFHVDHUBHT9POEXKJdFOlBT\ t7XuB_uEavIcvLevOgwSiwVkwYme`mf__gZMgY8gY8hY8hY8hY\ 8iY8iY8iY8iY8jY8jY8jY8kY8kZ8kZ8lZ8lZ8nZ8qZ8tZ8wZ8z\ Z8zZ8zZ8zZ8zZ8z_Az_Cz_Dz`Ez`FzaHzaJzbLzbMzcOzcQzdR\ zdTzeVzeXzfYzf_zgazgbzhdzhfzihziizjkzjmzknzkp_lr_l\ tZmuZmwYnyrw3pv8nuDmtHktMisRhrVfr_eqccphapm`oqZnvg\ zDfzIezMdzQczUbzYbzaazf`zj_znZzrYzvCz`DzaEzbFzcGzd\ HzeIzfIzgJzhKziLzjMzkNzlNzmOznPzoQzpRzqSbrTdsTetUg\ uVhvWjwXkxYmy1fN3gP4gQ5gS6hT7hU8hW9hXBiZCi_Di`EjbF\ jcGjdHjfJkgKkiLkjMkkNlmOlnPloRmqSmrTmtUmuVnvWnxXny\ fpxeoyeoyeoyeoyeoyeoydoydoydoydoydoydoydoycoycoyco\ ycoycoycoyboyboyboyboyboyboyboyaoyaoyaoyanzanzanz`\ nz`nz`nz`nz`nz`nz`nz_nz_nz_nz_nz_nz_nzZnzZnzZnzZnz\ ZnzZnzZnzYnzYnzYnzYnzYnzYnzrVOka`dhm2Nm3On4Pn4Pn5Q\ o6Qo6Ro7Ro8Sp8Tp9TpeQIgFN } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 26-03-09 (On the Run [7])
by Jim Muth 25 Mar '09

25 Mar '09

FOTD -- March 26, 2009 (Rating 7) Fractal visionaries and enthusiasts: I ended yesterday's FOTD discussion with a casual question about what benefits the space program has ever produced. And one of the replies was GPS -- the global positioning satellite system. This is indeed a benefit. In the bad old days, we actually had to do things like note the positions of the stars and the time of day, and then do some mathematics if we wanted to know where on earth we were. (I wonder if they still teach celestial navi- gation at the Naval Academy.) Luckily, there is no navigation problem with today's image, which was produced by subtracting Z^(2.6) from Z^(2.4). To see the action, simply load up the included parameter file, strike the 'go' button and within a few minutes the parameter file will generate the image. I named the image "On the Run". There is about as much reason behind the name as there is behind some of my ratings. And BTW, I have been considering dropping the rating system. All it does is deter some people from checking the images. If I do drop the ratings, viewers who want to know the quality of the day's image will have to calculate the image themselves or go view it on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and make their own rating. BTW, today's image rates an adequate 7. I really don't think it is worth much more. (Opposing opinions cheerfully accepted.) Increasing clouds marred Wednesday here at Fractal Central, though the temperature of 55F 13C was not at all bad. The fractal cats complained when their afternoon sun failed to appear, but otherwise were happy enough. My day was rather busy. Tomorrow should be the same. The next FOTD will be posted in 24 hours. Until then, take care, and I just saw a Higgs particle pass through the room. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= On_the_Run { ; time=0:06:49.61-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-1.766272449888003/+0.0115958894054906/\ 5.083122e+010/1/-20/0 params=1/2.4/-1/2.6/0/0/0/0 float=y maxiter=3000 inside=0 logmap=346 periodicity=10 mathtolerance=0.05/1 colors=000K5cK5cK5cK5cK5cK5cK5cK6cK7cK8cK9cLBcLDcL\ FcLHcLJcJIcHHcGFc1Ec2Dc4Cc5Bc7Ac9DZAFTBIOBMJEQKHSL\ KTMMUNPUOSROVNPXJQ_FRbBSe7Tg4TjBUlHVnNWpUXr_YteZi`\ VZWROSODNK3JH6HK9GNBFQEDTGCWJBZLA`O8cR7fT6iW4lY3o`\ 2rb1t`6s_AsZEsYJsXNsWRsVVsU_sTcsSgsRlsQpsPtsOxsMwm\ LvhJucItZGsTFrODqJCpEBp9EoCGoEInGKnJMnLOmNQmPSmSzz\ UzwWzrZzn`wkbmkddhbdf`ecZeaXfZVfXTfVRgSPgQNhNLhLJi\ IHVTmUZaUdRUjFUp4QoBNnHKmNHlTEk_Bjz8iz5hz6fr6dj7be\ 7``8ZV8YR8WN9UI9SEAQ9AO5AN1CO2DO2FP3GP3IQ4JQ4LR5MR\ 5NS5PS6QT6ST7TU7VU8cV8mV8vRBzODzLFzIHzEJzBLz8Nv5Pd\ AKNFG5JC4KE4LG4MI3NK3OL3PN3QP2RR2ST2TU1UW1VY1W_1W`\ 3XY5YW6ZU8ZSA_QB`ODaMFaKGbIIcGKdELdCNeAPf8Qf6Td8Vc\ 9YbA_`Cb_DdZEfYFYVPPSZGPh8Nr9Ft9Fv9KwBPrDUnFZjGchI\ hmKmrLrvNvzPzzzzJSzzUzzzz7Xzzzz7SzzzzDOzzMzzzzMIzz\ FzzzzWBzz9zzzzd5zz3zzzzh8zzzzeCzzEzzzz`JzzLzzzzWPz\ zRzzzzSWzzYzzzzaazzczgzzk } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 25-03-09 (Spring Has Sprung [6])
by Jim Muth 25 Mar '09

25 Mar '09

FOTD -- March 25, 2009 (Rating 6) Fractal visionaries and enthusiasts: A couple days ago Ted wrote that there are times when my rating system makes it really hard to believe that the system exists as something coherent and predictable, hopefully unaffected by the weather, my mood, or the stock market fluctuations. There is a good reason why this is so. My rating system is totally arbitrary, not at all coherent and predictable, with no scientific validity at all, and very much affected by my mood at the moment I decide on the rating. The original letter continues: A coherent rating system would mean a system which takes into account a set of different aspects of the rated object, evaluates some of the most signifi- cant, and by combining these values, offers a usable way of placing the rating of the object somewhere between 'Isn't it wonderful!' and 'What a waste!'. If I rated the images like this, it would be too close to doing statistical science to be much fun. I try to avoid doing things in a scientific manner as much as possible. It makes life far too scientific and far too little fun. For example, look at the trouble I have had since 2001 trying to convince hard-core skeptics that a form of precognition does in fact exist. Their devotion to a rational skeptical view forms a mental block that is almost impossible for them to overcome. (If they even wanted to overcome it.) By contrast, by avoiding the rational approach, I can indulge in far more interesting and outlandish ideas such as the possibil- ity that the universe is a fractal being constantly recalculated on God's cosmic computer. There is more to the original letter, and I'll have more to say about it in future FOTD's. Today's image came about when I calculated the Mandeloid formula Z^(2.01)+C at PI levels up the logarithmic ladder. At this transcendental level the parent fractal is a Mandelbrot set that has split apart on the west side and rotated a few degrees clockwise. Today's image is located in an area of chaos between the two split-apart parts of the main bud of the parent. I named the image "Spring Has Sprung". Its quality is about average, thus the rating of a 6. The name came to mind when I noticed the first yellow daffodil of the season in bloom this afternoon. The calculation time of 55 seconds makes calculating the image a pleasure. Equally joyful is the trip to view the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday dawned clear and cold, with a very un-springlike tempera- ture of 19F -7C, but by afternoon the strong sun had warmed it to 48F +9C and the light winds made the day quite pleasant. The fractal cats agreed as they competed for the best spot on the shelf by the sunny window. My day was rather busy. Tomorrow is likely to be even busier. The next FOTD will be posted in 24 hours. Until then, take care, and when will the common man see the benefits of the space program. Or perhaps the question should be, "where are the much hyped benefits of the space program?" Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Spring_Has_Sprung { ; time=0:00:55.64-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=-1.242701290941315/+0.0883396256393417/\ 1.217e+007/1/-85/0 params=2.01/0/3.14159265358979/0 maxiter=1500 inside=0 logmap=88 periodicity=10 colors=000Bsq5xx3oi1fW0YI8_MGaQOcUWeXcg`kidskhzmkr\ p_jsOcqC_mFWhHTbJPXLLRNILPEFRB9TDDXEG`FKdGNhHQkFRj\ DRiCRiENeGKaIHZKEVMBSG_XBw`CncDfeEYhEQjFHmG9oG1qL1\ kP1eT1`X1V`1Pd1Kh1El19Z4HL6P88WJ9bTAicBpmCwbQqSckI\ qfKmhLijMelIceFa_C`UldOUmaBuo8jk6_g4Qc2F_05W9C`HJd\ QQiYXmebqf_pgYphVphToiQojOojMoXG`KBM76884B83D92G91\ IC8JFEJIKKLQKOXLRbLUhMXnMSdKNVIILGDBE81DE9KJHQPOXU\ WbZbhQZyP`xPawPcwPdvOeuOguOhtOitLfoIdjFbeC`a9YX6WS\ 3UN0SJ1QO1OS1MX1K`1Ie1GiCLZMQOWUDTOIRINwo`lpWapSRq\ NGqJ5qF6oG6nH7mI7lI7kJ8jK8iL8hLB`ODTQFLTHDVJ6XX7Qi\ 8Jv8CmEDeJDXODPTDGYD8bDEcCJcCPdCUdCZeCdeCifCnfCphM\ qjVslctnlupunmrhjpbhnXelRcjL`hFZfHZZJZSLZLMZET`BZb\ 8dd5je3NchOgcPkZUvZXu__t`btadsbgrcjrdmqeopfrpguohx\ niznjvoisphophlqghrferfaseZtdUfTWdUYbW_`YaZ_cX`eVb\ gTdiRekOMlL3gR9cWE_`KWePSjVOo_Upd_pheqlkqqqruvryip\ vYnsLlp9kmBilDgkVbWPgcImj } 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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FOTD 15-03-09 (Waiting for Autumn [4])
by Jim Muth 25 Mar '09

25 Mar '09

FOTD -- March 15, 2008 (Rating 4) Fractal visionaries and enthusiasts: So today's image rates only a 4. What's wrong with a rating of a 4? I could rate it no higher because I put absolutely zero effort into the coloring. All the work was done by the Fractint program, which as today's image almost shows, sometimes creates unexpectedly good colors. The parent fractal was created when I subtracted 2 parts of Z^(-1.2) from 1/2 part of Z^(-5) and added (1/C). This parent is an oversized thing with a huge 'fan'. It is totally beyond verbal description, but may easily be seen by outzooming and turning off the logmap. I think today's scene is located near a larger minibrot in the East Valley area of a still larger mini- brot near the edge of the 'fan' of the parent fractal. Tha name "Waiting for Autumn" makes no sense at all, except for those who live in the Southern Hemisphere. Up here on the 'top' side of the globe, we're waiting for spring. I admit that the calculation time of 6-1/4 minutes is on the slow side, but watching fractals calculate is almost fun. Those not amused by this kind of fun may find satisfaction on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is or soon will be posted for instant gratification. The high temperature of 54F 12C made up for the hazy skies and weak sun here at Fractal Central on Saturday. But Nicholas, the oversized black British Shorthair fractal cat took little notice. He spent most of the day nursing his sore tail, which somehow got caught behind a closing door this morning. Given several extra treats of tuna, both Nicholas and his tail will survive. Cassie, the small blue-cream calico, bristled to twice her size when she heard Nicholas yell when his tail got caught in the door. But she soon deflated, and by evening all was forgotten and forgiven, with two contented cats curled on the living room rug. Except for the cat excitement, my day was average. The next FOTD will be posted in 24 hours. Until then, take care, and it's all relative. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Waiting_for_Autumn { ; time=0:06:15.63-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.21769662256/+16.35446828055/141603/1\ /50/0 params=0.5/-5/-2/-1.2/0/0/0/0 float=y maxiter=3400 inside=0 logmap=394 periodicity=10 colors=000IfVJcUK`SLYQMVONTNLSVJRbIQiGPqFPxOYnXfed\ nXemZgk_iiajhclfenegociqbks`mziswdpt_nqVkrPjnRikSi\ hTieUiaViZWiWYiTZiP_iM`iJaiCcmF`XG`_H`aI`dJ`fK`iL`\ kM`m1GJ6FOAFSEFXIE`MEeQEiUEmYIh`LccOZfRUiUPmXKp_Fs\ bAve5yh1xk9xmHwoOwqWwsbrpXnnRjlLfjFbh9Zf3bg4eh4hh4\ ki4ni4kh7ih9ghCehEcgGagJ_gLYgNafQdeShdVkcXob_raaxX\ 1nT8eQEWMLNJRDFY4Cc9AYD9TH8NM7IQ6CU57Y42fW4nw6ks8h\ p9emBbjC_gEXdFUaHRZIOWJLTLIQMFNOCKP9HR6ES3BT5CR7DP\ 8ENAFMBGKDHIEIHGJFIKDJLCLMAMN8OO7PP5RQ3SR2WU6ZXAbZ\ DeaHidLlfOpiSslWvnZbhTJbO0XJ6_HCaFIdENfCTiBZk9dn8i\ p6os5uu3zw2ys4yo5xl7xh8weAwaBvZDvVEuRFuOHtKItHKsDL\ sANr6Or3Pl4Rg5Sb6TY7UT8WO9XJAYEBZHCYJCYMCYOCYRCYTC\ YWCYYCY`CYbCYdCYeGVfKTfNRgRPgVNhYKhaIieGihEjlCjoAf\ qEcsH`uLYwOVxSSyVPzZMzaJzdNz`zzYzzVzzSzzPzzMzzJzzG\ zzDzzAzz7zz4zz7zzAzzCzzFzzI`zKYzNVzQSzSPzVMzYJz_Gz\ bDzeAzgCzeDzcEzaFz`GzZHzX } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 24-03-09 (Stinging Jellyfish [N.A.])
by Jim Muth 23 Mar '09

23 Mar '09

FOTD -- March 24, 2009 (Rating N.A.) Fractal visionaries and enthusiasts: I gave today's image no rating because it is not a new image. It is merely a slight modification of an FOTD image that I posted several years ago. I'll leave it to the curious to track down the original image. I occasionally re-use older images when I run into bad luck finding a worthy new one and time is running short. I named the image "Stinging Jellyfish" when I remembered a day on the shore of Chesapeake Bay many years ago, when I leaped into the water and found myself in a bunch of "sea-nettles". Of course, this name has nothing to do with today's image, nor does it have any similarity to the name of the original image. As for the parent fractal, the image is the parent fractal, a Julia set of the Z^(1.11)+C Mandeloid as it appears 111 levels up the logarithmic ladder. With a calculation time of 1-1/4 minutes, the image is a fast one, bringing no grief to those who would rather do it them- selves. Those spoiled by modern conveniences may see the image already finished on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where unimaginable happiness can be found. The crystal blue skies and brilliant sun were diminished by an un-springlike temperature of 36F 2C here at Fractal Central on Monday, with a very un-springlike low of 14F -10C forecast for Monday night. Not bothered by technicalities, the fractal cats enjoyed the sun while it was shining on their window shelf. My day was about average. The next FOTD will be posted (by me) in 24 hours. Until then, take care, and believe the unbelievable. It just might be true. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Stinging_Jellyfish { ; time=0:01:14.62-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=JuliaBC passes=1 center-mag=-0.120052/\ -0.119167/1.35/1/-87.5/0 params=1.11/0/111/0/\ -0.041/0.146/0/0 float=y maxiter=256 inside=bof60 logmap=yes periodicity=10 colors=000edddcacbZaaW_`TY_QVZNSYKPXIMWHKVFIUDGTCE\ SACR9AQ78P6zzz00000000000000040M60O80R90T90W90YA0`\ A0cB4eB9hBDjCFmDGoEFrFFtGEwHImIHoJHpKGqKGrKGsKFuJF\ vHEwFEx4aG5ZL6XQ7UU8SZ9QbANgBLlCIpDGujgqzv0zt0zr0z\ pVznWzlYzjZzhUzgPzeKzcAza0z_0zY0zW0zU0zT0zR0zP0INr\ HLsGJuFHvEFxHs4Gq7Go9GmCGlEGjHGhJFfLFeOFcQFaTF_VFZ\ XEX_EVaETdESfEQiEOkDMmDLpDJrDHuDFwJW1IT9HRHGPOGNWF\ KcEIjDGruLIpKNkJSfIXaHaXHfSGkNFpIEu5QZ6P`6Ob7Nc7Ne\ 8Mf8Lh9Lj9KkAJmAInBIpBHrCGsCGuDFvDExaoeZjhWfjTblQZ\ nOUqLQsIMuoQDhVGa`KVeNNjQGpU9uX2z_EybQxe`xhlwkwwno\ shgpc_lZTiTLeODbJ6_EG`HQaJZbLc_KhYJmVIrTIsUPtVWuVb\ vWiwXpwXvoVuhUuaTtVRtOQsHPsKSlMVfPY`R`VUcOWfIZiC`k\ 6Xj9UiCQhFNgIKgLEcG8_B3W76YE8_LAaRG_MMZISYEYW9cV5h\ U1bW3YX5TZ7O_9JaBEbD9cETQHkCJeBL`ANW9PR8QM7SH6UC6V\ BQKBh9LiIViRdj_njhwjpWV`4FM8INCKOGMPJOPNRQRTRVVSYX\ S`aWbf_dkcfpghukjzorh`ySM } 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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FOTD 23-03-09 (Sticky Sickles [6])
by Jim Muth 22 Mar '09

22 Mar '09

FOTD -- March 23, 2009 (Rating 6) Fractal visionaries and enthusiasts: There was no FOTD for March 22 because FL and I took the day off on Saturday to go antiquing. FL found a 'great' victorian lamp shade at a 'great' price and ended the day happy. I ended the day exhausted. Today's image is kind of a bedraggled thing, a little past its prime magnitude and showing its wrinkles. But it's still worth a quick look, especially since it takes only 2 minutes to finish on a SOTA machine. The parent fractal is little more than a grossly oversized network of intertwined filaments, mixed with a few small open areas. Today's image is located near one of the open areas. I had something in mind when I named the image "Sticky Sickles", though I have completely forgotten what I was thinking of. I do see a series of sickle-shaped things surrounding the central minibrot however, so I guess this had something to do with the name. The rating of a 6 is a bit liberal, though not as liberal as you know what. In all honesty I can not claim that the image is any better than merely average. The image is a fast one. Equally fast is the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the already-calculated image is posted in completed form for instant bliss and moderate satisfaction. Too little sun broke through the clouds here at Fractal Central on Sunday to keep the fractal cats happy while we were away. The temperature of 54F 12C was close to normal, but the cats would have preferred more. When we got back around 7pm, the cats were at the door, scolding us for our absence. I'll post the next FOTD in 24 hours. Until then, take care, and how is it possible for people who are clearly wrong to know that they are right? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sticky_Sickles { ; time=0:02:03.06-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.00012589545750500/-0.104475908247942\ 80/2.3209e+013/1/-40/0 params=1/2/-0.4/-0.8/0/0/0/0 float=y maxiter=1200 inside=0 logmap=141 periodicity=10 mathtolerance=0.5/1 colors=000GAKHAMIBOJCQKDSLEUMFWNGYOH_PIaQJcRKeSLgS\ MiSNkSOmSPoNQqKRrPSpURmZPkcNghLdkJelKemMenPfoSfpUf\ qXfr_gsagtdgughvimwlrxovyqzZPzF76ICALHEOMIRRMUWQX`\ U_eYbja`dc_ZdZTfXNgWHiVBjU6kS6lR6lQ6lP6mO6mN6mM6nL\ 6nK6nJ6oI6oH6oG6pF6pE6pD6pKCoRInYNmdTlkZkqcjoefmfc\ kg`ihYgiUejRckOalL_mHYnEWoBVp8`n6el4jj2gh5df8beB_c\ EXbHV`KSZNPYQNWTKVWHTZFS`EUZDWYCXXCZWB`VAaUAcT9dS8\ fR8hQ7iP6kO6lN8kP9kQAkRBjSDjTEjUFiVGiWIiXJhYKhZLh_\ Mh`LfYKdVJcSIaPI_NHZKGXHFVEFUCJVBNWBQXBUYBXYBWXDWX\ EVXFVXGVXHUWJUWKTWLTWMTWNSVPSVQRVRRVSRVTSSRTQQUOPV\ MNWKMXILYGKZEI_CH`AGa8Fb6Dc4Cd2Bd0AiE8nS6se4wr2vo6\ um9tkCsiFrgIqeLpcOo`RnZUmXXlV_kTbjReiPhhNkjPjkRjlS\ imUinVipXhqZhr_gsagtbgvdfwffxgeyzezzevzgszipzjmzlj\ zmgzodzpazrZzsWzuTzvXzs_zqbznezlhzjkzgnzeqzbtz`wzZ\ szWpzUmzRjzPgzNdzKazIZzGXzTWzeVzdUzdTzdTzcSzcRzcRz\ cOzbMzaKz`Iz`KzZMzYOzX9zP } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 21-03-09 (End of the Spike [5])
by Jim Muth 20 Mar '09

20 Mar '09

FOTD -- March 21, 2009 (Rating 5) Fractal visionaries and enthusiasts: Be warned! There will be no FOTD for March 22. I promised FL we would go on an antiquing expedition on Saturday, and there is no way to get out of it. (Besides, I kind of enjoy browsing through the stuff [they call it collectibles] other people threw out.) The next FOTD will be posted on March 23. In today's image we return to the most famous of all fractals, the Mandelbrot set, where we focus our interest on a tiny mini- brot near the tip of the main spike. Today's scene lies on a filament extending from the large bud on the northwest shore line of the main bay of the tiny minibrot. There's not much more to be said about the image, which rates only an average 5 because of its excess familiarity. The name "End of the Spike" is a misnomer, since the spike has no real end. The minibrots on it keep growing smaller as the limit of 2 is approached, but never come to an end. The calculation time of the image is 3-3/4 minutes. Most of this time is due to the magnitude, which makes arbitrary preci- sion math necessary. But why fiddle with calculating when the completed image is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather was a bit chilly for the first day of spring here at Fractal Central on Friday. The temperature of 41F 5C and brisk north wind made it feel more like early February. The fractal cats soon grew disgusted with the continued coming and going of the sun, and instead of waiting for the last cloud to blow by, decided to worry us for an extra treat of tuna. needless to say, their persistence was rewarded. My day was moderately busy. With the antiquing trip coming up, there will be no FOTD for March 22. The next one will be for March 23. Until then, take care, and be skeptical of the things skeptics don't believe in. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= End_of_the_Spike { ; time=0:03:47.14-SF5 on P4-2000 reset=2004 type=mandel passes=t center-mag=-1.94142793652340829363/6.7334784052237\ 1681e-4/6.335316e+016/1/-157.5/0 params=0/0 float=y maxiter=2750 inside=0 logmap=284 periodicity=10 colors=000KFczz6zw3zoLzoNzmPzlRzgTziVviXriWmiVhiVc\ hUZgUUg`Zggggmqgtn`mvZhrRSmUQhWOcYNZ`LUbJPdIKgGIiE\ LkDNnBPp9Rr8TSH02Q07O0BM0GKTKITOGTTETXCT`ATe8Ti6Tm\ 4SlDSkLRiTRh`RghNfkKrzHozElzBiz8fzCezFczDazB`z9`z7\ Zx5Xu3Vw1Uy3Uw4Wv5Xu6Zs7`r8aq9boAbnBcmCdkDdjEeiFeh\ 95X95V85S85Q75N75L75J8LsqBKeSQVhWVmNVrFXpFZoF_mFal\ FbjFdiFfgFgfFidFjcFiaDi_CiZAhX9hW7hU6hT5eW8bZA_aDX\ dFUgIRiKOmNLqPIuSFyUCzX9zZExYJqXOiXSbWXWVaOVfIUjCU\ _ORQ_OFkL5wI8tKBqLEoNHlOJiQMgRPdTSbUU_WXXX_VZbS_dQ\ `_TcWWeSZgOaiJclFfnBip7lr3nt5dp6Wm7Mj8DgCBbF9YJ8TM\ 6OP5JLEKHNKDVL9cL5lM2tM5rN7qO9pOBoPEnQGmQIlRKkRNjS\ PiTRhTTgUVfUTcRSaOR_LQYJTZMWZPoedkgagiZdjX`lUXmRUo\ PQpzMrzJszMtzPuzSvzUwzzxKzyKzzLzzLzzLzzMzzMzzNzzNz\ zOzzOmzzmzzmzzmzzzzszzpzzmzzjzzgzzdzzbzzFzzGzzIzzJ\ zzKzzLzzNzzOzzPzzQzzQzzQzzQzzQzzQzzQzzQzzQGzQCzQ8z\ Q5zQ6zN6zL6zI6zG6zD6zB6z8 } END PARAMETER FILE=========================================

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Wrong formula in March 19 par file
by Jim Muth 20 Mar '09

20 Mar '09

Fractal fans: I put the wrong formula in the parameter file for the March 19 FOTD. Mistakes will happen especially in times of rush. I have included my basic.frm formula file, which contains most of the formulas I use for the FOTD images. Copy this formula file into your Fractint directory in text format with a .frm extension. If I put any more wrong formulas in the paramater file, the program will automatically go to the right formula. ========================================================= MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } 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 } DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } DivideBrot5Julia { ; Jim Muth z=pixel, c=(p2), a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } DivideBrot6Julia { ; Jim Muth z=pixel, c=(p3), a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } MandNewt12 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-1)*(z-b) j=c*z^d+g z=z-e*h/(f*j), .0000000000000000000000000000005 <= |h| } =================================================

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FOTD 20-03-09 (Looping Bridges [In Doubt])
by Jim Muth 19 Mar '09

19 Mar '09

FOTD -- March 20, 2009 (Rating in Doubt) Fractal visionaries and enthusiasts: Today's strange image is a scene in an almost-Julia set of the northeast shore line of the main bay of the Mandelbrot set. It is not part of a Julia set, nor is it part of a perturbed Mandelbrot set. It is an oblique slice through the Z^2+C Julibrot figure oriented within a degree or so of the Julia direction. The straight bright bar across the lower part of the scene is what I call a bridge. It appears straight because regardless of where Z is initialized in a perturbed M-set, the points will always settle into the same orbits unless they escape first. I had no idea how to rate such an image, so I left the rating in doubt. The name "Looping Bridges" describes the many loops and spirals dancing around the bridge. The calculation time of 2 minutes is thankfully fast, though the trip to see the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> could be even faster. A cloudy start gave way to a partly cloudy afternoon here at Fractal Central on Thursday. The fractal cats enjoyed the times when the sun was shining and made the best of things when it was not. The temperature hovered around 52F 11C most all afternoon. My day continued busy. The next FOTD will be posted in about 24 hours. Until then, take care, and look for light. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Looping_Bridges { ; time=0:02:08.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=t maxiter=18000 center-mag=0.00665081/0.170958/3.138989/1/-90/0 params=90/90.07/92.48/89.01/0.2438/0.5139/-0.0081/\ 0.5024/2/0 float=y inside=0 logmap=-3 periodicity=9 colors=000jRhh0efVbd0_bYX`AVZaSXKPVdMTKKRgHPKENkBK\ N4Ml9OMDQcHRLLTWQVKUXVYW0cYQaZ0`_NZ`0YaNXb0VcNUe0S\ fURg0QhVOi0NjSMk0KmTJn0HoVGphlqijrnCsXBtYDtYEzzFtz\ GtzHtZJtZKCzxCzxCzxDzxDzxDzxDzxEzxEzxEzxEzxFzxFzxF\ zxFzxGzwGzwGzwGzwHzwHzwHzwHzwIzwIzwIzwIzwJzwJzwJzw\ JzwKzwKzwKzwKzwLzxLzxLzxLzvMzxMzxMzxMzxNzxNzxNzyNz\ yOzyOzyOzyOzyPzyPzyPzyPzyQzyQzyQzyRzyRzyRzyRzzSzzS\ zzSzzSzzTzzTzzTzzTzzUzzUzzUzzUzzVzzVzzVzzVzzWzzWzz\ WzzWzzXzzXzzXzzXzzYzzYzzYzzYzzZzzZzzZzzZzz_zz_zz_z\ z_zz`zz`zz`zz`zzazzazzazzazzbzzbzzbzzbzzczzczzczzc\ zzdzzdzzdzzezzezzezzezzfzzfzzfzzfzzgzzgzzgzzgzzhzz\ hzzhzzhzzizzizzizzizzjzzjzzjzzjzzkzzkzzkzzkzzlzzlz\ zlzzlzzmzzmzzmzzmzznzznzznzznzzozzozzozzozzpzzpzzp\ zzpzzqzzqzzqzzqzzXzzXzzXzzYzzYzzYzzYzzYzzYzzYzzYzz\ YzzYzzYzzYzzYzzYzzZzzZzzZzzZzzZzzZzzZzzZzzZzzZzzZz\ zZzzZzz_zz_zz_zz_zz_zz_zz } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 19-03-09 (Seahorse-Plus [8])
by Jim Muth 19 Mar '09

19 Mar '09

FOTD -- March 19, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a view of the very well-known Julia set of Seahorse Valley of the Mandelbrot set. For some reason however it doesn't look like that Julia set. The weirdness arises because the Mandelbrot set is an augmented one, with much extra stuff surrounding it. So it should be no surprise that the Julia set of its Seahorse Valley has all this extra stuff around it. The expected Julia set actually lies at the center of the image, though it is somewhat obscured by all the extra detail filling it. The image was rendered with the outside set to 'imag' and the inside set to the color 255. Setting the outside to 'atan' also gives a pretty good image. I named the image "Seahorse-Plus" and rated it at an 8. The calculation time of 9-1/4 minutes is a bit slower than ideal, but may be avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday began with fog and murky low overcast here at Fractal Central, but by 10am the sky quickly cleared, leading to a most spectacular sunny afternoon, with a temperature of 68F 20C and gentle south breezes. Needless to say, the fractal cats purred their satisfaction with the conditions. My day was too busy to allow as much enjoyment of the conditions as I would have liked. The work will be slower tomorrow, but the weather will likely be much less pleasant. The next FOTD will be posted in 24 hours. Until then, take care, and why are so many simple questions unanswerable? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse-Plus { ; time=0:09:14.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6Julia center-mag=0/0/0.2993 params=-32/36/1e-016/0/-0.75007/0.007 float=y maxiter=5000 inside=255 outside=imag symmetry=origin periodicity=10 colors=0008Xz9WxAVuAUsBTqCSoCRmDQkEPiEOhFNfGMcGLaH\ KZHJYIIVJHLJGIKELLCOLAMM8KN6IN4GO3EO2CQ3AS48U59W6B\ X7CZ8D`9FbAGdBHeCIgDKiELkFMmGOnHPpIQrJStKTvLUxNUwM\ VwMWvMWvMXuLXuLYtLYtLZsKZsK_rK_rK`qJaqJapJbpJboIco\ IcnIdnIdmHemHemHflHglGgkGhkGhjGijFiiFjiFjhFkhEkgEl\ gEmfEmfDneDneDodDodCpcCpcCqaDxbCtcCqdCneCkfBhgBegB\ bhB_iBXjAUkARlAOmALmAInCJlDKnELfGMgHNiIOcJPbJQcFRd\ 8SdETiBUiHVnDWnCXoFYoHZoJ_oL`oOaoQboScoUdoXeoZfo`g\ obhoeiogjoiknmjomkolkokkokkpjkpikphkphkpgkqfkqekqe\ kqdkqckrbkrbkrakr`lr`ls_lsZlsYlsYlsXltWltVltVltUlu\ TluSluSluRluQlvPlvPlvOmvNmvNmwMmwLmwKmwKmwJmxImxHm\ xHmxGmxFmyEmyEmyDmyCmyCmxHixLfxQbwU_wZWwbTuYPsUMqQ\ JoLFmHCkD9nHEqLJtPOvSSmYOebKXhGPmCLnJInPFoVBo`8pf5\ pl2prBfgKXXTNMaDBi41dA4`G7XMATSDPYGLcJHiMDoOYYUqG_\ oGamFdkFfiEhgEjeDmcCoaCq_BtYBvWAxVAzWHnXObYURZ`FZf\ 3Zg8ZgCZhH9Hr9Kq9Op9Rp9Uo } frm:DivideBrot5Julia { ; Jim Muth z=pixel, c=(p2), a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 18-03-09 (The Warm Fuzzies [7.5])
by Jim Muth 17 Mar '09

17 Mar '09

FOTD -- March 18, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Warm fuzzy feelings are what one gets when they go to a benefit concert to help the victims of some disaster, where the produc- ers get a bundle of money, the attendees hear some acceptable music and the victims get little or nothing. Today's image has a kind of warm-fuzzy feeling about it. This was all the reason I needed to name it "The Warm Fuzzies". The rating of a 7.5 includes a 1/2 point bonus for my semi-expert coloring. (The fuzzy appearance was not all that easy to bring about.) The parent fractal is a Mandelbrot set surrounded by superfluous rings of fractal stuff, which increase in number as the set is approached. Today's scene is found in one of these rings in the north branch of Seahorse Valley of the parent. The tiny value of the real(p2) parameter is very critical. The bailout radius of 4, set by the imag(p2) parameter of -12, is also critical. The calculation will take all of 30 seconds on a SOTA computer. On an older unit it will take only a couple minutes. But all calculating cares may be dispensed with by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Lots of warm sun, a temperature of 59F 15C and a gentle south wind made the fractal cats very happy here at Fractal Central on Tuesday. Work that was well under control made me very happy. FL was happy because I agreed that we would go antiquing this Saturday as long as we avoid places selling the non-antique, phony-country, warm-fuzzy, feel-good stuff known as 'primitives'. The next FOTD will be posted in 24 hours, which should keep the fractal fans happy. Until then, take care, laugh often, live long, and eat hearty. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Warm_Fuzzies { ; time=0:00:30.43-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 center-mag=-0.769024762174\ 031/+0.1886307303294928/1.397934e+008/1/152.5/0 params=-63/67/1e-018/-12 float=y maxiter=1500 inside=0 outside=summ logmap=49 periodicity=10 colors=000NsrqtrruttwvuxwvtsvppwllwiiweexabxYZzVWm\ OXbIRSCII6QGA0EVTCfSTTLiFFz19w68uB7rG6pL5mQ4kV3h_2\ fm1gZ2hU3zc4jL5kG6lC6dIHXOSQTaIZlBcvHdpNdkTdfZd`dd\ WidRceTZeVUeWPeYKe_Fe`Aeb5ecDfZKfURgPYgKdhFkhBefF_\ dIVbLPaOJ_SEYV8WY3V`7SZAPYDMWGJVJGTMDSPAQS7PRDVQJ`\ POeOUkN_qNdvXTrfHno5kpDmqLorTqs`sshuUdgScVQbJPa7Rc\ 5Se3Tf1Sg5Sh8bBYlASv9MrDJnGGkJEgMBcP8`S6aZ5be5ck4d\ r4dx4_r5Vm6Qh6Lc7HZ7LbAOfCSjEVnGZrJavLezNhzPMbqPnh\ Sy_RvVRsRRpNRmJRjERgARd6Rb2PTJNJ_MAoVCqcEslGuuHvvT\ jvc_voPvzEqqDlhDg`DbSDYKDaLHdMLhNPkOTzzXzz`zzczzfz\ zizzlzz`zzazzbzzczzczzdzzezzezzfzzgzzgzzhzzizzizzj\ zzkzzazzbzzczzczzdzzezzezzfzzfzzgBzhAzh9zizzjzzjzz\ kzzazzYzzVzzSzzOzzLzzIzzMzzPzzSKzVKzYKz`JzcJzfJziJ\ zl`zTrzAlzKfzT`zbVzkPztQzgRzVSzISz5KzECzN5zVnzGlzR\ kz`izjhztKzhJzmIzqHzuHzyGzxGzxGzxGzxGzxFzxFzxFzxFz\ xFzxEzxEzxEzxEzxEzxHzvKzt } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 17-03-09 (The Faces of Fear [6])
by Jim Muth 16 Mar '09

16 Mar '09

FOTD -- March 17, 2009 (Rating 6) Fractal visionaries and enthusiasts: The name of today's image, "The Faces of Fear", sounds something like the name of one of those 'shocking' reality shows that fill the TV programming. But the name is fully justified. The first thing I noticed when I saw the finished image was the ring of stylized but terrified profiles of human faces surrounding the central minibrot. These profiles are most obvious in the lower left part of the image. All this fear was generated when I combined 7.5 parts of Z^(-0.5) with 0.75 part of Z^(-5), added (1/C) and iterated the mixture with a bailout radius of 40. The parent fractal is little more than an empty circle with something that looks like a lobster claw on its northeast shoreline. There is an obvious mandel-type bud in this claw however, with a curving filament extending from it. Today's scene is located far out on this filament, near the point where it terminates. The rating of a 6 is near what I think the image is worth. The calculation time of only 39 seconds makes running the included parameter file quite a bargain. But the best bargain of all can be found on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the image already has been or soon will be calculated and posted for immediate viewing pleasure. The temperature of 54F 12C was fair enough here at Fractal Central on Monday, but the cloudy skies totally failed to satisfy the fractal cats, who spent most of the day in the living room, sulking conspicuously. The treat of tuna cheered them some, though they still would have preferred an afternoon in the sun on their sun shelf. My day was average, which means just enough work to keep boredom away. I'll post the next FOTD in 24 hours. Until then, take care, and when one is young, science has the all answers. But the older one grows, the fewer questions science can answer. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Faces_of_Fear { ; time=0:00:39.41-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.3338053113603147/+0.0914822065138245\ /3.05e+010/1/-22.5/0 params=7.5/-0.5/0.75/-5/0/-60\ /0/0 float=y maxiter=1600 inside=253 outside=tdis logmap=17 periodicity=10 mathtolerance=0.05/1 colors=000x3ON7s53z79u9FqBLmDRiFXeHaaQdeYgifjlnmpv\ os6Yu7Vq8Tm9QjAOfBMb00KTJOSFOCERkSnoZosdpzzzzzzzoX\ weBwYHtRMlLSbHXZDbVAgPGZJMQDSHczcZjfadie_khUnlPpoJ\ srEujLvbRwVXzObxGhy8nz1tz9frGTjNFbU2VX5T_8RbBQeEOh\ HMjJLiPZhUlgZzfXtfWzfUhfTcfRYfQSfOMfNHXPTORcSPYWOS\ _NNcLHgKCkJ6nI1TqAMnFFlK9jPBeSCaVDYYEU`GQcHMfIIiJE\ kLIiMLhOPgPSfQVdSZcTabUdam2Xm3Ym3Ym4Ym4Ym4YeB_ZH`S\ OaLUbE`c7fd0le2gf3cf5_g6Wg8Sh9OhBKiCGiLW_UkRazIawQ\ atXaqcankakrahybfwbdubcsbaqb`obZmbYlgXhlXeqWbuW_Wg\ f6smHpdSmWbjNmgExe5rcBlaHg_NaZSXXYRVcMUhLThJSgHRfG\ QfEPeCOdBNd9Mc7Lb6Kb4Ja2I`1H`DBkP6uJBdDGO7L8AI9CGA\ FEAHBBK9BM7CP4CR2DT0DSAKRJRWghNkcEp_6tWEoYMk_Ugaac\ ch_eYhdNqcDzbHtcLncPhcSbcWXc_RcbLccIVdGMeEDeC4`ICW\ NKRTSMY_IbfHdhGejFflEgnDhpCirCjtEisGisIisJisIloHnl\ GpiFsfaRZcYXVSRMNMDIG4DBFKAQR9`Y8kd7vk6tfDsaJrXQqS\ WpOahVd``fUfhiNYZfzeaNkfH } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 16-03-09 (Beige Blunder [5])
by Jim Muth 15 Mar '09

15 Mar '09

FOTD -- March 16, 2009 (Rating 5) Fractal visionaries and enthusiasts: I named today's image "Beige Blunder" when something went wrong with the coloring. The parent fractal was created when I combined 7.5 negative parts of Z^(-1.3) with 3.25 positive parts of Z^(-3.3) and added (1/C). This parent fractal is basically a huge 'fan'. In fact, that's just about all there is to it. Actually, I think I have a tendency to color my fractal images a bit too intensely, so the more subdued colors of today's image might not be as big a blunder as I implied in the name. Today's scene is located in a tiny valley near the origin of the parent. I rated it at a 5, which might be a bit conservative. The calculation time of 13-1/3 minutes is slow, so I recommend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday began cloudy but soon turned clear and sunny here at Fractal Central. The hazy, sunny afternoon with a temperature of 59F 15C seemed almost like a day in mid-autumn. The fractal cats, well settled after Saturday's excitement, passed the afternoon on their shelf in the sunny window. I passed the day doing as close to nothing as I could manage. FL thought of an antiquing trip, but when I began discussing quantum mechanics, soon forgot it. I'll post the next, but far from the last, FOTD in 24 hours. Until then, take care, and together we can save the world from something. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Beige_Blunder { ; time=0:13:21.22-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+4.253333487671743/+0.3674515879141611/\ 6e+007/1/122.5/0 params=-7.5/-1.3/3.25/-3.3/0/0/0/0 maxiter=18000 inside=0 outside=tdis periodicity=10 colors=000zruWMLWLLWLMWKNWKNWJOVINWJOWJOWKPWKPXLPX\ LQXLQXMRXMRYNRYNSYNSYOSYOTZPTZPUZPUZQUZQV_RV_RW_SW\ _SX_SZ`T_`Tc`Ue`Ug`UkaVoaVvaW_dY_cY`dY_dZZeYZeZYdZ\ YcYXaXW`VW_UV_TVZSUZRTZQTYPSYOSYNRXNQXMQXLPXJPWOOW\ OOWNNVNMVMMVMLVLLULKULJUKJTKITJITJHSJGSIGSIFSHFRHE\ RHDRGDQGCQFCQFBPE8QFAQFBRFDRFERGGSGHSGJTGKTGLTHNUH\ OUHQVHRVITVIUWIVWIXXIYXJ_XJ`YJbYJcYJdOCQB59E6BG6DI\ 6FK6HM7JO7LQ7NS7PU8QW8SY8U_8Wa9Yc9_e9ag9ciAdkAfmAh\ oAjqBlsBnuBpwBryBsxCrxDrxErxErxFrxGrxGrxHrxIrxIrwJ\ qwKqwKqwLqwMqwMqwNqwOqwPqwPqvQpvRpvRpvSpvTpvTpvUpv\ VpvVpvWpuXouXouYouZou_ou_ou`ouaouaoubotcntcntdnten\ tentfntgntgnthntintinrjoqjopjonjomkolkokkoikohlpgl\ pflpdlpclpbmp`mp_mpZmpYnqWnqVnqUnqToqRoqQoqPoqNnrO\ oqOoqPoqPoqQoqQopRopRppRppSppSppTpoTpoUpoUpoVqoVqo\ VqnWqnWqnXqnXqnYqmYrmZrmZrmZrm_rm_rl`rl`rlaslaslbs\ lbskbskcskcskXOIXOJXNJWMK } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 14-03-09 (Beyond all Limits [5])
by Jim Muth 13 Mar '09

13 Mar '09

FOTD -- March 14, 2009 (Rating 5) Fractal visionaries and enthusiasts: Today's image is as far as we can go into the center of the Hyper-Mandelbrot thing that appeared as yesterday's FOTD. Even at the incredible magnitude of almost 2*(10^14) there is no end in sight to the bottomless pit, which appears to go on to infini- tesimal infinity, with new scenery all along the way. The math- tolerance entry in the parameter file is necessary to assure that the image calculates at the extreme magnitude, which is actually a little beyond the limit of full definition. I named the image "Beyond all Limits" because there appears to be no end in sight. Then I gave it a rating of a 5. It's hard to give a higher rating to the third consecutive view of the same object. The calculation time of 3-2/3 minutes is easy to live with, as is the trip to enjoy the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A rather pleasant but slightly chilly late winter day prevailed here at Fractal Central on Friday. The fractal cats enthusiasti- cally approved the brilliant warm sunlight that flooded their window shelf all afternoon, while I interrupted my work several times to also enjoy the cheerful show. Unless some weekend distraction, such as an antiquing trip, arises, I'll post the next FOTD in 24 hours. Until then, take care, and what will we turn to when we outgrow science? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Beyond_all_Limits { ; time=0:03:41.07-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 center-mag=+0.2527592\ 487851626/-0.0002262879051008/1.578045e+014/1/-87/0 params=0/0/0/0/-4.085/0/1e-015/0 float=y inside=0 maxiter=2400 logmap=1319 periodicity=0 mathtolerance=0.05/1 colors=0009iZAgWBdSCaPDYLEVIFSEGPBHN7HL4GK7FKAELDD\ MGCNJBOMAQP9RS8SV7TY6U`5Vc4We8Z_C`VGcQKeKOhFRjAQlD\ PnGOoJNqMMsPMtSOuRPuQRuQSuPUvOVvOXvNYvM_wM`wLbwKcw\ KPQnIANCBO6CPADQEGRHISIKTJMUKOVLQWDSX5VY6Y_6``6ca6\ fX7iS7lN7oI7qEBoFFlGJhHNcIRZJVUJZPKbKLfFMjANn5Or1O\ q2Mp3Lo3Ko4In4Hm5Gl5El6Dk6Cj7Ai79i88h86g95g94iG5kN\ 5lT6n_6oe7ql7rr7giIY`SNSbDJl3BvSnEZoCeqBls9rt8TkC3\ bFDaJN`NWaRe`Vo_ZsaXucUwdLyfCzh4ze3za2zY1zT0xPHsJI\ jKKhILzzMSJOVHPZFQaDSeBTh9Ul7Wo5Xs3Yv1Zw2_w3`w3aw4\ bx4cx5dx5dx6ex7fy7gy8hy8iy9jy9jqDijHhcLgXOgVQhTShR\ ViPXjNZkL`lJbmHdnFfoDhoSRue9zdCwcFubIsaLq`Oo_RmZUj\ YXhX_fWbdVebUh`UkZPaXLSWGIVC8UF7VH7WJ7WL6XO6YQ6YS6\ ZU5_W5_Z5``4ab4ad4bf4bTNNFd8IXKLQzOczRBz0gH4hG8hGB\ iGFiGJjGMjGQkFTkFXlF`lFcmFgmFjmFcXyZasUemPihKnbFrX\ BvSAzUAzWmzXzzZzz_zzazzbzzdzzezzgzzhzzjzzkzzmzznzz\ lzzjzzhzzgzzfzzezzezzdzzc } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 13-03-09 (On the Inside [7])
by Jim Muth 12 Mar '09

12 Mar '09

FOTD -- March 18, 2009 (Rating 7) Fractal visionaries and enthusiasts: In yesterday's brief discussion I commented that the center of yesterday's image looked interesting. Since then, a quick inspection has shown that the center of yesterday's image is indeed interesting. Today's scene is a blow-up of the eye-shaped object at the center of yesterday's image. At first glance it appears to have 6-way symmetry around the center, but a closer examination will reveal that the symmetry is actually 3-way, with only the opposing arms being similar. An even closer exam will show that there is no symmetry at all. The whole thing is an illusion. So enjoy the illusion of symmetry while it lasts. I suspect that even more interesting things lie deeper in the center of today's image, and I'll check there later today. Unfortunately, we are already near the limit of resolution, so I'm not sure how much deeper I'll be able to go. The rating of a 7 is based mostly on the unusual mathematical aspects of the image. The name "On the Inside" indicates the location of the image with respect to yesterday's image. The calculation time of 1-1/2 minutes is reasonable enough to please a rationalist who enjoys fractals. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will please the more credulous. Winter staged a sudden return here at Fractal Central on Thursday. The fractal cats staged a fine show of sulking when the sun failed to shine on their window shelf in the afternoon. Cassie asked me to turn on the sun; Nicholas just sulked. An extra large treat of tuna restored their normal cat moods. For me the day was busier than I would like to have seen, but not so busy that things got hectic. The next FOTD is due in 24 hours. I expect that it will actually be posted at that time. Until then, take care, and if we found extraterrestrial life, would it prove the believer's view that the universe was inten- tionally created to generate life, would it prove the skeptic's view that extremely unlikely things sometimes do happen, would it prove none of the above, would it prove both of the above, or would it prove nothing at all? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= On_the_Inside { ; time=0:01:28.01-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 periodicity=0 center-mag=+0.25275924878512120/-0.000226287905106\ 45/2.05197e+011/1/172.5/0 params=0/0/0/0/-4.085/0/\ 1e-015/0 float=y maxiter=1850 inside=0 logmap=840 colors=000XNsWOsVPsUQsTRsSSsRTsQUtPVvOWxNZvMbuLetK\ gsMjrOkqQlpSloUopUppWrp_tpcupgwpkxpozpszpwzpvzovyn\ uxmuwltukttjssisrhrqgrofqneqmdplcpkcoj_niXmhTlgQpj\ KlgNidQfaTbYW_VZWTaURcRPfOMiLJlIGoFDrCCr8Fr9IrALrB\ OrCTrDYrDbtEgvFlxGqzHvzIzzIzzHamGZhFWcET_DQYEOaFMd\ FKgGIjHGmHEpOHqPKpQKoRInSGmTElUFkWGjYHiaIheJhiKhmL\ hpLkmMlkNliOmgOmePncQnaQn`Ug`Ya_aW_eQfiKmmEsqAqoKo\ mUmkckimigcgeUecLcaQa_UaYZcWchUhmSlrQevO_zTUzYNzbH\ zgBzY5NYCKYIIYPFYVCY`AYg7Ym5YsCXnJXiPWdkH8dIGZINSJ\ VLKbFKiEIcDHZCFTCEODDMDDLEDJEDIFDGFDFGDDGDCGDBHD9H\ D8ID6ID5JD3JD2JD1zzQzzPzzOzzNzzNzzMuzLmzKdvKcrJbmI\ ahH`eH`eH`eI`eJ`eJ`eK`fL`fL`fM`fN`fN`fO`fOadNacNab\ NaaNa`Na_zbZzbYzbmzbzzbzzbzzbzzczzczzczzczzczzczzc\ zzdzzezzfzzgzzhzzizzjzzkzzlzzmzznzzozzmzzlzzkzzjzz\ izzhzzgzzezzdzzczzbzzazz`zz_zzZzzXzzWzzVzzUzzTzzSz\ zwzzvzzvzzuzztzzszzrzzrzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 12-03-09 (The Fourth Dimension [Rating 6])
by Jim Muth 12 Mar '09

12 Mar '09

FOTD -- March 12, 2009 (Rating 6) Fractal visionaries and enthusiasts: Due to a hyper work rush, today's scene in the HyperMandelbrot set is being posted 12 hours late. Once again, I have no idea of what's going on here. All I know about the image is that it's something different, which I have never seen in the perturbed two-dimensional M-sets. And that little thing at the center looks interesting also. I might check it later today. If I find anything interesting there, it might appear as tomorrow's FOTD. Today's image rates only a 6. I named it "The Fourth Dimension" because it is obviously a scene in a higher-dimensional object. The calculation time of 2 minutes will pass in a flash for the true fractal fan. The trip to see the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will pass in another flash. Due to the work rush, a pleasant late winter day here at Fractal Central on Wednesday passed almost un-noticed by me. The partly cloudy skies and temperature of 63F 17C kept the fractal cats on their window shelf most all afternoon however. With today's FOTD so late, the next FOTD will be due in only 12 hours. Whether it actually is posted is anybody's guess. Until next time, whenever that is, take care, and stick with those stem cells. They can cure anything. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheFourthDimension { ; time=0:02:08.35-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 center-mag=+0.2527592\ 50409/-0.000226286238/1.760141e+007/1/-150/0 params=0/0/0/0/-4.085/0/1e-015/0 float=y maxiter=5000 inside=0 outside=real periodicity=0 colors=000XXKceAjm1dg4Zb6TY8NTAHODBJF5EH09JdJlaPm_\ UnXZoVdpSiqQnrOsrMnmKikJdiI`gHYeGVcFSaEP_DMYEKaFId\ FGgGEjHCmHApODqPGpQGoREnSCmTAlUBkWCjYDiaEheFhiGhmH\ hpHkmIlkJliKmgKmeLncMnaMn`Qg`Ua_YW_aQfeKmiEsm9XOuY\ SiZVY_ZM_aB`XG`SLaNQaJUaEZb9cb4hb0l`5eZ9_XDUVINTMH\ RQBQU5NUCKUIIUPFUVCU`AUg7Um5UsCTnJTiPSdWS`bSWhRRmR\ MqRIpNJjJKcFK_BLT7MP4MK9SJEXLIaMNgORlPWqQ_vOcmMghK\ kcKoZKnUKiPKdSK`VKWZKRaKNdKUhK`lKfoKmsJsvMlqOemQZh\ SSdVL_XEWZ7R`1NRHKIWI9jF0yD8hFGSHNaPTjXZscbkZfdVgY\ QeQM_JHdCDg59jABlFDmKFkPGgUIdZKacLZhTcm_hsgmxnrzov\ zrzzzzzzV2MX1HZ0B`06_14_23_32_41_40Yr7ap5en4im3mk2\ qi1uh0QPKaaSln_wzfntbeoZYiVPdRGZN8UJ53L9vxCrpEoiHk\ bJhWMeOOaHRZATW3X_B`cJcfRgjZjmehlgflhdkibkj`kkZjlX\ jmWjn`ajqeAkZReTg7I1MLVaKx_NwZQvXTuWWtVZsUWnUTiTQd\ TN_SKVPDWRFTSHRTIPUKMVMKWNIYNN_NR`NVbN_cNceNggLnfN\ kfOhePfeQcdS`dTZcUWOSUQOU } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 10-03-09 (Mandelbrot or Not [7])
by Jim Muth 11 Mar '09

11 Mar '09

FOTD -- March 10, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image might be real or it might be an artifact, but whatever it is, it's interesting. I named it "Mandelbrot or Not?" because it might be a real scene in the Hyper-Mandelbrot set, or it might be an artifact of the rather strange HyperMan- delbrot2 formula that creates it. The scene is located on a filament extending from the northeast shore of the main bay of the large minibrot on the main spike of the parent fractal, which is basically a fancy M-set. The object in the image is a minibrot, or at least it is sup- posed to be one. And at any distance from the minibrot there is nothing unusual in sight, but as the minibrot is approached, something goes awry. The original shore line of the minibrot has become diffuse and spread into the interior, where it forms something entirely new. I guess the thing in the image is better called a hyperminibrot. The rating of a 7 seems about right, considering that this type of effect has appeared several times already in FOTD images. The calculation time of 21 seconds is fast enough to make the effort worthwhile. And as always, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies, brisk winds, and a temperature of 54F 12C made Monday a rather pleasant March day here at Fractal Central -- at least the fractal cats thought so. My day was fair enough -- once the work was out of the way, that is. I'll post the next FOTD in 24 hours. Until then, take care, and the best is always yet to come. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandelbrot_or_Not? { ; time=0:00:21.44-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 inside=0 center-mag=-1.74593089071/+0.0201490666/328965.8/\ 1/-84.44/0 params=0/0/0/0/-4.18/0/1e-015/0 float=y maxiter=15000 outside=real logmap=55 periodicity=0 colors=000k0Ah0Ae0Ab0A_0AX0AV0AR0BO3CN3IQ3NS3TW3SZ\ AXYHXYJWXLWYJXZHXXGYVFZU8ZR2ZWAa_HdcPggWilclpjotrr\ xytmtlbpdSlXHhP6dHBiJGnLKrNZuelwwbZdTANQFPOJQMNSKR\ THWUF_WDcXBgYVdcnbikhjhnketlTmhGfdI`ZKWUMQPOLKQFFR\ AAgBVxCnvLdtTWr`NqhEceOQcYDagKchQdiWejafkhhlnimtjn\ zknrmpknrdptYqvTrpOskKseFt`BtWptporkoqfnpannYmmTml\ OmkKkjGjjCii8hi4gi0ag2Xe4Rc6Mb7H`9BZB6XD1WEATCIRBQ\ OAYM9eJ8mH7oN6pS6qX6ra6tf6uk6vp6wu6zwEzzMzzTzz`zzh\ zzozzlzzizzfzzgz0gz0cz0oz0zz0zz0zzcMzcVzmXxzWcWVhb\ UmhUrkcvvmzzzUXOJ9LQBIXDFcFCjHAmMCpRDsVE7Qd9WYB`SC\ fMEkGFpAl0zSMlzg_m`TmVNmPHmJBmG9mE7zC6z94z73z51z30\ GeiMOPupqgmoUjmNSzMVxLXvK_tJarIdpHznktD`pPQl`KewIf\ sHgonP1GzJGzOGzTzNYzVbzagzbizcjzzjzzkzzkzzkzzlzzlz\ zgzzjzzkzzlzzEzzJzzNzzSzzWzz_OzdKzhbzpRznkzyUzaNzg\ nz`izbezc`zeXzfTzhOziKzkAzBBzGCzLDzQDzUEzZizLjzSkz\ Zlzemzlnzslztkztjzuizuhzv } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 11-03-09 (Obscured Ogive [Rating ?])
by Jim Muth 10 Mar '09

10 Mar '09

FOTD -- March 11, 2009 (Rating ?) Fractal visionaries and enthusiasts: A tiny bud appears on the east edge of the circular hole at the center of the main bay of the pseudo-minibrot in yesterday's image. This tiny bud is the brilliant background object in today's image. The bright white arc at the bottom of the image is part of the circle that appears in the main bay of the minibrot of yesterday's image. This figure, with its ogive-arch in the background and converg- ing arms in the foreground, is quite prominent in the minibrots of the HyperMandelbrot sets. These scenes appear to be non-crit- ical, yet I have never been able to find any starting points that would clear away the arms and reveal the true shape of one of the arches. Perhaps more investigation is necessary, or per- haps there is no unique 2-dimensional critical Mandelbrot plane in an 8-dimensional Julibrot figure. I named the image "Obscured Ogive" purely as a description. Since I have no idea how successful I was at revealing the true scene, I was unable to give the image a rating. When the image calculates from the parameter file, it starts off as though it will finish in less than a minute. But don't be fooled. The calculation soon slows to a crawl, and a full 15 minutes will be needed for the calculation to finish. I recom- mend viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds, occasional rain sprinkles and a temperature of 43F 6C spoiled Tuesday here at Fractal Central. The fractal cats sulked and soon turned their thoughts to tuna. In my department things went about average. I'll post the next FOTD in an average time of about 24 hours. Until then, take care, and an ogive is a pointed gothic arch. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Obscured_Ogive { ; time=0:15:25.72-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 passes=1 outside=real center-mag=-1.74593077988/+0.02015008205/1.95e+007\ /1/5.56/0 params=0/0/0/0/-4.18/0/1e-015/0 float=y maxiter=15000 inside=253 logmap=-534 periodicity=0 colors=000DKdCKeBKfAKg9Kh9Kk9Kj9Ki9KhdKgcKfbKeaKd`\ Kd_KcZKbYKaXK`WK_VKZUKYTJYSIXRHWQGVPFUOEUNDUMCULBU\ KAUJ8TI7SH5RG4QF2PE1OD0NC0MB0LA1K92K83K83K84K85L86\ M77N79O7BP7DQ7FR6GS6HT6IU6IV6JW5KX5LY5MZ5N_5N`4Oa4\ Pb4Qc4Rc3Qc4Rc5Rc6Sc7Sc8Tc9TcAUcBUcCVcDVcDWcEWcFXc\ GXcHYcIYcJZcKZcL_cM_cM`cN`cOacPacQbcRbcSccTccUdcVd\ cVdcWecXecYfcZfc_gc`gcahcbhccicdicdjcejcfkcgkchlci\ lcjmckmclncmncmocnocopcppcqqcrqcsrctrcuscvseztgxsi\ wskvsktsjsshrsgqrforenrcmrblrajr`irZhqYfqXeqWdqUcq\ TaqS`pR_pPZpOXpNWpMVpKTpJSoIRoHQoFOoENoDMoCFp5Is8L\ rBNqDQpGSoIVnLXmN_mQbmTdmVgmYim_lmbnmdmmemmflmglmh\ kmikmijmjjmkimlimmhmnhmnhmogmpglqfkrfjseisehtdhudg\ vcgwcfxcfxbewbewbdwadwacvacv`cv`bv`bv_bu_au_auZauZ\ `uZ`tY`tY_tY_tY_tXZsXZsXZsWYsWYrWYrVXrVXrVXrUXqUXq\ UWqTWqTWqTWpTWpSWpSWpSWpRWoRWoRWoQWoQWoLUnLUmKUmJU\ mIUmHUmGUmFUmEUmszzY_VY_V } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD 04-03-09 (Astro Iterations [6])
by Jim Muth 09 Mar '09

09 Mar '09

FOTD -- March 04, 2009 (Rating 6) Fractal visionaries and enthusiasts: Heaven only knows why I named today's image "Astro Iterations". The parent fractal, which came about when I subtracted 2 parts of Z^(-1.8) from 2 parts of Z^(0.75) and added (1/C), resembles nothing as much as a tiny rubber duck. Today's image is located on the duck's back, at the base of its rather lengthy neck. Much of the figure-eight-shaped network in the image consists of 'inside' stuff made visible by the 'bof60' inside fill. With the regular work being rather heavy here at FC on Tuesday, I had little time to devote to the coloring, limiting the image to a rating of 6. The calculation time of 3-3/4 minutes borders on slowness, so I recommend a speedy trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image at leisure there. Sunny skies made the outdoors appear pleasant here at Fractal Central on Tuesday. But this was true only from indoors. When one went outside, the biting north wind and temperature of 19F -7C brought the truth home -- it is still winter, and will be for almost three weeks. The fractal cats did not worry them- selves about the calendar. They spent the entire afternoon enjoying the warm sunlight streaming in the window and warming their watch-shelf. And I spent the day working. With the work now caught up, the next FOTD is quite likely to be posted in 24 hours. Until then, take care, and walk with confidence. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Astro-Iterations { ; time=0:03:44.91-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.594363042293016/+0.011311085972806/\ 122518.3/1/-150/0 params=2/0.75/-2/-1.8/0/0/0/0 float=y maxiter=950 inside=bof60 periodicity=10 colors=000ZPn_Rm_Tm`Vm`XlaZla`lbblbdkcfkchkdjjdlje\ njepjdqicricshbshbtgaug`vg`vf_wf_xeZyeZyeZqhZljZfl\ Z`oZVqZPsXNoWMlUKiTJfSHcQG`PEXNDUMBRLAOJ8LI7IH6FG5\ GF5GF5GE5HD5HD5HC5IB5IB5IA5JA5J95J85K85K75K65L65L5\ 5L45M45M35M35M57N68O7AP8BQ9DRBESCGTDHUEJVFKWHLXINY\ JOZKQ_LR`NTaOUbPWcQXdRYdSZeTZfUZgV_hV_iW_jX`kY`lZ`\ mZ`mY`nXanWaoVaoPYpKUpFQqAMqBOnCQlDSiETgFVeFXbGY`H\ _ZIaWJcUKdSKfPLhNMiLNkIOmGmrEhnEclEZkEUjEWhEXgEZfE\ _eEadEbbEdaEe`Eg_EhZEjYEkXEmWEnVEoUEpWEpXEqYEqZEr_\ Er`EsbEscEtdEteEufEugEuhEvgFvfFvfFveGveGvdGvdHvcHv\ bHvbIvaIvaIv`Jv`Jv_Jv_JtUGrODpIAnC7l64j02i25i37i4A\ f6Cc7EzUHvPJoKLlFOiDQiFSiGViHXiJZiKaiLciMejNckOblP\ `mQ_mRZnSXoTWpUVpVTqWSrXRsYPsZOt_Nu`LvaKvaJtbKscKr\ cKqdKpdLoeLneLmfLlgMkgMihMhhMgiNfiNejNdkNckOblOalO\ `mO_mOZnNYnNXnNWoMVoMUoMTpLSpLRpLQqRPqdOqzBfzFYzJO\ ANF8PGHRHQTIZVJgXJoYLnZNn } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 09-03-09 (Abyss of Destruction [No Rating])
by Jim Muth 09 Mar '09

09 Mar '09

FOTD -- March 09, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image with the ominous name was created with the Mystic2 formula, a formula that does God only knows what. I certainly don't know. One thing I do know is that the image consists entirely of 'inside' stuff brought to life by the 'bof60' active inside fill, which colors the points according to how close they come to the origin in their wanderings. The Mystic2 formula draws nothing but blank circles of radius 1. All the action comes from the trapped areas inside the circles. As today's image shows, the things that might be done with the areas inside the circles are endless. The image reminds me of the cover of a cheap "terror" novel so I named it "Abyss of Destruction", a name that might be given to such a story. I gave no rating because I consider it unworthy of one. The image is sensitive to the values of the parameters, particu- larly both parts of the p3 parameter. The fast speed of the image makes experimentation very easy. Changing the function totally changes the image, as does changing the inside fill. So actually, an entire range of images are waiting to be made manifest by tweaking these parameters. The calculation time is only 25 seconds on my P4-2000mhz unit, a time that will bring satisfaction to those, if any, who might be disappointed by the result. Of course, calculation may be entirely avoided by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A partly cloudy springlike day with a temperature of 75F 24C when I left Old Fractal Central at 1:00pm on Sunday turned into a raw overcast drizzly day with a temperature of 48F 9C by the time I reached New Fractal Central at 4:30pm. The new fractal cats greeted me when I arrived, caught a scent of Thomas, the old fractal cat, and asked what I had been doing for the past 32 hours. I answered their question with a double treat of tuna and cheddar cheese. The next FOTD will be posted in about 12 hours. Until then, take care, and let me know when the world ends. I don't want to miss it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= AbyssOfDestruction { ; time=0:00:25.45-SF5 on P4-2000 reset=1960 type=formula formulafile=jim.frm formulaname=Mystic2 function=cotan passes=1 center-mag=0.0541584/-0.60902/5.821744 logmap=yes params=-0.065/-5.122/6.003/-6.845/5.664/0.303 float=y maxiter=300 inside=bof60 periodicity=10 colors=000zzzwvptrcpmYlhWhc0dZ0`U0XP0TKFNFKICI8DG0\ DE0DC0BC0CC0DC8DDCEFECFOEGIGMHHOFMTJShM_mQgrTmvZrw\ `uvdwuhwtkrsglrlhqpfpqelmchjbcfa_b`WZZSVYORXKOWFKU\ BGT7LU9QVAVWC`YEeZFj_Ho`ItaKpbMlbNhcPdcR`dSXeUSeWO\ fXKfZGg`Cga8hcFkZ4hdoNXdLSUKOJIK6FF9HGBJGELHHNIKPI\ MRJPTKSVKVXLXZM_`MbbNedOgfOjhPqjRmjQijOdiN`iLXiKTi\ IPiHKhFGhEChCCiBDkADl8En7Eo6Ep5Fr3Fs2Ft1Hu7IuDKuIL\ vOMvTOvZPvcUgT_TJdE8iCAmACr8Er9DrACrBBqCAqD9qE8qF7\ qG6qH5qI4pJ3pK2pL1pM0pM0mO2kP4hR6fS8dT9aVB_WDYXFVZ\ HT_JR`KObMMcOP_NSWMVSLYOL`KKcGJfCIi8HiAIhCJhEKgGLg\ IMfKNfMPfOQeQReSSdUTdWUcYVc_WxoWupWrpWoqWlrWirWfsW\ ctW`tWYuWVvWSvWPwWNwWMtXLqXKnXKlXJiXIfXHcXHaXGZXFW\ XETXERXDOXCLXNZbXkigyohwkjtgkrblpZnnVokRqiNrgJseEu\ bAv`6s`6q_5n_5kZ5iZ4fY4dY3aX3ZX3XW2UW2SW2NR8JMDFII\ BDO79T34YCAVLFSULPaRLjWIsaFs`Hs_Ks_MtZPtYRtXTtXWtW\ YtV_uUbuUduTguSipRjjPkeOl } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END PARAMETER FILE=========================================

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FOTD 07-03-09 (Leftover Goodies [6])
by Jim Muth 06 Mar '09

06 Mar '09

FOTD -- March 07, 2009 (Rating 6) Fractal visionaries and enthusiasts: The curious thing about today's fractal image is that its parent fractal is not there at all. The parent consists of a few lopsided circles and crescents well off the screen to the right. But a deeper investigation reveals tiny clumps of detail around these crescents, and today's image shows that this detail is infinite in the true fractal manner. Despite appearances, the image is not located on the X-axis of its parent. It lies 0.01+ below the X-axis, which therefore re- quires an angle of 178.5 degrees to make the minibrot perfectly horizontal. I named the image "Leftover Goodies" when, studying the boring parent, I had the impression of something that once was there but now is gone, leaving a few splotches to carry on. Then I decided that the splotches were a bit too boring for a rating above an average 6. The calculation time of a mere 28 seconds will waste no one's time even if they find no enjoyment in the result. The finished image is posted, for immediate gratification of course, on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The sun shone and the temperature reached 64F 18C here at Fractal Central on Friday. The fractal cats were totally happy with the conditions. I was a bit too busy to enjoy the early spring however. I'll be back at Old Fractal Central from late Saturday morning until early Sunday evening, keeping Thomas, the one remaining old fractal cat company, while my sister is away visiting an old friend. Because of my absence, the next FOTD will not be posted before March 9, and possibly not until March 10. Until next time, take care, and have a peaceful panic. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Leftover_Goodies { ; time=0:00:28.15-SF5 on P4-2000 reset=2000 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=+6.014911330674471/-0.0126065468392344/\ 1.536035e+010/1/178.5/0 params=1/1000/-100/-1/\ -0.95/0/0/0 float=y maxiter=300 bailout=25 inside=0 logmap=29 symmetry=none periodicity=10 colors=000bev`mwZkxXtyWzzUgeTVMRJ1U_dXSm_LreEwm7zz\ FzzZzLVEKSEIOFHLFFHFEEFCAFB7FA4F97I8BL7EN6HQ5KT4NV\ 3QY3Tq8PzCLVHGTLCQP8NT4LU8LWBLXFKYIK_MJ`PJaTJbWJbX\ IfZKiaLmcNpeOibMb_JWXHPUEIRCBPACSFDVKEYPF`UGcZHfcI\ ihJlmKorLqvKlsKgqKcnJclJciJcfJcdJcbJc_IcYIcVKcWzcY\ zcZzc_zc`zcbzcczcdzcezcgzchzcizcjzckzcfzdbzeYzeUzf\ PzgKzhGziBzj7zk7zl7zm6zn6zo6zp5zq5zr5zs5zt5zu5zv4z\ w4zx3zy3zz3zzFzzQzzRzzSzzTzzTzzUzzVzzWzzWDzXCzYBzY\ AzZEz`HzbLzdOzfRzgOzcMz_KzX8z8IzTGzPEzMBzI9zE6zB4z\ 72z3BzKAzI9zG7zD6zB4z83z62z41z2gzweztczrazo_zmZzjX\ zhVzeTzcRz`PzZNzWLzUKzRIzPGzMEzKCzHBzF9zC7zA5z73z5\ 1z2XziVzgUzeSzcRz`PzZOzXMzVLzTJzRIzPGzNFzKDzICzGAz\ E9zC7zA6z84z63z41z2YzHWzGUzFSzEQzDKzCMzBKzAJz9Hz8F\ z7Dz6Bz59z47z35z23z11z0RzHKzDDz86z4PzDJzACz66z3gz9\ 1zm1zk1zh1zf1zd1za1z_1zY0zV0zT0zR0zO0zM0zK0zH0zF0z\ D0zB0z90z70z40z2hzsfztdzu } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 06-03-09 (Technicolor Dream [7])
by Jim Muth 05 Mar '09

05 Mar '09

FOTD -- March 06, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal is named "Technicolor Dream". The name came about when I had trouble getting the over-abundance of colors under control. The rating of a 7 indicates that I never did totally control the colors. The calculation time of just over nine minutes leaves plenty time to pour a drink or do other convenient things while the parameter file at the end of this discussion is running. Those with no drink to pour or no convenient things to do may avoid the calculation time by surfing to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the already-calculated image posted there. The formula behind the image subtracts 2 parts of Z^(-1.8) from 2 parts of Z^(0.75), then adds (1/C). This formula creates the rubber-duck parent fractal of the "Astro-Iterations" image of March 4. Today's scene however is located on the front of the rubber duck's neck. There is a disconnected hole just east of the parent rubber duck, which I have yet to check. If I find anything of interest there, it will appear as tomorrow's FOTD. The total sun continued here at Fractal Central on Thursday, but this time the temperature reached 50F 10C, which made things really feel like spring. The sun in the window was actually a bit too much for the fractal cats, who deserted their shelf for the floor when the shelf got too warm for cat comfort. Unfortunately for me, the day was still very busy, leaving no time at all to think of outdoors, though I did notice a look of gardening thoughts in FL's eyes. If the work slows down, the next FOTD will be posted in 24 hours. Until then, take care, and like it or not, good luck always trumps hard effort. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Technicolor_Dream { ; time=0:09:17.23-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-0.3478657298924145/+0.1805475756575933\ /9.249713e+011/1/-152.5/0 params=2/0.75/-2/-1.8/0/\ 0/0/0 float=y maxiter=3600 inside=0 logmap=640 periodicity=10 mathtolerance=0.05/1 colors=000mUUmUUmUUmUUmUUmUUnUUzYUzMUpTUgQScJPbFN_\ IKXIHUJFRHCOF9LD7IB4GA2HB4HB6IB8IBAJBCJBEKBGKBIFPR\ DOPBNO9MN7LM6LL7KK8KK9KKAKKBKKBKKCJJDJJEJJFJJGJJGJ\ JHIKHHLHHMHGMHFNHFOHEPHEPHDQHCRICSIBSIBTIAUI9VI9VI\ 8_I7XI7oI6YJ6ZJ5_J4`J4qJ3sJ3bJ2cJ1cJ1dJ0eJ0eLplKom\ KnmKnmKmmKmmKlmKlmJkmJkmJjmJimJimJhmJhmIgnIgnIfnIf\ nIenIdnIdnHcnHcnHbnHbnHanHanH`nH`nJalLbjNchPdfRedS\ fcUgaWh_YiY_jWakUblTdmRfnPhoNjpLlqJmrIosGqtEsuCuvA\ vv9sqEpmImiMjeRgaVeYZbUb_QgXMkUIoSEsTDqTDpUDoUDmUD\ lVDkVDjWDhWDgWCfXCuXCkYCbYCaYC_ZCZZCYZCXWGUTKSRdPO\ ZNLVKJYIGaFEdDBhA8f86o5zs3mw13u2zz26t28s2Ar2Br2Dq2\ Fp2Gp2Io2Kn3Ln3Nm3Pl3Ql3Sk3Uj3Vj3Xi3Yi3Xe8XbDWZIWW\ NVSSVPWVL`UIeUEjTBoT7tT4zU6zV8zWczXczYczZcz_cz_cz`\ czaczbczcczdczeczzczzUzzTzzTzzTzzTzzTzzSzzSzzSzzSz\ zSzzRzzRzzRzzRzzRzzQzzQzzQzzQzzQzzNzzKzzHzzEzzBzz8\ zz5zzWzzVzzUzzTzzSzzRzzQz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 05-03-09 (Sparkling at Night [8])
by Jim Muth 05 Mar '09

05 Mar '09

FOTD -- March 05, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image came about when I subtracted Z^(1.1) from Z^(-0.7) and added (1/C). This particular combination creates a parent fractal consisting of a lopsided Mandeloid with a generic fractal hole a short distance to the northwest. The scene of today's image is near the end of the main filament extending from the largest bud of the lopsided Mandeloid. Perhaps the most impressive thing about the image is its magnitude of over 10^13, which is normally beyond the range of perfect resolution, but for some reason works quite well in today's image. I rated the image at an 8, mostly because of the inspired (IMO) coloring. I named it "Sparkling at Night" because I liked the sound of the phrase. The calculation time of a mere 15 seconds is close enough to the speed of light to make the relativistic effects almost noticeable. The non-calculating fractalists may match the speed of light by zipping out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to enjoy the already-calculated image posted there. Total sun and lighter winds made the temperature of 34F 1C feel almost like spring here at Fractal Central on Wednesday. The fractal cats agreed as they stretched to their full length on their shelf by the window, and stayed there most all afternoon. My day was quite busy. I'll post the next FOTD in 24 hours. Until then, take care, and we get ahead by doing what everyone else is not. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sparkling_at_Night { ; time=0:00:15.74-SF5 on P4-2000 reset=2001 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=+0.02429494176869804/-0.11802495669603/\ 1.0305e+013/1/34.5/0 params=1/1.1/-1/-0.7/-2/800/0\ /0 float=y maxiter=280 inside=0 logmap=19 periodicity=10 mathtolerance=0.05/1 colors=000zpAzjBzfCzaDzXEnRBcM8TH60000000000000000\ 00000A27C1EF1KK2QL3WM4aN5gPDaQKXSRSTYNUeIWlzXszYzz\ bqzfhzjcHncMrcRvcVvcQvcLvcGvcBvc7bcNKca1dpImcZuSek\ KkbCqU5_UEIUNK`JLfENmAOs6Mt8Lt9KtAbrJuqRtoOsnMslJr\ kHqiEqhCzlBzoAzrAzu9zx9gHSgN7jP8mQ9zzMzzDzz5zzZzza\ zzdzzgzzjzzlzzizzfzzczz`zzYzzVzzZzzbzzfzzjzznzzszz\ xzzpzzhzzazzUzzNzzFzz8zzDzzIzzNzzSzzWzzXzzXzzXzzYz\ zYzzYzzazzezzhzzlzzpzzszzwzzzzzxzzwzzuzztzzszzqzzp\ zzozzrzztzzwzzyzzuzzqzznzzjzzfzzczzfzzhzzjzzmzzozz\ qzzrzzszzszztzzuzzuzzszzqzzozzmzzkzzizzgzzezzvzzdz\ zOzzUzzZzzczzhzzmzzrzzwzzMzzMzzMzzLzzLzzZzzUzzOzzJ\ zzXzzizzvzzhzzVzzHzzFzzEzzDzzCzzBzzAzzIzzQzzXzzczz\ jzzqzzbzzOzzAzzBzzBzzCzzCzzCzzDzzDzzDzzJzzPzzUzz_z\ zdzzjzzozzJzzOzzTzzYzzazzWzzQzzKzzEzz9zzBzzCzzEzzF\ zzGzzLzzQzzVzzZzzczzhzzmzzqzzXzzdzzlzztzzczzOzz8zz\ DzzIzzNzzSzzXzz`zzbzzdzzd } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 03-03-09 (Contemplation [8])
by Jim Muth 02 Mar '09

02 Mar '09

FOTD -- March 03, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's semi-glorious but rather gloomy image came about when I combined 5.5 negative parts of Z(-0.5) with 5.5 negative parts of Z^(0.5) and added (1/C). This expression produces an under- sized parent fractal somewhat resembling an arrowhead with bits of debris along its edges. Today's scene lies in the debris along the northwest edge of the arrowhead. I named the image "Contemplation" partially because of all the somber dark shades of blue and gray that fill it, and also because FL decided against my advice to go on the internet and check the value of our investments, causing her to spend the next half hour in a state of minor panic. I rated the image at an 8, mostly because I tend to appreciate the darker aspects of life, which are quite necessary for full appreciation of the brighter things. The calculation time of under one minute is quite fast, though not quite as much fun as viewing the finished image posted on the internet at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Light snow in the morning here at Fractal Central on Monday gave way to partly cloudy skies in the afternoon, while the tempera- ture hovered around a bone-chilling 21F -6C and the wind blew briskly from the north. The fractal cats would have preferred more sun, but they found enough contentmant with the intermit- tent sun to stay out of trouble. My day was moderately busy, both with work and with calming FL. The next FOTD will be posted in 24 hours. Until then, take care, and wait for salvation with bated but not abated breath. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Contemplation { ; time=0:00:51.48-SF5 on P4-2000 reset=2001 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.05445382918/+0.01773957999/6.5e+007/\ 1/-32/0 params=-5.5/-0.5/-5.5/0.5/0/300/0/0 float=y logmap=45 maxiter=1300 inside=0 periodicity=10 colors=000QOSOOTPNRNNRNMPMMPLLNLLNKKLKKLJJJIIIHHH0\ FGFFFA0EG0DE0GC0EA0D80E60C40V21Y34`39c3Cf3Fi4Jl4Mo\ 4Rr4Vw6Yr6bm6eh6hj8mm8po8vpKyrUytdzupzwwzypzvdztUz\ pLwoOrkRojVjfWfeZbcbZ`eVZhRWkMToJRrFOtCMw8Jz4Iz0Fz\ 0Dz0Az09z08z09z0AzmAz0Cz0Dz0DzmFz0Fz0GzmIz0Iz0Jy0L\ w0Lv0Mv0Mt0Or0Pp0Pp0Ro0Tm0Tk0Vk0V`0TR3RI9R9FP0LP0R\ O0YO0`L0bJ0eI0fG0jD0kC0oA0p91t63v44y38z19z0zz0zz0z\ z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0Pz0Rz0Rz0\ Rz0Pz0Oz0Mz0Mz0Lz0Jz0Jz0Iz0Gz0Fz0Fz0Dz0Cz0Cz0OzAZz\ YfzZpz`yzbzzbwzcmzcczcVzeMzeCzf3zf0zf0zf0zj0zk0zo3\ zp8ztCzvFzyJzzOzzRzzWzwZzoczffzZkzRozJtzCwz4zz0zz0\ zz0zz0zz0zz4zzCzzKzzRzzZzzfzzozzwzzzzzvyzorzhkzbez\ WZzOTzINzCGz6Az0Cz4Dz9DzDFzIFzMGzPGzVIzZIzcJzhJzkk\ z0oz0pz6rzAvzGwzMyzRzzYzzczzh`zz8zzBzzDzzGzzIzzLzz\ OzzPzzVzjYzPVzRRzTOzTLzVIzWFzWCzY9zZ6zZ3z`0zb0zb0z\ c0zc0z`0zZ0zW0zV0zR`ztbzw } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Re: [Fractint] Fractint mail
by david 02 Mar '09

02 Mar '09

Charles Crocker wrote: > David > > I am in the middle of a painful transition from dial up to a high speed > internet connection and have run into something that I just have to ask > about. Had a little difficulty in changing my address with Fractint so > am signed up twice. > > This means two copies of messages. The time on both of them is 6:15 so > they presumably were sent at the same time. Here is the puzzle. On the > dialup connection I got the full text of Jims message. On the high speed > connection I only got the first two and last three lines of it with > ..snip.. on a line in between. > > I can conceive of you being fast enough to make the change and somehow > get the two versions sent in the same minute. If that is the case why > didn't I get four copies? If it's not the case who did the snipping? > > Charles Sorry, Charles, I have no idea. I'm sending this on to the Fractint list. Maybe the list admin or someone else has an idea? -- David gnome(a)hawaii.rr.com authenticity, honesty, community

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FOTD 02-03-09 (Blues in the Night [9])
by Jim Muth 02 Mar '09

02 Mar '09

FOTD -- March 02, 2009 (Rating 9) Fractal visionaries and enthusiasts: A lot of blue fills today's image, which led me to the name "Blues in the Night". The parent fractal was created by a formula very much like the MandelbrotMix4, the MandelbrotMix3. This formula mixes four parts of Z instead of the two parts of the MandelbrotMix4 formula. One big drawback is that a critical point of the entered expression must be calculated by hand (which ain't no fun) and entered as the real(p5) parameter. In today's case I calculated 1.0037...etc. and entered it manually. The parent fractal of today's image resulted when I combined various portions of Z^(+1.8), Z^(-0.8), plain (Z) and Z^(+0.8), and then added (1/C). This combination produces a fractal with its open part shaped somewhat like a pair of angel wings filled with a mass of chaotic material. A rough Mandeloid shape fills most of this chaos, though today's scene is located at the southern edge of the open area. A good part of the image consists of inside stuff made visible by the 'bof60' inside fill. The inside stuff makes up the smoother areas of the image. The irregular shaped patches are outside stuff rendered in the normal 'iter' manner. When the time came to rate the image, I studied the image for quite a while, at least 3 minutes, before deciding on a rating of a lofty 9. I kind of enjoy the purples that tint a good bit of the 'outside' parts of the image. The three-dimensional effect is also rather striking. The calculation time of 5 minutes is a bit slow, so to kill all possibility of impatience, I suggest viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The increasing clouds and temperature of 39F 4C kept the fractal cats happy here at Fractal Central on Sunday. The forecast of snow tonight did not worry them. My day was pleasant enough. The next FOTD will be posted in 24 hours. Until then, take care, and when we fight the forces of evil, who decides what is good and what is evil? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Blues_in_the_Night { ; time=0:05:04.64-SF5 on P4-2000 reset=2004 type=formula formulafile=dec-02.par formulaname=MandelbrotMix3 function=recip passes=1 center-mag=-0.34313191980537870/-0.226238684265287\ 00/2.78678e+008/1/-50/0 params=0.4/1.8/2/-0.8/-1/\ 1/2/0.8/1.1003729163945/0 float=y maxiter=1800 inside=bof60 periodicity=10 colors=000RnBMsDIwEQ2HP2IP2JP2JO2KO2KO2LO2LN2MN2MN\ 2NN2NM2Oorznqzmpzlozkmzjkziizhgwgetfdqecndbkcahb`e\ a_c`Za_X_ZWYYUWXSUVQSTOQRMOOKMLIKIGI000MJEMMCMPAMS\ 8MV7MW8MY9M_9NaANcANeBNfCNhCNjDNlDNnENoEPkHQgKScMT\ _PVWRWSUXPWWT`WWdW_iWbmWfrWivWlzSjyPhxMgwJevh`vgZu\ fXteVsdTscRqaQo_PmYOkWNiULhSKfQJdOIbMH`LH_KGYLGWMK\ UONSPOQQPPRQNTRLUSJVTHWUGZWIcYKh_LmaNrcOveQzgSziTz\ kVzlWzn`oodlqihrmetrbuv_vzYtxXsvVrtUpsToqRnoQlmPkl\ NjjMihLgfJfeIecHcaFb_EaZD_XBZVAYT9XSCVREURGSRIRQKQ\ QMOQONQRLPTKPVJPXHOZGO`FObDOeCNgANi9Nk8Mm6Mo5Mq4Mq\ 6Lq7Kq8Kq9JqBIqCIqDHqEGqFGqHFqIEqJEqKDqLCqNCqOBqPA\ qQAqR9qT8qU8qV7qW6qX6pZ5o_5n`4ma4mb3lc3kd2je2jf2lg\ 4ng6pg7rg9shBuhCwhEyhGzhHyfGxdGwcGwaGv`GuZFtYFtWFs\ VFrTFrSFpRKoROmQTlQXjP`iPegOifOmdNrcNvbNzdInfDbh8R\ i4Fj5Jj6Mk7Qk7Tl8Xl9_m9cmAfnBjnBmoCqoDtoDwqGtrJqtL\ ouOlwQjxTgnQ3iV5d_6`d8WiA } frm:MandelbrotMix3 {; Jim Muth z=p5, c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4): z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <= 100 } END PARAMETER FILE=========================================

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FOTD for 3/1/09
by Brian Prentice 02 Mar '09

02 Mar '09

Jim, From time to time in your discussions you mention critical points. Could you explain what they are and why they are important to the generation of your fractals. Also, if you can calculate a critical point for your MandelbrotMix3 formula by hand, why can't you do so in the associated code? Todays image is very beautiful! Brian Prentice

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FOTD 01-03-09 (Marking Time [6])
by Jim Muth 01 Mar '09

01 Mar '09

FOTD -- March 01, 2009 (Rating 6) Fractal visionaries and enthusiasts: In yesterday's FOTD I stated that unless another Saturday expedition happened, today's FOTD would be posted in 24 hours. Since this FOTD is being posted 39 hours after the previous one, the reader may safely assume that an expedition happened. Today's image came about when I combined 0.03 part of Z^(+13) with 0.03 part of Z^(-23) before adding (1/C) to create a parent fractal that is little more than an open ring of radius 1 around the origin. Today's scene is located in some insignificant detail just north of the western inner edge of this ring. I named the image "Marking Time", not that the name has any connection to the image. I rated it at a 6, the most frequently awarded rating. The calculation time of 11 seconds could hardly be faster. The trip to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> might not be quite as fast, but it is a lot more fun. A mix of sun and clouds and a temperature of 36F 2C kept the fractal cats cozy enough while we were away on Saturday. But the feline duo did demand an extra treat when we returned after dark. I'll post the next FOTD in around 8 hours. Until then, take care, and if the universe is a fractal, where is the computer and how did the program come to be written? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Marking_Time { ; time=0:00:11.73-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip center-mag=-0.95974698691729/-0.01756139847702436/\ 41544.75/1/-72.5/0 params=0.03/13/0.03/-23/0/0/0/0 float=y maxiter=600 inside=0 logmap=13 sound=off colors=000_0SY6QV0QQ2L240160TXWzzzmbXzXFwNGmQGWTHS\ WHOZIKaIHdIMHs2ZSBTVKNXTHZ_WNfiCmw1HCOB91JKKRVbZet\ ZchZbYZaNZ`CZ_1UcFPfTKifGltMeqRZnXTkaMhgFel9ceE_ZJ\ WTOSKShCVyERzGOzHLzJHzKEzMBzN8zYQfhgOejQclRaoS_qTX\ sUVvVTxWRzXWwT`uQerNjpKomHtkExiBnb`dWzeVweVtfVqfVn\ fUkgUhgUegUciVekWgmXhozjqzkszmtznXzt9zyHzkOzYVzL`z\ RezXgz_hzaizckzflzhmzjnzlgz`azQVzFPz4LzCIzKEzSBzZ7\ zf4zn1zu5zE5zK5zP5zU5zZ5zd5zi5zn5zs5zyGzjQzWOzSMzO\ QzKUzGYzCaz8ez4gzAhzFizKezHazFYzDUzBQz9Mz7KzBJzEHz\ HGzKEzNDzQCzTIzYOzaUzfZzjXzdVz_TzVRzQPzLOzGNzINzKN\ zMNzOGzJ9zE3z9DzJNzTXzaczeizhozluzomzpezqYzrQzsIzt\ BztDzrFzpHznIzlKzjMzhNzfMzbLzZKzVJzRIzNEzJHzJGzFnz\ jezaXzTOzKVzLSzJQzINzGLzFIzD9zcAz_BzXCzTDzQEzMFzJG\ zF5zI7zH9zGAzFCzEDzDFzCSzMMzHtzjiza_zTQzK`zIYzHVzG\ TzFQzFNzELzDIzCwzVlzQazLRzGazzWzmRz`LzOuz0nz2gz4zz\ 6Uz8NzA7zg9z`BzVDzOFzIpzZ } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 28-02-09 (Color Collapse [5.5])
by Jim Muth 27 Feb '09

27 Feb '09

FOTD -- February 28, 2009 (Rating 5.5) Fractal visionaries and enthusiasts: Friday afternoon FL again asked me why I am so fascinated with fractals. It was a harmless question, but it surely got my philosophical muse active. I replied that I enjoy fractals for the same reason that I would enjoy being an officer or even a crewman on the Starship Enterprise. Since I will never have a chance to explore the unknown of physical outer space, I chose the consolation prize of exploring the unknown virtual world of fractals. Then FL turned a bit wistful and told me it was a shame that I had been born a few centuries too soon. This actually struck me as amusing. I replied that I had not been born too early, that in fact there never would be a right time. In my opinion, Man will never permanently spread his ever-increa- sing numbers to any place but the surface of the earth -- not because we will never have the knowledge or technology, but because we will never have the resources to meet the economic cost. As an example, imagine what would happen if, in today's economic situation, our president were to announce that he had decided to appropriate 10-trillion dollars to establish a permanent U.S. colony on Mars within 10 years. The outrage would be deafening. People would surely claim that having steady jobs and affordable necessities today was far more important than receiving nightly news and weather reports from Mars 10 years from now. The appro- priation bill would die a fast and celebrated death in congress. IMO, if the economy permits, a few men might walk on Mars in 25 years or so, and I might be around to see it. But that is as far as man will go. Our unmanned probes will continue to return interesting data from the other planets and their varied moons. Those probes might even discover extraterrestrial life somewhere else in our solar system. But we must face the harshest fact of all -- we are prisoners of our frail bodies and the life-support- ing environment of earth's surface that permits those bodies to survive. Wherever we hope to go, we must either take a bit of earth's surface conditions with us or create those conditions in our off-earth colonies. Even with any future technology we might develop, the cost of doing this on the scale of the 'Star Trek' TV series would be so overwhelming that it would never be seriously considered. And yes, I do watch those pop-science shows about worm holes on the discovery channels. (Of course, if we could find a way to explore the galaxy with our minds without dragging along our physical bodies, all bets would be off! But I have no idea how we might do this and then bring back valid scientific evidence of what we had observed?) Yes, we do have a fractal for today, a relatively harmless one, a scene in a small valley in the parent fractal that results when various portions of Z^(-1.6) and Z^(-5.8) are combined and (1/C) is added. This parent is an oversized irregular thing with many odd-shaped bays, and nooks and crannies everywhere. Most of the effect was achieved by rendering the image with the outside set to 'tdis' and the inside set to 'fmod' with a proxim- ity value of 0.6. The little bit of effort I put into smoothing the colors earned the extra half-point in the rating of 5.5. I thought of the name "Color Collapse" when I struck the wrong button and lost the first color palette, which was decidedly inferior. The calculation time of just under 7 minutes is true when the image is calculated at a resolution of 640x480x256 on a Pentium-4 machine running at 2000mhz, the resolution at which I calculate all the FOTD images. This time may be cut to nothing by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The heavy clouds and occasional light showers here at Fractal Central on Friday were made quite pleasant by a temperature of 57F 14C, which made it feel more like April than February. The fractal cats never even noticed that no sunlight was coming in their window. A heavy squall passed over at nightfall, but by then the cats had retired to their evening resting p[laces. In my department, the work was heavy, the philosophy on the negative side, and the fractal acceptable. Unless FL comes up with a project on Saturday, I'll post the next FOTD in 24 hours. Until then, take care, and is a realistic but negative view better than a positive view based on wishes? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Color_Collapse { ; time=0:06:56.38-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.315293015211623/-0.2904341824425853/\ 699884.1/1/162.5/0 params=6/-1.6/0.8/-5.8/0/0/0/0 float=y maxiter=3200 inside=fmod proximity=0.6 outside=tdis periodicity=10 colors=000HLRMOPRRNVULnbYpbWraUpaVnaWl`Xj`Zh`_f_`d\ _abZc`ZdZZeXYfVYhTYiRXjPXkMWmNWkOWhQWeRWcSW`UWYVWW\ XWTYWQZWO`WLaWIcWFcVGbUHaTIaRJ`QK_PL_NMZMOYLPYKQXI\ RWHSWGTVEUUDVUCXTBYS9ZS8_R7`Q5aQ4bP3cO1eO1eN1eM1eM\ 1dL1dK1dJ1cJ1cI1cH1cH1bG1bF1bE0aE2bE5cD8dDBeCEfCHg\ BKhBNiAQjATk9Wm9Wk9Wh9Ve9Vb9V_9UY9UV9TS9TP9TM9SK9S\ H9SE9RB9R88Q5amgaflbZqbZqbYrbXrbWsbVtbUtcTucSucRvc\ QwcPwcOxdNydPvcRscTpbVmbXjaZfa`c`c``eY_gV_iRZkOZmL\ coImqFwtBztBwsCmsDcrEWrFWqGWqHWpIWpJVoKVoLVnMVnMVm\ NUmOUlPUlQUkRUkSTjTTjUTiVTiWShXThXViXWiXYjX_kX`kXb\ lXdmXemXgnXhnXjoXlpXmpXoqXqrXrrXtsXvtXssXpqXmoXjnX\ flXciX`eXYaXUYXRUXORXLOXHMWHKWHIVHHVIIUIJUIKTJLTJM\ SJNSKORKPQKQQLRPLQPLPOMPOMPNKPNKPMOPMSPLTPKRQLTQMU\ QOUQPVQRUQSUQUWQVXQXYQY_Q_aQ`cQaeQcgQdiQfkQgmQioQk\ qQmsRnuSowSpxSrxRpvQmtPjrOhpNeoMbmL_kKYiJVgISfHPdG\ NbFK`EHYDEVEHRFKMGNUUQDIM } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 27-02-09 (Rings Around Mandy [No Rating])
by Jim Muth 26 Feb '09

26 Feb '09

FOTD -- February 27, 2009 (No Rating) Fractal visionaries and enthusiasts: With the work still piled up, there's little time for fractals. So let's get right to today's image. The scene lies on the main spike of the fractal that results when 0.6 part of Z^(-5.6) is subtracted from 6 parts of Z^(-1.6) and (1/C) is added. I'll not even try to describe this parent fractal, but it can be seen easily enough by redoing today's image at a magnitude of 0.3 and turning off the logmap. Since I put only a couple minutes into the image, I gave it no rating. The name "Rings Around Mandy" has little significance. And the very fast calculation time of 1-1/4 minutes will cause no one any difficulty. An even simpler way to see the image is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is posted in completed form. A veil of clouds that dimmed the sun did not dim the fractal cats' spirits here at Fractal Central on Thursday, as the temperature of 50F 10C made up for the weak sun. My day was very busy. I guess I should be thankful, but I would rather have had things a bit quieter. I'll post the next FOTD in 24 hours. Until then, take care, and if you can't be positively negative, be negatively positive. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rings_Around_Mandy { ; time=0:01:14.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.288637588535473/0/3.18068e+011/1/180 params=6/-1.6/-0.6/-5.6/0/300/0/0 float=y maxiter=1500 inside=0 logmap=138 symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=000NKD006IJE926GHGBLGABBfmcYaVQQNHEEtr_nkWh\ dSbZOXSLRLHLFDF89vaKlUHbNETGBJ98p7Sm6Qj6Pg6Ne5Mb5L\ _5JX4IV4HS4FP3EM3CK3BH2AE28B27zduyaquZmpWilTegQacN\ YZKUVHQQEMMBIfccgddgedgfeggfggfeigcjgblh`mh_nhZkgZ\ ifZgeZedYccYabY_aYY`YW__YXa_VbaSdcQedOgfLihJjjGllE\ mmCojDphDqfDrdDtbDu`DvZDwXDyVDzTDzRDzPDzNDuSHnWKg_\ N_dRThUMlXRnWVoVZpUbqUfrTktSouSsvRwwQzxQuQctTfrXiq\ _lpbooerpfjqgcrhXrhQsbUtYYuT`uOdvJgwEkw9noBkgCi_Dg\ SEeKFcLLfMQhNWjO`lPfoQkqRqsRvuPupOtkMtfLsaKsXMnUNi\ SPdQQ`OSWLTRJVMHWIF`REe_EjhEnpEilppomvrjghpXWXNJET\ MJZONdQRjSVpU_vWczYgz_kzZfzZbzYZxYVuXQsXMqWIoWElZL\ j`ShcYeedchkajq`QV_69R5KI5VA5dCBfDGgEMiFRjHXlIamJg\ oKlpIplHshFveEyaDzZTtThmNwfIycLz`OzYRzVUzSXzP_zMbz\ KevQ`iVXX_T_YVbWXdUYgS_jQalPbhPZdPV`PRXPNTPJQPGYQK\ eQNlQRtQUzQYzQ`zT_wWZqYYl`XfbW`eVWgVOjVHlVAnVKfQTZ\ LaSGbUFcVEcWDdXCeYBeZB`XC } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 26-02-09 (Miserable Minibrot [5])
by Jim Muth 25 Feb '09

25 Feb '09

FOTD -- February 26, 2009 (Rating 5) Fractal visionaries and enthusiasts: Too much work, too little time, and imperfect health ganged up on Wednesday to hold today's image to a rating of a 5. The image shows not the ultimate minibrot, but a miserable little runt of a minibrot stuck on the ridiculously long main stem of one of the Z^(1.25)+C Mandeloids. It's a minibrot so tiny that it is actually starting to break up. I named the image "Miserable Minibrot". Don't try to zoom in on any part of the scene. Some parts of it are already starting to break up. The calculation time of 1-2/3 minutes will ease any disappoint- ment felt when the image is finally seen. Of course, all risk of disappointment and wasted calculation time may be avoided by hurrying to the FOTD web site and viewing the image there. The FOTD web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Warm sun and a temperature of 46F 8C kept the fractal cats glued to their shelf in the sunniest window here at Fractal Central on Wednesday, while the work kept me glued to the computer desk. Little else of importance happened. I'll post the next FOTD in 24 hours. Until then, take care and adopt a positive attitude, but don't let it take over your life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Miserable_Minibrot { ; time=0:01:41.66-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-5.440828082143497/-8.144751993539984/\ 6.591033e+010/1/-167.5/0 params=1.25/0/0/0 float=y maxiter=25000 inside=0 logmap=100 periodicity=10 mathtolerance=0.05/1 colors=000hWQh_RhXShYTh_Uh_VfaWcbV_dUWeTTeTQgSNiRL\ kRMmQNlQOlQPkQQjPRjPRiPSiPThOUgOVgOWfOXeNXeNYdNZdN\ _cM`bMabMbaMbaMacO`dQ_eSZgUYhWXiYXk_WlaVmcUodTpfSq\ hSsjRtlQunPwpOxrNytNzuPwrQtpRrnTolUmjVjgWgeYecZ`a_\ `_`VX_VVYSTWORWOPYKN_GMaCLc8Ke4Jg5Hi6Fk6Dm7Bo79q87\ s95u93wA1zA0s98o8Gk7Og6Vc5b_4jW4qX6rY8rZAr_Cr`EsaF\ sbHscJsdLteNteOtfQtgSuhUuiWujXukZvl`vmbvndvnevodto\ drodqodoodmodlodjodhodgodeodcodbpd`pdZpdYpdWpdUpdT\ pdRpdPpdOpdMpdKpdJocIobHoaGo`Fo_EoZDoYCnXBnWAnV9nV\ 9nU8nT7nS6mR5zQ4zP3zO2zN1zM0zM0zN2zO3zP5zQ6zR8zS9z\ TBzUCzVEzVFzXGzYGzZHz_Hz`IzaIzbJzcJzeKzfKzgLzhLziM\ zjMzkNzlNznzzozzpzzqzzrzzszztzzuzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzfzzfzzfzzfzzfzzfz\ zfzzfzzfzzfzzTzzFzz2zz5zz8zzAzzDzzGzzIzzLzzOzzQzzT\ zzVzzYzz`zzbzzezzhzzjzzmzzozzfzzezzdzzdzzczzbzzbzz\ azzazz`zz_zz_zzZzzYzzYzzX } 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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FOTD 25-02-09 (Elephant Playground [6])
by Jim Muth 24 Feb '09

24 Feb '09

FOTD -- February 25, 2009 (Rating 6) Fractal visionaries and enthusiasts: I've recovered enough to visit fractal land, but not quite enought to be fully back on my feet. Today's image was a quick and easy find. With my health still borderline and the work backed up, the image is a quickie, with obvious East Valley characteristics. I named it "Elephant Playground" because of the bits and pieces of elephants and sub-elephants that fill it. The rating of a 6 is close to my opinion of the image, though the calculation time of 10-2/3 minutes is a bit more than the image is worth. All problems may be eliminated however by surfing to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the fully rendered image there. The cold but bright days continue here at Fractal Central, while the fractal cats continue their vigil in the sunny window, watching for whatever fractal cats watch for. The next FOTD will likely be posted in 24 hours. Until then, take care, and implicate the expletive. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ElephantPlayground { ; time=0:10:41.70-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 center-mag=+6.295606145505\ 362/-0.1802309418750937/1.279637e+010/1/67.5/0 params=1.6/20 float=y maxiter=10000 inside=0 logmap=1626 periodicity=10 mathtolerance=0.05/1 colors=000vamvbmvcmvdmvemvfmvgmvhmvimvjnvknwlowmpw\ npwoqwprwqrwrsxstxttxuuxvvxwvxxwxyxxyxvyvsyuqysoyr\ mypkyoiynfyldykbyi`yhZxgXxeVxdSxbQxaOx`MxZKxYIxWGv\ VEsUKoSPfRVVQ_MPZOSZPUZRWZSYZT_YVaYWcYXeYZhY_jmUOj\ hhifmhdqZWuPNyPTlPZ`PdPPjDTnLXrT`u`djVh_PkQKoFEr59\ m9HiCOeGW`JbXNjTQqUSjVUcVWXWYQX_JXaD`bFdbGgcHkcIod\ KrdLveMyeNufHqgBfpHWxMVZcV9uKH3NM2PQ2RV2TZ2Vb1Xg1Z\ k1`o1ljKxfbueWrdQodKlcEjc8mfGphOsjWvlcujdtiesgfrfg\ qehpciobjoajFKPDSSBZVAeY8l`6sc5ze9zdCzdFzdIzdMzdPz\ dSzdVzdRv_OrVLnRIjMFfHCbDHXBMR9RL7WF5_A3aCIcDWeFjf\ GxmVgtiRzxBpp9gh8Y`7PT5FL46D3WHBtKJsSHr_GrgFqoEqvD\ npHlkKjeNh`QfVUdQXbK_`Fb_M__SYZZWZdTYkRYqPaeLeVIfJ\ Fr8CzC8zK4zc1tc7nUDhKJbJPXJVRJ`WLc_NedPghRilTlqVnu\ XpyZrocsegtWhuMhvDmvFmqHrmJviPzeUzaZzYczUhzpmzOrzU\ vz_zzezzkzzlzzmzznzzozzgzz_zzSzzKzzCzz4zz5zz5zz5zz\ 5zz5zz5zz5zzHzzSzzczznzzk } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] ???
by JackOfTradeZ＠comcast.net 24 Feb '09

24 Feb '09

. it seems recently when I use IExplore to access the FOTD individual posts I get this error: The XML page cannot be displayed Cannot view XML input using style sheet. Please correct the error and then click the Refresh button, or try again later. The server did not understand the request, or the request was invalid. Error processing resource 'http://www.w3.org/TR/xhtm...It isnt a big deal since I use firefox mostly, only IExplre when I want to save a page as a MHT condensed file. Anyone else have this problem? .

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Re: [Fractint] Under the work
by Jim Muth 24 Feb '09

24 Feb '09

FOTD fans: Well, the fractal cats and chicken soup worked. I'm pretty much out from under the weather, but now I'm under the work that got behind while I was out of action. If things go well, the next FOTD will be the one for February 26. And if things go exceptionally well, there could even be a FOTD for February 25. Jim M.

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Re: [Fractint] AOTD
by JackOfTradeZ＠comcast.net 23 Feb '09

23 Feb '09

. After tweaking the colors a bit, FOTD 2/17/09, "Dawn Song", really looks like Mars (sorta...). So...... Use your imagination! You're a rich space tourist on a mission to Mars. You approach the red planet from deep space, descend into orbit, then make planetfall into one of the large canyons known to exist there. You rocket above and over the surface looking for a smooth place to land among the sand dunes and mountains. <i>...... And you wish you had hired a better pilot ......</i> Mission to Mars: http://www.fractal-animation.net/vid/m2m.zip .

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Under the weather
by Jim Muth 22 Feb '09

22 Feb '09

FOTD fans: I had the word processor set to 'overstrike' instead of 'insert' when I added the 'frm:' in front of the formula in the par file for February 20, which explains the missing 'Mand' part of the formula name. I noticed it shortly after posting the FOTD but assumed that everyone already has a copy of the correctly named formula in their Fractint 'frm' files. BTW, I've been down and out with the fractal flu bug or some- thing else like that for the past two days, which explains the missing FOTD for Feb 21. If all goes well and I shake the bug, the next FOTD will be the one for Feb. 23. Meanwhile, the fractal cats are keeping me warm and FL is keeping me well supplied with steaming hot chicken soup. Jim Muth

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FOTD 20-02-09 (Just Another Fractal [5])
by Jim Muth 19 Feb '09

19 Feb '09

FOTD -- February 20, 2009 (Rating 5) Fractal visionaries and enthusiasts: I hear that the moon is missing from the icy "Mystic Moonlight" image that I posted 3 days ago. In the original discussion I neglected to mention that the moon is a virtual moon that lacks the fractal energy to become a real moon. Of course, if the image were an oblique view of the rings of Saturn, we would need no moon. The distant sun would be causing the glare. Today's image is nowhere near as striking as the moonlight picture however. In fact it's just another fractal, which is exactly what I named it. The parent fractal came about when I subtracted 0.2 parts of Z^3 from Z^2. This parent fractal is basically a Mandelbrot set with several new bays out the negative X-axis. Today's image is located in a valley between two of these bays. Since the image is just another fractal, I had to give it a rating of a very humdrum 5. The calculation time of 11 minutes is admittedly slow, but relief is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted. Flurries of snow, brisk winds and a chilly temperature of 30F -1C made life outdoors unplasant here at Fractal Central on Thursday. Luckily, I had no reason to wander far fron F.C. so the cold didn't bother me. The fractal cats passed the day by the heat. I will post the next FOTD in 24 hours. Check back then to see what kind of mischief I can get into. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= JustAnotherFractal { ; time=0:11:11.17-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.6541923616778935/+0.0000018876245717\ /1.515809e+010/1/-85/0 params=1/2/-0.2/3/0/0/0/0 float=y maxiter=3000 inside=bof61 periodicity=10 colors=000DTBE`9Fg6Go4Hv2InAJgHK_PKTWLMbMEjN7qN0xS\ 6sXBoaHjeMfjSaoXYsaUchLPoCAu4Et9IsEMsJ000UrSXqX`pa\ dpehojloopntsnxojwlgvhdueatbZsZWrWTqTQpWNkYLg_JcbH\ ZdFVfDRwBMz9Iz7EzCDzGCzKBiOAiSAhW9g_8fc7eg6ek6000b\ fKadR`bX_`cZZjYXp3Cf6Dh9DjBDkEDmGDnJDpLDqODsQDtTDv\ VDwYDy_Dz`EvaFsbGpcHmcIidJfeKcfL`fLYdMabMe`MiZNmXN\ qVNusXX000aIBUB0TIOSPkQThOXfM_dLcaJf_HjYGnVEqTCuRB\ xPFqSIjVMcYPY`OVXOSTNPPNMMNLLNLLNLKNLKNLJNKJNKINKI\ NKHNKHNJGNJGNJFNJFNJENJE7gDIg9Tg6bg3cbKdZ`dVqfUihT\ ajSUkRNfPPbORZMTVLVRKXNIZJH`FFbBEd7DeDEgKFiQGlXHnE\ 29J5IO8RTB_YEhYxlZpm000000000bOphZggWifTjeRkdOmcMn\ bJoh2Wg5Zf7ae9ddBgcDjbFmqy9mmKibVeSeR84UBHXDT_Fdhd\ ieTmSk4UeDW`LYWT_R`aMhHJ8PINWHaYH6000`mUaHeJUKzpSw\ VmK_DOWLSSTVOjbKt960D87H9zLBKOCRSDYWFc_GjhYjfUleRm\ dNncKo2SJCPSLM_UJhuCsqDrmEqiFqeGpCPdGOfJNgNMiQLjTK\ lXJm_Ioq7s`TKaN`NIXQH`CLE } frm:AutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 18-02-09 (Mystic Moonlight [9])
by Jim Muth 19 Feb '09

19 Feb '09

FOTD -- February 18, 2009 (Rating 9) Fractal visionaries and enthusiasts: Today's image is another reworking of an old FOTD image. The old image is named "Europa". It is an imaginary scene on the icy moon of Jupiter, which appeared on June 21, 1997. I did little to the original image other than intensify the colors and rotate it an infinitesimal bit. The result is a fractal that strikingly resembles a photograph of an icy but peaceful seacoast in the light of a full moon. I named the new version of the original image "Mystic_Moonlight". One glance of the image will explain the name. I wrote the formula, Man-YZ-XZ, when I was experimenting with rotating images in the 4-D Julibrot figure. Looking at the formula today, I'm not sure how it was supposed to work. I rated today's image at a 9. I could have been more conserva- tive with the rating, but just because my politics tend to the conservative side doesn't mean I can't be liberal with my FOTD ratings on occasion. The calculation time of 66 seconds will pass like nothing. The trip out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to stare in awe and wonder at the finished image posted there, will not only avoid all unpleasantness, but will bring instant fulfillment. Tuesday was a nondescript day here at Fractal Central, both with the weather and the fractal cats. Sunny skies and a temperature of 39F 4C kept the cats in and out of their favorite window. At one point a squirrel leaped onto the opposite window sill, but scampered away before the sleeping cats were aware of it. My day was average. The work was finished early in the after- noon, which left plenty of time to work on the colors of today's fractal. The next in the unending series of FOTD's will be posted in 24 hours. Until then, take care, and if it leads to madness when we wonder what lies behind our sensory images of the 'outer' world, this probably explains how I could keep the FOTD going for almost 12 years -- I must be mad! P.S. My current re-working of old images does not mean I will stop posting new images. I am simply tweaking a few of my older images that I have long thought need improvement. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mystic_Moonlight { ; time=0:01:06.74-SF5 on P4-2000 reset=1960 type=formula formulafile=jim.frm formulaname=Man-YZ-XZ passes=1 periodicity=10 center-mag=-0.00000686598512544/-1.845082873438826\ 00/8.246947e+010/-5.121e-005/359.99905692/-89.9990\ 597420641762 params=0/0/1/0 float=y maxiter=5000 inside=255 logmap=yes colors=00008z08z06z06z06z04z04z04z02z02z00x00v00q0\ 0n00k00i00g00e00b00Y00X00U00S00Q00O00M00H00F00D00B\ 00900800600400000020020020000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 000000000000000200200400600600800800900900B00D00D0\ 0F00F00H00K00K00M00M00O00O00Q00S00S00U00U00X00Y00Y\ 00`00`00b00b00e00g00g00i02i02kU4n04n04qU6qU6sV6sW8\ vX9xXDzYUzZUzdZzgazk`v`WvXQiT0kB0g00`00`00X00e98i9\ 0qBMzBMzBMzBOzDQz0YzFSzFSzFSzHUzHUzHUzKXzKXzMYzMYz\ MYzO`zO`zQbzQbzQbzO`zO`zO`zM`zKzzrzzuzzzzzuzzzzzrz\ zzzzzzzuzzHAzFAzFAzFAzFAzDAzD`zDAzDAzBAzBAzBAzBAz9\ Az9Az9Az9Az8Az8Az8Az8Kz6Az6Az6Qz6Az4Oz4Kz4Kz4Oz2Oz\ 2Mz2Mz2Mz0Mz0Mz0Mz0Mz0Kz0Kz0Kz0Kz0Kz0Kz0Kz0Hz0Hz0H\ z0Hz0Hz0Hz0Hz0Fz0Sz0Uz6Az } frm:Man-YZ-XZ {; primitive effort at rotation ; p2 = 0 = Julibrot YZ plane ; p2 = 1 = Julibrot XZ plane ; p2 = >0 <1 = Oblique planes z=real(pixel)+flip(real(p1)), c=imag(pixel)+flip(imag(p1)), a=p2, b=flip(cos(asin(p2))): z=sqr(z)+((a+b)*c), |z| <= 25 } END PARAMETER FILE=========================================

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FOTD 19-02-09 (Comets in Flight [8])
by Jim Muth 18 Feb '09

18 Feb '09

FOTD -- February 19, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image is . . . well, it must be something, but I can't think of what to say about it. It resembles four comets whizzing around a tiny minibrot, so I named it "Comets in Flight". The parent fractal combines various negative portions of Z^(-1.111) and Z^(-11.11). This parent is an oversized thing with a huge 'fan' and many interesting but ultimately disappoint- ing areas to check. I rated the image at an 8. I guess I'm just in the mood for swirling comets. The calculation time of under 2 minutes is fast enough to keep things moving right along. But if a traffic jam develops, the calculation may be avoided by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Wednesday turned into the most unpleasant day of the winter here at Fractal Central, with an all-day combination of snow, graupel, (tapioca snow), ice pellets, freezing rain, and just plain rain, which by the end of the day left about 1-inch 2cm of slush on the ground. The fractal cats took one look outside and curled up beside the big radiator. Being occupied by other things, I did not worry myself too much with the weather. I'll post the next FOTD in 24 hours. Until then, take care, and if you want nothing to worry about, become a nihilist. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Comets_in_Flight { ; time=0:01:55.90-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=-2.76376966932386/-3.9925175076021/26012\ /1/150/0 params=-6.6/-1.111/-0.6/-11.11/0/0/0/0 maxiter=1750 inside=0 logmap=159 periodicity=10 colors=000KAaLB_LC_LDYMEWMFUNGSNHQNIOOJMOKKPLIPMGN\ NEPOFRQGSSHUUHWWIXYJZ_K`aKacLcfMhhNhjNmlOmnPrpQrrQ\ vtRvvSzxSzvRvuQvsPrrOrpNmoMmmLhlKhjJciIchHZfGYeFWc\ EUbDT`CR_BQYAOX9NV8LU7KT7MU8OV9QWASWBUXCWYDYYE_ZFa\ _Gc_He`IgaJiaKkbLmcMncNmdNldNleNkeNkeNjfNjfNigNhgN\ hgNghNghNfhNfiNeiNdjNdjNcjNckNbkNamObkNbiNbhMbfMcd\ MccLcaLc_LcZKdXKdVKdUJdSJeQJePIeNIeLIeKHfIHfGHfFGf\ DGfCG`ALW8PQ6UL4YN5XP6WQ7VS8UT9TVATWASYBRZCQ`DPaEP\ cFOdGNfGMgHLiLLjPKlUJmZIncHjh6fmHbqRZu`_pZ`kXafVba\ TcXRdSPdQOhSUnU_pWdsYioXgkVfgUdcSc_RaYNZWQ`USbSVdR\ XfP_gNaiMdkKfmIioGmsHkpHinHglHejIchIaeI_cIYaJW_JUY\ JSVJQTKORKMPKKNL9MKJLJSKIazHjzGszHrzIrzIqzJqOJqPKp\ QKpRLpSPoTUoUZlTciShfQmcOrZMvUKzzJzzJzzJzzJzzJzzJz\ zKzzKzzKzzKzzKzzKzzKzzKzzNzzQzzTzzWzzZzzazzezzdzzc\ zzbzzazz`zz`zz_zzZzzYzzXzzXzzWzzVzzUzzTzzSzzSzzRzz\ QzzPzzOzzPzzOzzOzzNzzNzzN } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD Mystic Moonlight - Rings of Saturn
by Hal Lane 18 Feb '09

18 Feb '09

---------- JackOfTradeZ(a)comcast.net said: --------- > Europa? Loox to me more like flying down into > the plane of the rings of Saturn ... This effect is heightened if you calculate the fractal at 4096 x 3072 and then average 16 pixels (4 x 4) down to one pixel and view the resulting 1024 x 768 image. This operation smoothes out the 'rings' granularity. With the image's 'rings' color variation really, they do look very much like the false color pictures of Saturn's rings. - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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Re: [Fractint] FOTD Mystic Moonlight
by JackOfTradeZ＠comcast.net 17 Feb '09

17 Feb '09

. Europa? Loox to me more like flying down into the plane of the rings of Saturn ... .

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Re: [Fractint] FOTD Dawn Song
by JackOfTradeZ＠comcast.net 17 Feb '09

17 Feb '09

. Interesting image, although I might suggest hues of maroon and crimson rather than blue/purple if you wanna emulate Mars. BTW, to see a REAL Martian sunset go here: http://antwrp.gsfc.nasa.gov/apod/ap090110.html Cheers JoTz .

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FOTD 17-02-09 (Dawn Song [9])
by Jim Muth 17 Feb '09

17 Feb '09

FOTD -- February 17, 2008 (Rating 9) Fractal visionaries and enthusiasts: For today's image I turned the clock back nearly 12 years to May 13, 1997, where I found a fairly harmless fractal named "Martian", which was created by Fractint's built-in 'manzpower' formula. The original intent was to create a fractal that resembled an imaginary scene on the planet Mars. The effect of that ancient effort was only moderately successful. But my fractal coloring has improved in the 12 years since I posted that image, and today's image, which is a slight re- cropping of that old image, has been totally recolored to resemble a sunrise on the same rocky Martian plain. This new effort is far more effective at creating the feeling of a scene on an alien world, this one just before sunrise. I gave today's image the poetic name "Dawn Song", leaving it to the individual viewer to decide who or what might be singing on an apparently lifeless world. Whatever is singing however, IMO the image rates a 9. Those who do not care for other worldly scenes might consider it worth something more like a 6 or 7. The calculation time of only 40 seconds is fast enough to get a space craft to Mars and back in less than a day. This is nowhere near the velocity of light, but it is still fast enough to prevent boredom. Those who prefer to avoid speeding may view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies and a temperature of 36F 2C . . . what could be more typical of mid-February at Fractal Central? The fractal cats didn't question, they simply enjoyed the sun while it was shining and curled up when it was not. My day was typical also. The next FOTD will be posted in 24 hours. Until then, take care, and if one starts with the faith that the world is real, science soon follows. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Dawn_Song { ; time=0:00:40.60-SF5 on P4-2000 reset=2004 type=manzpower maxiter=550 inside=253 center-mag=-0.42022201070671390/-0.000011670951500\ 99/81420.7/2.3247/-5.15/0 params=0/0/3.25/0 float=y colors=000oYamYblXdjXehXggXheWjdWkbWm`Wn_VpYVqjY_b\ YZVYZMXYEXY6XXrY_qY_qY_pY_pZ_oZ`oZ`nZ`mZ`mZ`lZ`l_`\ k_`k_`j_ai_ai_ah_ah`ag`ag`af`ae`ae`ad`bdabcabcabba\ brY_qZZTNYTMYSMZRMZRM_QM_PM`PL`PKaPJaPIaPFbOCcNBcN\ AdMBeMCeMDfLEfLFgLGhLHhLIiMJjNLlOMnPNoQOqSPrTQrURs\ VSsWTtXUuYVuZWv_XvZWsYWpXWmWWkVWhUWeTWcSW`RWYQWVPV\ TOVQNVNMVLLVIKVFJVCIVAHV7GV4GV2HU4IT5IS6JR7KQ9KPAL\ OBMNCMNENMFOLGOKHPJJQIKQHLRGMSGOSFPTEQUDRUCTVBUWAV\ W9WX9YY8ZY7_HpWGnWGlXFkXFiYFgYEeYEcZDaZD__DY_CX`CV\ `CTaBRaBPbWFyXHxYIwZJv_Ku`LtaMsbNrcOqdPoeQnfRmgSli\ TkjUjlVinWhqXgtYfw_ezadzcczeczgbziazkZzmYzoWzrWzzV\ zzVzzTzzPzzXzzVzzKzzIzzHzzFzzDzzCAUBBUABU9CU8CU7DU\ 7EU6ES5FQ4FO3GM2GK1HI0JK3KM5MO8OPAPRDRTFTVIUXKWZNY\ _PZaS`cUbeXcgZeiagjchlfjnhlpkmrmotpqurrwutywryroyl\ kygudZue_sebrffphmcccfUwllwctZercXidO`fERg5Ih7Jh9K\ gBLgEMgGNgIOfKPf00POReQSe } END PARAMETER FILE=========================================

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FOTD 16-02-09 (Son of Wackyland [No Rating])
by Jim Muth 16 Feb '09

16 Feb '09

FOTD -- February 16, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's FOTD is late because I was drawn into another antiquing expedition on Sunday, this time to Lewistown. The late return left no time for a totally new FOTD image, but, going into the vast FOTD library of images, I found an image from April 1998, the 19th of April to be exact, and made a new version of it. The original image was named "Wackyland". I re-cropped and re-colored the original image and named it "Son of Wackyland". Perhaps the most striking thing about the image is its strange resemblance to a scene on an alien planet. Examining the scene, I see a rock-strewn desert with alien cacti dotting the rim of the regolith dune. Others may see far more fantastic things. The generating formula is the MandNewt12, a formula I have not used for many years. Like so many of my old formulas, I have forgotten what it was originally supposed to do, but it makes interesting images regardless. The formula will probably be a new one for all but the most ancient FOTD old-timers. Since today's image is a second effort, I could give it no rating, though in my opinion it shows about a one-point improvement over the original version. The original version has no rating. The calculation time of 20 seconds is not faster than light, but it is still faster than a speeding bullet. And for even more happiness, the finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Bright sun and a temperature of 37F 3C made Sunday a perfectly average day here at Fractal Central. The fractal cats must have enjoyed the sun to the maximum while we were away, for they were waiting in the window when we returned just after dark. My day was pleasant enough despite the antiquing expedition. The next FOTD will be posted in 24 hours. Until then, take care and live life in a wonderland. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Son_of_Wackyland { ; time=0:00:20.75-SF5 on P4-2000 reset=1960 type=formula formulafile=basic.frm formulaname=MandNewt12 center-mag=+1.4989355/-0.04\ 00645/91/1/-105/0 params=-2.06/4.81/-3.31/-0.91/1/1 float=y maxiter=95 inside=bof61 logmap=yes periodicity=0 colors=000ThzThzThzThzQhzThzThzThzThzThzTczTczTczT\ czTczTazT`zT_zTZuTYtTXtTWtTVtTUtTTtSSsSSrSSqRRoRRn\ QQmQQkPQj3NiQJ0OMfNUea4VMNbMNaMN`LMZLMYKLXKLVJLUJK\ TIKRIJQHJPHJNGIMGILFHJFHIFGGKJFPMEUPDZSCcVBcYAc`9h\ c8mc7rc6vc5zc4wc3wc5wc7wc9zhBzmDzmEzmGzmIzmKzmMmZO\ ZYQYWSXVUWTWVSYUQ_TPaUI0UK0UK0UK0UA0UK0N_0P`0Ra0Tb\ 0Q5pQ4sR3uR2xS7rUBmVGgWKbXPXZTR_YM`aGbfAbdCcbFc`Id\ ZKeWNeUQfSTgQVhOYhM`iJcjHejFhkDkkFkjGjjIjjJiiLiiMh\ iOhiQghRghTfhUfgWegXegZdf_dface_ccYcbWc`Uc_ScZQcXO\ cWMdUKdTIdSGdQEdPCdNAdM8dK6eL6eO5dR4cU4bX3a_2``7ba\ CdbHfbLhcQjdVle_nfamgclgejhfiihhjjgjlekndlpcmqbms`\ nu_oqapncqjerggrcis_ktXmuTolVjdXeWY_O_VFaQFaPFaPFa\ OEaNEaNEaMEaLEaKEaKEaJEaIDaIDaHDaGDaGDaFDaEDaDCaDC\ aCCaBCaBCaACa9Ca9Ca8Ba7Ba6Ba6Ba5Aa4Ca7FaBHaEKaIMaL\ PaPSaSUaWXbZZbbabedbifblibpkbsnbwnbunbtncrncpncnnc\ modkodiodhodfoddoeboeaoe_ } frm:MandNewt12 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-1)*(z-b) j=c*z^d+g z=z-e*h/(f*j), .0000000000000000000000000000005 <= |h| } END PARAMETER FILE=========================================

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Re: [Fractint] Be My Valenfractal
by JackOfTradeZ＠comcast.net 16 Feb '09

16 Feb '09

It loox cool, may make an interesting zoom, but I think there is error in the post, especially the colors part. Fractint keeps giving me that "oops" error response. Is it me or anyone else have this problem? Also, if you copy and paste the PAR entry, the CRLF is missing - it is all one long line. Never had that before.

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FOTD 15-02-09 (Be My Valenfractal [7])
by Jim Muth 15 Feb '09

15 Feb '09

FOTD -- February 15, 2009 (Rating 7) Fractal visionaries and enthusiasts: The name of today's image is "Be My Valenfractal". Yes, I realize that Valentine's Day was yesterday, but I am writing this Yesterday, so it really is, or was, Valentines Day. I haven't the slightest idea what a valenfractal is, and a glance at today's image will be of no help in solving the mystery. But the image is one of those that calculates faster than light and therefore finishes before it starts. The image is located on the main stem of its parent, which is just starting to morph from an order-13 Mandeloid into an oversized Mandelbrot set. The many minibrots in the image are still of order-13, with 12 lobes, but don't ask what the minibrots with 25 lobes are doing in the image. All I can say is that fractals are very mysterious. I rated the image at an average 7. As I said above, the 4-second image finishes before it starts, so don't forget to start the calculation when the image appears already finished on your screen. Failure to follow these instructions will set off an unstable feedback in time, which will result in the destruc- tion of the universe. To avoid all such apocalyptic dangers, hurry to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completed image there. Actually, the image is a rather pleasant one, with the overall pattern repeating itself at ever smaller scales all the way to infinitesimal infinity. Valentine's Day brought very real flurries of snow to Fractal Central, while the temperature of 37C 3C made sure the snow melted as fast as it fell. The lack of sun brought dissatisfac- tion to the fractal cats, while the reasonably quiet day brought peace to the rest of us. The next FOTD will be posted in 24 hours. Until then, take care, and stand out above the crowd. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Be_My_Valenfractal { ; time=0:00:04.32-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 center-mag=-3.328155158369\ 073/0/5.2654e+011 params=13/2 float=y maxiter=1500 symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=000zwzWUU_`d`_a`Z_`ZX`YV`XSEMvIOqLQlORgSTcV\ UZYWU24_89YEEWKJVQOTWTRFHhKLdOO`TRXK00O00Q00S00U00\ W00Y00_00a00c00e00gAIiEDlG9lMBoPCpUDrYEubFvdGs_DpS\ AhH7_64QA8LEBaPUOIESMHVQKYUNJgRMeQPcQRbQU`QW_QZYQU\ bvvt9rpCnlFkhIgdLc`O9GrJMhSSZ4UcFVZQWU3HC8KEDMGIOI\ NRKSTMXVOAYDEXFHXHLXIOXKRXMVXNYXPV0vW6pXBkYHeZM`_S\ VOgmTceX_Y4ZAAYDFYGLYIQXLWXOggwAMzEOtIQoMRjQTdUU_Y\ WVgDct5tpAnmFijJdfO_cTVph_mfYjdWhbVe`TbZRx`4t_8pZC\ lZFhYJdXN`V8`WB`WD`WF`WH`XK`XM`XOku4hnAehFbbLvkzrh\ tofoldjibdf`_cZVV`JexJdrLclMbgOaaPasy`km`caH8bLD_P\ IXTNVXSS2Io7KkBMhGOeKQbOSZTUWXWTQQCTSGWUJZWNz4Jv8K\ sCLpFMmJNiNOfQPcUQ0fHAcKJaMSZOPxaRt_SqZUmXVjWXfUYc\ T__R3Kc8MaCO_GPYKRXPTVTUTXWRx34lIFw92sD6oHAkLEgPIc\ TModPUJBVLDWNFXPHYQJZSL_UN`WPsPRUZCWYFXYHYYJZXM_XO\ mWZkXXiXWhXVfXUdXTcXSaXR3RyKUgPzeRubTp_VkYXfVZaSTc\ yVapX_gZYZ1Cu7FpCIkHLgHLg } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 14-02-09 (Search for Reality [8.5])
by Jim Muth 13 Feb '09

13 Feb '09

FOTD -- February 14, 2009 (Rating 8.5) Fractal visionaries and enthusiasts: I named today's image "Search for Reality". The name came about when something in the image reminded be of the sub-atomic realm, which is a totally different form of existence. I have been fascinated with 'reality' ever since my father introduced me to the puzzle of reality when I was around age 12. Until then, I had wondered why there was such a fuss about the nature of reality. I had automatically assumed that the world we see around us is real, and that was that. Then on a Sunday morning, as my father and I were looking from a second floor window at a ringing bell swinging back and forth in the tower of a church a block away, he turned to me and asked if the sound we were hearing were the actual bell itself. Thinking it was a test of my scientific knowledge, I replied that we were not hearing the bell itself, we were hearing only the sound waves from the real bell. Then he pointed to the bell swinging in the tower and asked if that were the actual bell. Without thinking, I replied that yes, that is the actual bell that is making the sound. But when I said this, my father told me that I was wrong. We were not seeing the actual bell, we were seeing only the light waves coming from the real bell. When he said this, I asked him what then is the real bell, and he told me that no one knows what the real bell is. The real bell, as well as the reality behind everything else we see in the world, is a mystery, and this mystery is what all the philosophical fuss is about. Ever since then, I have been wondering what, if anything, is really out there. And now I find myself wondering if even fractals are really out there. One thing certain (I hope) is that today's image really exists. Its heavenly blue tints and gently curved neon rings have earned it a rating of an 8-1/2, 1/2 point of which is a reward for the coloring. The parent fractal is the same one that has supplied the past 3 days' FOTD images. The calculation time of 1-3/4 minutes will pass like magic once the heavenly colors come into view. Those who doubt that heaven exists may see the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> without fear of eternal condemnation. Heavy clouds, continued breezy conditions and a temperature of 41F 5C made for a typical midwinter day here in central Pennsyl- vania. The fractal cats were restless due to the lack of sun, and almost got into a fight over a catnip mouse. My day was rather uneventful, which, taken wrongly, might imply that there actually was an 'event'. The next FOTD will be posted in 24 hours. Until then, take care, and would the real reality please stand up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Search_for_Reality { ; time=0:01:46.43-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip float=y center-mag=+1.703904359650447/-9.221842800854315/\ 1.5e+010/1/138/0 params=-11/-1.1/-1.1/-11.1/0/100/\ 0/0 maxiter=1500 inside=0 logmap=187 periodicity=10 colors=000QKlNNiKNgJOiIPjIPkHQlGQmGRoFRqESsETuDTwC\ UzCUzBVzBVzHRvNOsTLqYIp_Oo`UnbZmcdlejkzzzzzzzzzzzz\ HorIlqIjqIgqIeqIbqI`qIYqJWqJTqJRqJOqJMqJJqJHqJFq9T\ xDSsHSnLRiORdSQ_WQV_QQbPLfPGjOBnO6qO2iYGagUVpgPgZJ\ _RDSJ7KB8MD9OF9QHASJATLBVNBXPCZRC`TDaVDcXEeZEg`Fib\ Fjc`lRYiTWfVUcXS`ZQY`OVbMSdKPfHMhFJjDGlBDn9Ap77r54\ t31u99pFGlLOgQVcWbZaiVfpReqPdqOcqMcqLbrJarI`rG`rF_\ sEZsCYsBYs9Xt8Wt6Vt5Vt4FZO0Dg2Cc4B_6AW89SA8OC7KE6G\ G5CI48K34M20Y11i02e17b2C_3HX4MT5RQ6VN7_K8dG9iDAnAB\ s7Bw6Cs6Co6Cl6Dh5Dd5Da5EY5EU4ER4FN4FJ4FG7HKAJNDKQG\ MTJNWMPZPQaSSdVTgOZhIdiCij6ok0tk1ql2nl2km3hm4en4bn\ 5_o6Yo6Vp7Sp8Pq8Mq9JrAGrAErEHpIJnMLlQNkUQiYSg`UfdW\ dhZbl`apb_tdYwfXriUnlRioOerLauJzzHzzGzzFzzEzzCzzBz\ zAzz9zz7zz6zz5zz4zz3zzazz`zz_bzZczYdzYfzXgzWhzVizU\ kzTlzSmzRnzRjzYfzdbzkZzrWzoUzmRzjPzhNzfKzcIzaGz_Dz\ XBzV9zT6zQbzpazs`zuXzrUzo } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 13-02-09 (Gilded Grandeur [6.5])
by Jim Muth 12 Feb '09

12 Feb '09

FOTD -- February 13, 2009 (Rating 6.5) Fractal visionaries and enthusiasts: The name of today's image -- Gilded Grandeur -- might be somewhat of an exaggeration, but the image, which comes from the same general part of the same parent fractal as yesterday's image, is at least a slight improvement. The rating of a 6-1/2 includes a 1/2 point golden-parachute bonus for my moderately successful attempts at coloring, though in this case, I have no intention of leaving the world of fractals in the foreseeable future. The calculation time of 2-3/4 minutes will pass like lightning once the image starts to appear. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will pass like greased lightning, though I cannot imagine how one might apply axle grease to a bolt of lightning. The temperature of 45F 7C here at Fractal Central on Thursday was fair enough, and the partly cloudy skies were no problem, but the wind, which gusted to 65mph 100kph through the day made walking around every corner a challenge. The fractal cats spent most of the day at their big window, watching the trees thrash about and various objects blow past. When a sudden gust brought a number of trash containers clattering down the middle of the street, the cats ducked for cover, but curiosity soon brought them back to the window. My day was close to normal, and with any luck, tomorrow will be the same. The next FOTD will be posted in 24 hours. Until then, take care, and be sharp. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Gilded_Grandeur { ; time=0:02:45.28-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+4.3509231858/-2.6606863958/368010/1/\ -157/0 params=-11/-1.1/-1.1/-11.1/0/100/0/0 float=y maxiter=1200 inside=0 logmap=158 periodicity=10 colors=000PiePidPQcKbXFXRBRL6LF2F9NTHcgc`TYchcYRcc\ VxZExUmxRRcOetLMeJZqGToDQmALk8Hj5Ch27f03elEPmGOnHO\ nIOoJOoLOpMNpNNqONrQNrRNsSMsTMtVMtWMuXMuYMr_Lo`Kla\ JicIgdHdeGagFZhEqiDUjDnlHdmLjnPooTzuXzq_yp0woZvoZu\ nYtmYMH9NKAOMCPPDQSERVFRXHR_zRbJOwfRdKTdMVdNYdP_cQ\ acSdcTfcVhbWkbYmbZob`qba2Ut5Tq8ToBTmETjHShKSfNSdQS\ aTS_WRYZRVaRTdRRhcIgRPfEVf2`d6_bA_aE__I_ZM_XQ_WT_U\ X_T`_Rd_Qh_Ol_QsdNo_zkBJgSGcNE_JCWFATBEVCHXCKYCN_C\ R`DUbDXcD_eDcl7bfDaaI`XN_STZNYT7cZIbcSaia`nk_su_eb\ SSKLTPMUUMVZNWcNXhOYmOVcVSVaQLhNCoJ0vL3uM5uO7uPAtR\ CtSEtUGtVJsXLsYNs_Qr`SrbUrgYBcWrbYoaZl`_z``f_azZb`\ ZczYdWXezXfQWgzVhKVizUjETkzTl9RkzPjEOiGMhILgLJfNIe\ PGdREcTDbWBaYA`_8_a7Zc9YeBXfDWgEWhGWiIWjJWkLVmNUnP\ ToQSpSRqUQrVOtWMwYKz_IzaGz_EzXDzVGzTIzQLzONzMPzJSz\ HUzFXzCZzAaz8cz6ez8fz9fzBfzCfzDfzFfzGfzIfzJfzKfzMf\ zNfzPfzQfzRfzQgzQgzQhzzzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 12-02-09 (Anything Goes [2.5])
by Jim Muth 12 Feb '09

12 Feb '09

FOTD -- February 12, 2009 (Rating 2.5) Fractal visionaries and enthusiasts: Today's fractal is not only 12 hours late, it is hardly worth a mention. But it does exist -- this is an undeniable fact. The image is one that I would normally toss in the fractal waste bin at once, but for some strange reason, I decided to make it the FOTD for February 12. I guess I did it to show the kind of stuff I usually throw out. I named the image "Anything Goes" because I can find nothing in it that might make any kind of a theme. It consists basically of random blotches of uncoordinated shapes and clashing colors. Despite the unimpressive colors I actually dared to give myself a half-point bonus for the coloring, which raises the overall rating to a pathetic 2-1/2. The scene is located in a filament extending from a kind of bud on a kind of minibrot at the edge of the 'fan' in the parent fractal of yesterday's image. The calculation time of 6-1/3 minutes is admittedly slow for such a poor image, but to see what all this negativity is about without waiting for the calculation to finish, go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image will soon be posted for instant relief. We had a little touch of spring here at Fractal Central on Wednesday, with lots of sun and a temperature of 64F 18C. The fractal cats peak of excitement came when they saw a pair of ravens light on the chimney of the house across the street. My peak of excitement came when I got the day's work finished. The next FOTD will be posted in 12 hours. Until then, take care, and keep your spirits up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Anything_Goes { ; time=0:06:21.79-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip center-mag=+2.149764823835/-2.574942088379/315766/\ 1/22/0 params=-11/-1.1/-1.1/-11.1/0/100/0/0 float=y maxiter=6000 inside=0 logmap=646 periodicity=10 colors=000HAUHU9cBBGBUGUFcCHC4UGUJcKLMSOQ_QTgTWoVZ\ wXdoRieMjgMjiMkkMkmMloMlqMmsMMDr_ZamtM_gZMVj9JvCMr\ FPoISkLVhRciNYeKTbHN_EIWBCT87Q52NHDUTN_dXee_efaegc\ egeehgeiiefuslmgikefjdchbagaZe`WdZTbYtUDeYNRaXXDw8\ kbDefH_iLUmQOpUItYCwa6zTDoKJeBPVbw9LhF3VLS4R6QbAUX\ EYRIaMMeGQiAQr3Tm5Wi7Zd8a`AkIbmL_oPXqSUsVSpVRmVQjV\ PgVOdVNaVMZVLWVKSNHOFFK8DZKFIGGIKIHOJGSLGWMF_OFcPM\ ZTSVXZR_dMckIfqEjwAmiEpXIrKMu7Pw9_tBjqDunGtkIsiLrg\ NrePqcSpaUo_WoY_lZciZgf_jc_n``rY`uV`sUXrTUqSRpROoU\ QoXRnZSnaUmcVmfWmhXQeL3S9WWAMQAVKATEB`JBu2BuGFdhta\ Ks_MpZOmXQkPIYiUfTWcExDLjQSXaFgfPWjZKmyMht5uh9pXDk\ LHfAKaTEWCPRccMIIZMVjQgvUeqYdlabgeabi_YmZTeFntVMqY\ On`PkcRhfSZ`Bwj_fhTRjLRhMRfNRdORcORaPR_QRWRRZQR`QR\ bQRdQRfQHiKRhQktYenX`hWWcVRYUMTUNUYOUaPVdQVhOSeQVk\ SYpU`uWczUeqSghQi_7k_GmVOoREqANsHWuNcvTlwZtxdly_dz\ VYzQQzLKzLJzGJzBIz6Iz2Hz5 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 11-02-09 (Secluded Shoreline [6])
by Jim Muth 10 Feb '09

10 Feb '09

FOTD -- February 11, 2009 (Rating 6) Fractal visionaries and enthusiasts: Today we are faced with another of my genuine evaporated fractals. An evaporated fractal is exactly what the name implies -- a fractal with a bailout radius so large, (in today's case, one-googol), that the entire fractal has melted away to nothing but trapped 'inside' stuff. The generating formula combines various negative portions of Z^(-1.1) and Z^(-11.1) to create an indescribable parent fractal with the usual prominent 'fan' opening east from the origin. Of course, with a bailout radius of one-googol, the parent fractal is a totally blank screen before the 'bof61' inside fill is applied. When the inside fill is applied however, the parent fractal appears, with today's scene lying in a curving valley at the eastern edge of the 'fan'. I thought of the name "Secluded Shoreline" when I noticed the effect of waves breaking on an idyllic secluded tropic shore. I rated the image at a 6 when I found only slight satisfaction with the coloring. The calculation time of 6 minutes means that little time will have been lost if the finished image fails to please. And the finished image may be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> with no risk at all of wasted time. Tuesday here at Fractal Central was spoiled by clouds and occasional showers. The temperature of 43F 6C was fair enough, but the fractal cats need more than mild temperatures to bring contentment. They displayed their dis-satisfaction by getting into a noisy tussle over a catnip mouse. The work was a little lighter than usual, which, considering the supposed economic meltdown, was not too bad. The next FOTD, glorious or not, will be posted in 24 hours. Until then, take care, and when you've finished taking care, have some fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Secluded_Shoreline { ; time=0:06:08.83-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+4.71691044048/-0.18503827863/3.94e+007\ /1/-110/0 params=-11/-1.1/-1.1/-11.1/0/1e+100/0/0 float=y maxiter=2100 inside=bof61 periodicity=10 colors=000bpPcoOcoNcnLdmKdmJdlIdlHekFejEejDfiCfiBf\ h9gg8gg7gf6fh6gf5ge5hc5hb5ha4i_4iZ4jY4jW4jV3kU3kU3\ lR3kR2lO2jM2mM2cK2nJ1eI1oG1fF1oE1hUzDDSEGTEIUEKVFM\ WFOXFQYFSZGU_GW`GYaG_aHbbHdcHfdIheIjfIlgInzJpzJrzJ\ tzJvzLtzMrzOpwPnwRmtQlsPksPkrOjrOiqNiqMhpMgpLgoLfo\ KenKenJdmIcmIclHblHakGakF`jF_jE_iEZiDYh9XfDYhGZiKZ\ jN_kR`lU`mXan`bocbpgcqjdrndsqetwfxteuqdrncokblhbie\ afb`d__aXZZUZWRYTOXQLXOIWLFWICVF9UC6V94S73RA3OC3LE\ 3JG3JI3HK3FN3FP3ER3FT2FV2FX2GZ2Ga2Hc2He2Hg2Hi2Gk2G\ m3Fn4Fn4Fn5Fo6Gq6Gs7Ht8Hu8Hv9Hw9HxAHyBLzBOzCSzDVzD\ YzE`z8czEfzJjzOEiTEeYEacEXhETmEPrELxDIwEHvEHvFHuFH\ uGHtGHtHHsHHsIHrIHrIHqJHpJHpKHoKHoLHnLHnMHmMHmNHlN\ HqLFlNHhPJdRK_TMWVNSXPOZQJ`SFbTBdV7fW9gVAhUBiTCiTD\ jSEkRFkRGlQHmPInOJnOKoNLpMMpMNqLOrKPsJQsJRtISuHTuH\ UvGVwFWwFXrEXnDXiDXeCXaBYXBYTAYP9YK9YG8YC8ZG9ZJAZM\ AZPBZSCZVC_YDbpQarTbqRbpQ } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 09-02-09 (Siegels on Parade [6])
by Jim Muth 10 Feb '09

10 Feb '09

FOTD -- February 09, 2009 (Rating 6) Fractal visionaries and enthusiasts: In yesterday's discussion I mentioned Siegel Disks. Actually, I'm not sure of the significance of Siegel Disks. The math encyclopedia defines the Siegel Disk Fractal as a Julia set (of the Mandelbrot set) with c=-0.390541,-0.586788i. But why this particular fractal is special is a mystery. I can see nothing unusual or unique about it. The corresponding point of the Mandelbrot set lies exactly on the boundary of the main bay, but other points on the boundary give similar fractals. The answer must lie somewhere in one of the fractal books I have not yet come upon. Today's image is an extension of the Siegel Disk idea, a Julia set of a point on the boundary of the Z^6+C Mandeloid. It is filled with things that closely resemble Z^2+C Siegel Disks, with six large disks and an infinity of smaller ones, their position made obvious by the coloring. The fractal is rather attractive, though its familiarity prevents it from earning a rating above a 6. I named the image "Siegels on Parade", and why not? After all, a parade with an infinity of marching Siegel Disks would take forever to pass the reviewing stand. Luckily, the march is only symbolic, and the fractal takes only 3-3/4 minutes to calculate. And even better, the already-calculated image is or soon will be posted on the FOTD web site for immediate and intense gratifica- tion. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday brought a prelude of spring to Fractal Central, with total sun and a temperature of 55F 13C. The wind was a bit higher than ideal, but the fractal cats didn't mind a bit. My day was uneventful, though I heard that a rather sizable job will be coming in sometime Monday. The next FOTD will be posted in 24 hours. Until then, take care, and is skepticism always the most rational approach? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Siegels_on_Parade { ; time=0:03:45.73-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=JuliaN passes=1 center-mag=0/0/0.928 params=6/0/0/0/-0.4241305333947207/0.6631595440171\ 235 float=y maxiter=3200 inside=bof60 logmap=yes symmetry=origin periodicity=0 colors=000A4fA5eA6dA7cA8bA9aAA`AB_ACZADYAEXAFWAGVA\ HUBITBKSCMRDNQEPPoROpTLqUIrWFsYCtZAu_9v`9wa9xa8yb8\ zc8zc8zd7ze7ze7zf7zg6zh6zh6zi6zj5zj5zk5zl5zl4zm4zn\ 4zpUzqZztczwhzzjsZKgVOfRSfNWfJ_iFbfGcdGdbGe_GeYGfW\ GgTGgRGhPGiLDjNGiOJiPMhRPhSSgTVgVYgW`fXcfZfe_ie_ng\ `keaidbfccdadb`e__fYZgWXhTWiRVjPTkMSlKRlHNmIQmITmI\ WmIZnIanIcnIfnIioIloIooIrpJvoItnIrmHqlHokHmjGliGjh\ GihFggFefFdeEbdEacE_bDYaDX`DV`CT_CSZCQYBPXBNWBLVAK\ UAIW7GUAHTDIRGJQIKPLKNOLMQMLTNJWOIZOH`PFcQEfRPvUDh\ REgTEfUFfVFeWGeXGdYHdZHc_Ib`IbaJacJadK`eK`fL_gL_hM\ ZiMYjNYkNXlOXmOWoPWpPVqQUrQUsRTtRTuSSvSSwTRxTRyQWt\ N_oLdjIheEmZGl`HlaJkbKkcMkdNjePjfQigSihTiiVhkWhlYh\ mZgn`goafpcfqdfrfesgetheugctfbsf`se_rdZrdXqcWqbUpb\ TpaSo`Qo`Pn_Nn_MmZLlYJlYIkXGkWFjWEjVCiUBiU9hT8hS7g\ S5gR4fR3fO5dL7bJ9aGB_DDYBEXFFYIGYLGYOHYRHYUIY7Jh6I\ j6Hk6Gl6Fm6En5Do5Cp5Bq5Ar } frm:JuliaN {; Jim Muth b=p1, z=p2+pixel, c=p3: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 10-02-09 (High-Order Chaos [5])
by Jim Muth 09 Feb '09

09 Feb '09

FOTD -- February 10, 2009 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal is a surprisingly varied scene in a Z^100+C Julia set. The Mandelbrot set of this formula is basically a circle of radius-one centered at the origin, with 99 tiny bays around its perimeter. The Mandelbrot point of today's Julia image is at an angle of 45 degrees from the origin, at a distance of a tiny bit more than 1, which puts it in the narrow strip of action along the edge of the circle. As is the case with many Julia fractals, a bit of tweaking will show that the image is extremely sensitive to the slightest change in the parameters. The name "High-Order Chaos" is a brief description of the image. The rating of a 5 means that I had no chance to work up a better color palette. The colors in the image are adequate, but could be far better. The calculation time of 4-1/3 minutes borders on slowness, but the threat of impatience may be avoided by viewing the image in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Warm sun and a temperature of 48F 9C kept the fractal cats happy here at Fractal Central on Monday, while the big job kept me busy. The next FOTD will be posted in 24 hours. Until then, take care, and fractals are not sold in stores, BUT WAIT! they are available for free all around you. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= High-Order_Chaos { ; time=0:04:19.84-SF5 on P4-2000 reset=2004 type=julzpower passes=1 float=y center-mag=-0.00902307/0.830711/47.88985/1/-10/0 params=0.7087301008243692/0.7071245054773092/100/0 maxiter=3200 inside=255 logmap=85 periodicity=0 colors=000cNDdNEeNEfOFgOGhPHjPIkQIkQJfOKeQLePLdQMd\ QNdROjXziXziYziZziZzi_zh`zh`zhazhbzgbzgczgdzgdzgez\ ffzfgzfhzfhzejzekzekzelzenzdnzdozdpzdpzcqzcrzcrzcs\ zcszaqz`ozZmzYlzWjzVhvTgrSemQbhPahN_bMYZKVUJTSIQRG\ PPEOODNMBNLANKDNLFNLHNMKNMMNNONNQNNTOOVPOXQPZRP`SP\ aSQbSQdSReSRgSRhSShSSiSTjSTkSTlSUmSUmSUmTVjVZhXce_\ hcamacrZfvXhzUjzSmzPozNqzLszJqzHozFmzEmzCmzAmz8mz7\ mz5mz3mz1mz0mz1mz2mz3mz4mz4mz5mz6mz7mz7mz8mz9mzAmz\ AmzBmzCmzDmzDmzEmzFmzGmzGmzHczIXmJScJSUKSELSEMSFMS\ FNSFOSGPSGPSGQSHRSHSSISSITSIUSJVTJVTKzUKzcKYVLzhLz\ hM_WMzhMzhNaXNbXOzYOzYOzZPzZPzZQf_Qg_Qh`Ri`Ri`ReYM\ aWHZUC_TD_TD`TE`TE`TFaTFaTGaTGbTHbTHbTIcTIcTJdTJdT\ KdTKeTLeTLeTMfSMfSNfSNgSOgSOhSPhSPhSQiSQiSRiSRjSSj\ SSjSTkSTkSUlSUzj0zM0mR0mR0zRXUC0UC0UC0UC0UC0UC0UC0\ UC0UC0UC0UC0UC0UC0UC0UC0UC0_H0ZG0ZG0ZF0YF0YE0YE0YD\ 0XD0XD0XC0ZC0WB0WB0jK0jK0 } END PARAMETER FILE=========================================

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Re: [Fractint] Julia More or Less
by JackOfTradeZ＠comcast.net 08 Feb '09

08 Feb '09

. Re: Internet problem. I dont know about you, but I do not leave my connection on all the time. I use the hardware switch on the cable modem and only turn it on when I am going on line. Usually it is instant, but sometimes it takes a few seconds to "connect". During this time, if I try to access a web page, I get the same error (obviously). The only way I know is a little icon in the tray which animates while connecting. Just waiting for the connection to establish and reloading the page is then ok. Also - about the image. The black lake in the middle has horizontal lines. I noticed something like this this years ago during some of my exotic julia zooms and morphs, thought it was a genuine part of the fractal and it looked cool (like "eye of hell #2 viddie). Turns out it was a software "issue" in fractint, or thats what some people in this forum said. Is that the case here or not? Any rate it is an interesting image, I may try to animate it. Hopefully will be better than the last one <g>. Stay Amazed JoTz .

1 0

FOTD 08-02-09 (Starry Seven [7.5])
by Jim Muth 07 Feb '09

07 Feb '09

FOTD -- February 08, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: To celebrate the warmest day in several months, FL and I took a trip into the surrounding country on Saturday. Perhaps not by chance, we came upon an antique emporium we had not yet visited. Luckily, the place was small and we made it back to F.C. well before nightfall, which left ample time for my fractal ambitions. The image shows an order-8 minibrot on the northwest shore line of a monumentally enlarged Mandelbrot set. The location is in the area where Siegel disks appear in the corresponding Julia sets. (Siegel disks are a story for another day.) For no rational reason I named the image "Starry Seven". Then I rated it at a 7-1/2, giving myself a 1/2-point bonus for the extra effort I put into the coloring. The calculation is exactly seven minutes, within 1/100th of a second. I think this is the first time this has happened. But the time is a bit on the slow side, so for convenience, the finished image has been or soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Some clouds moved in here at Fractal central on Saturday, but when the temperature reached a high of 48F 9C, it felt almost like a day in mid-May. The fractal cats watched the scene from the big window, waiting patiently for our return. My day was average. The next FOTD will be posted in 24 hours, with no guarantee of its quality. Until then, take care, and is it unreasonable to fight for reason. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Starry_Seven { ; time=0:07:00.00-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 center-mag=-39.7877072626944/+37.25223239209976/\ 1.685524e+008/1/48.75/0 params=8/75 float=y maxiter=3000 inside=0 logmap=500 periodicity=10 colors=070UK0cN9cKCc8Ec7Ic7Lc7Jc7Ic9GcCEcGDcLCUSAK\ Z9Ie9E`5DV2CQ0AL09I0X81z78t7Am7Df7Gb7JX7NS7QN8TJ8X\ T7mb7zV7zQ7zL7zG7zC7z87z57z27z07z08z08z07z07t07h07\ `07S07L07D078073070070070070E7Jz7zy7zm7td7hVAXNDOG\ GG9L84S31X04U08Q0DN0JL0QJ0XG0dF0mD0vB0zA0tE0hI0ZL0\ QQ0IV0C`06e01k00r00x00z00z00v01r04m18i4Dg9JcEQ`LXX\ SdUZmSfhPhfNkbLm`KoXIqVGtSFvQEvOCyLBzJAzGAzE8zC8zA\ 7z97zA7zA8zA8vA8qA9mAAhAAbAAZABVACSADOADLDFGEICGJ9\ JL6LP4NQ1OU0SX0TZ0Vb0Xc0Oe0Gg09i05i01k00m00m00r00t\ 00v10x50z80zC0zI0zN0zS0zZ0zd0zk0zt0zz0zz0zz1wJJt0O\ q0Tn0Zj0cc0gZ0kV0mR0mP0mK0mG0mL0mS0rX0vc1zi2zr4zz5\ zz7zz9zzAzzDzvGzkIz`LyQOtJQqCTo8Xk7Zh7bf7dh7dh7dk7\ dk7dk8dmAdmCdmFdoIdoLdoPdqMfqMhqLktLmtLotKovKqvKtv\ KvyLyyLzyNzzPzzSzzTzzWzzYzz`zzbzzbzzbzzbzzbzzbzzbz\ zbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzbzzb\ zzbzzbzzbzzbzzbzzbzzbzzbz } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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R: FOTD 07-02-09 (Julia More or Less [?])
by jakovll＠libero.it 07 Feb '09

07 Feb '09

Don't know why I get this message when I try to go to the site, any idea? thanks, Jacopo. Rome 'Page URL Not Found!! The requested page does not exist on this server. The URL you typed or followed is either outdated or inaccurate. Type your search term above instead or click here to let us help you find web pages you are looking for!' >----Messaggio originale---- >Da: jamth@mindspring. com >Data: 07/02/2009 4.40 >A: <fractint(a)mailman.xmission.com> >Ogg: [Fractint] FOTD 07-02-09 (Julia More or Less [?]) > > >FOTD -- February 07, 2009 (Rating ?) > >Fractal visionaries and enthusiasts: > >Today's image is not a Mandelbrot set, nor is it a Julia set. >It is an Oblate set, a hybrid mixture of Mandeloid and Julia >stuff. The X-axis lies in the Julia direction, while the Y-axis >lies in the Mandelbrot direction. > >I have not yet made up my mind about today's image, which is why >I gave it a rating of a question mark. At times, these four- >dimensional slices through the Julibrots can be spectacular, but >at other times, they are just plain ugly. Today's image lies >somewhere in between. > >The name "Julia More or Less" is absolutely true, but only as >long as we consider the horizontal direction. When we turn to >the vertical direction, we are moving through a Mandelbrot set. >The other directions lie in the Julibrot, and are neither Julia >nor Mandelbrot dimensions. > >The parallel blue stripes in the background are the 'bridges' >that exist only in planes in which only one direction is perpen- >dicular to the Mandelbrot orientation. When all directions are >perpendicular to the Mandelbrot orientation, which is possible >only in spaces of four or more dimensions, we have a Julia set. > >Maybe I'll continue this four-dimensional stuff in upcoming >FOTD's, maybe not. I've gone over it several times in the past. > >Perhaps the best feature of today's image is its brief calcula- >tion time of only 49 seconds. And even this minor effort may be >totally avoided by surfing electronically out to the FOTD web >site at: > > <http://home. att.net/~Paul.N.Lee/FotD/FotD.html> > >and viewing the finished image there. > >Not a single cloud marred the spectacularly blue sky here at >Fractal Central on Friday, while the temperature of 36F 2C felt >like spring. The fractal cats enjoyed the weather from their >sunny shelf by the big southwest window, taking their breaks >only when hunger called. My day was busy enough that one would >never guess we are supposed to be in economic hard times. The >next FOTD will be posted in 24 hours. Until then, take care, >and it's all real, whatever that means. > > >Jim Muth >jamth(a)mindspring.com >jimmuth(a)aol.com > > >START PARAMETER FILE======================================= > >Julia_More_or_Less { ; time=0:00:49.79-SF5 on P4-2000 > reset=2004 type=formula formulafile=basic.frm > formulaname=DivideJulibrot passes=1 maxiter=3600 > center-mag=2.31005/0/9.197812/1.3049 params=0/0/90\ > /0/- 1.3243408/0/0/0/3/1.4 float=y inside=0 > logmap=6 symmetry=xaxis periodicity=10 > colors=000P9bL9fI9iE9mA9p69t39w6Br9CnBEjEFeGHaIIYL\ > ITOIPNILNIGOICPI8QI9RI9SI9TI9UH9VGAXEAYDA_DA`CAbAB\ > c9Be7Bg6Bi4Bi3Bm9GqFLuLQxQVuSYrT_oUalVciXefYgcZia_\ > kZagWccUd_RfWOhSMiPJkLGmHEnDKp9Kq6Kq6Kp7mo7mo7mn7m\ > n8zm8zz8zz8zl8mk9mj9mj9mi9Bi9BhABgABfABeACdACcBCcB\ > CcBCcBCcBCcCCcCCcCDcCDcCDcDDcDDcDDcDDcDDcEDcEEcEEc\ > EEcEEcFEcFEcFEcFEcFEcGFcGFcGFcGFcGFcHFcHFcHFcHFcHG\ > cIHcJHcJIcKJcKJcLKcLLcMLcMMcNMcNNcOOcOOcPPczQczQcz\ > RczSczSczTczTczUczVczVazW_zXYzXWzYUzZSzZQz_Qz_Qz`Q\ > zaQzaQzbQzcQzcQzdQzeSzeUzfWzfYze_zdazdczcczcczbczb\ > czaczacz`cz`cz_czVczZczZczYczYczXczXczWczWczVdzZez\ > YdzYdzYdzYczYczYczYczYbzYbzYbzYazYazYazYazY`zX`zX`\ > zX`zX_zX_zX_zXZzXZzXZzXZzXYzXYzXYzXYzXXzXXzWXzWWzW\ > WzWWzWWzWVzWVzWVzWVzWUzWUzWUzWTzWTzWTzVTzVSzVSzVSz\ > VSzVRzVRzVRzVQzVQzVQzVQzVPzVPzVPzTKzJ2zK3zK3zK3zK4\ > zK4zK4zK4zL5zL5zL5zL5zL6z } > >frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots > pix=pixel, u=real(pix), v=imag(pix), > a=pi*real(p1*0. 0055555555555556), > b=pi*imag(p1*0.0055555555555556), > g=pi*real(p2*0. 0055555555555556), > d=pi*imag(p2*0.0055555555555556), > ca=cos(a), cb=cos (b), sb=sin(b), cg=cos(g), > sg=sin(g), cd=cos(d), sd=sin(d), > aa=-(real(p5) -2), bb=(imag(p5)+0.00000000000000000000001), > p=u*cg*cd-v* (ca*sb*sg*cd+ca*cb*sd), > q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), > r=u*sg+v*ca*sb*cg, s=v*sin(a), > c=p+flip(q)+p3, z=r+flip(s)+p4: > z=sqr(z)/ (z^(aa)+bb)+c > |z|< 1000000 } > >END PARAMETER FILE========================================= > > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi- bin/mailman/listinfo/fractint >

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R: Re: R: FOTD 07-02-09 (Julia More or Less [?])
by jakovll＠libero.it 07 Feb '09

07 Feb '09

I tried holding the shift, no hope... >----Messaggio originale---- >Da: Maryetta.C(a)Earthlink.net >Data: 07/02/2009 16.48 >A: <fractint(a)mailman.xmission. com> >Ogg: Re: [Fractint] R: FOTD 07-02-09 (Julia More or Less [?]) > >jakovll(a)libero.it wrote: >> >> Don't know why I get this message when >> I try to go to the site, any idea? >> >>> ----Messaggio originale---- >>> ........ >>> And even this minor effort may be totally avoided >>> by surfing electronically out to the FOTD web >>> site at: >>> >>> <http://home.att. net/~Paul.N.Lee/FotD/FotD.html> >>> >> > >Seems to be working fine for me. Try refreshing your browser (you >may need to hold down the SHIFT key while you do it). > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi- bin/mailman/listinfo/fractint >

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FOTD 07-02-09 (Julia More or Less [?])
by Jim Muth 06 Feb '09

06 Feb '09

FOTD -- February 07, 2009 (Rating ?) Fractal visionaries and enthusiasts: Today's image is not a Mandelbrot set, nor is it a Julia set. It is an Oblate set, a hybrid mixture of Mandeloid and Julia stuff. The X-axis lies in the Julia direction, while the Y-axis lies in the Mandelbrot direction. I have not yet made up my mind about today's image, which is why I gave it a rating of a question mark. At times, these four- dimensional slices through the Julibrots can be spectacular, but at other times, they are just plain ugly. Today's image lies somewhere in between. The name "Julia More or Less" is absolutely true, but only as long as we consider the horizontal direction. When we turn to the vertical direction, we are moving through a Mandelbrot set. The other directions lie in the Julibrot, and are neither Julia nor Mandelbrot dimensions. The parallel blue stripes in the background are the 'bridges' that exist only in planes in which only one direction is perpen- dicular to the Mandelbrot orientation. When all directions are perpendicular to the Mandelbrot orientation, which is possible only in spaces of four or more dimensions, we have a Julia set. Maybe I'll continue this four-dimensional stuff in upcoming FOTD's, maybe not. I've gone over it several times in the past. Perhaps the best feature of today's image is its brief calcula- tion time of only 49 seconds. And even this minor effort may be totally avoided by surfing electronically out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Not a single cloud marred the spectacularly blue sky here at Fractal Central on Friday, while the temperature of 36F 2C felt like spring. The fractal cats enjoyed the weather from their sunny shelf by the big southwest window, taking their breaks only when hunger called. My day was busy enough that one would never guess we are supposed to be in economic hard times. The next FOTD will be posted in 24 hours. Until then, take care, and it's all real, whatever that means. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_More_or_Less { ; time=0:00:49.79-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideJulibrot passes=1 maxiter=3600 center-mag=2.31005/0/9.197812/1.3049 params=0/0/90\ /0/-1.3243408/0/0/0/3/1.4 float=y inside=0 logmap=6 symmetry=xaxis periodicity=10 colors=000P9bL9fI9iE9mA9p69t39w6Br9CnBEjEFeGHaIIYL\ ITOIPNILNIGOICPI8QI9RI9SI9TI9UH9VGAXEAYDA_DA`CAbAB\ c9Be7Bg6Bi4Bi3Bm9GqFLuLQxQVuSYrT_oUalVciXefYgcZia_\ kZagWccUd_RfWOhSMiPJkLGmHEnDKp9Kq6Kq6Kp7mo7mo7mn7m\ n8zm8zz8zz8zl8mk9mj9mj9mi9Bi9BhABgABfABeACdACcBCcB\ CcBCcBCcBCcCCcCCcCDcCDcCDcDDcDDcDDcDDcDDcEDcEEcEEc\ EEcEEcFEcFEcFEcFEcFEcGFcGFcGFcGFcGFcHFcHFcHFcHFcHG\ cIHcJHcJIcKJcKJcLKcLLcMLcMMcNMcNNcOOcOOcPPczQczQcz\ RczSczSczTczTczUczVczVazW_zXYzXWzYUzZSzZQz_Qz_Qz`Q\ zaQzaQzbQzcQzcQzdQzeSzeUzfWzfYze_zdazdczcczcczbczb\ czaczacz`cz`cz_czVczZczZczYczYczXczXczWczWczVdzZez\ YdzYdzYdzYczYczYczYczYbzYbzYbzYazYazYazYazY`zX`zX`\ zX`zX_zX_zX_zXZzXZzXZzXZzXYzXYzXYzXYzXXzXXzWXzWWzW\ WzWWzWWzWVzWVzWVzWVzWUzWUzWUzWTzWTzWTzVTzVSzVSzVSz\ VSzVRzVRzVRzVQzVQzVQzVQzVPzVPzVPzTKzJ2zK3zK3zK3zK4\ zK4zK4zK4zL5zL5zL5zL5zL6z } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 06-02-09 (Cubic Consequences [7])
by Jim Muth 05 Feb '09

05 Feb '09

FOTD -- February 06, 2009 (Rating 7) Fractal visionaries and enthusiasts: The parent fractal of today's festive cubic image resembles a seven-pointed star with a cubic Mandeloid at its center, the whole thing packed neatly inside a circle. Today's scene is located deep in the southernmost point of the parent's star. I named the image "Cubic Consequences" though I do not speculate on what the consequences might be. The rating of a 7 means that I consider the image to be about the current FOTD average. The calculation time of 11-1/2 minutes is slower than I would have liked, but the small wait is worth the sight of such an unusual cubic minibrot. And even this small wait may be avoided by hurrying to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and staring in awe and wonder at the finished image posted there. The full day of sun here at Fractal Central on Thursday was spoiled by a morning temperature of 9F -13C and a brisk wind that made it feel even colder. The fractal cats spent an hour or so in their sunny window, then retired to the comfort of the warmest radiator. My day was notably average. The next FOTD, hopefully better than average, will be posted in 24 hours. Until then, take care, and be of stout constitution, but don't overdo it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cubic_Consequences { ; time=0:11:27.84-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 center-mag=+0.850393972204\ 9394/-3.70774079064822/9.308278e+009/1/-7.5/0 params=-6/11/0.0015/0 float=y maxiter=9000 inside=0 logmap=1339 periodicity=10 mathtolerance=0.05/1 colors=000KQWPSPUgIZjLclNooQkqShtVevXds_dqbcoecmgc\ kjbimbgpber`ZpZSnYMlVLhSLdPKaMKYJJUGJRDINBIKDFOECS\ F9WG7_7LuBPvFTvIXvM`vPdvUgUZj1aV2dG3XQBPZIHgQApXCl\ YEiZGe_Hb`GYUGTNGOHGJAGE4MN5SW6Xd6bm7gv7uJbmQdeWfY\ bgQhiJnjJYRJI7HUSFekD_fCVaBQY9KT8FP7AK65G9DJCKLFRO\ IZQLeTOlVCfP0aJGmHVxFUvEUtDTrCTpCSnBSlARj9Ri9OtNLv\ QJwSHxUInUJeUKXULNUMEUN5USBZXHcaNgfSlkYppcuthyobuk\ XqgRmcLiZIhUGhPEhKBhF9hA7h65hD4dK3aQ3ZX2Wc1Ti1Qp0N\ v0Kp5Oj9SdDWZHZTLbNPfHTiGcPGm4YeLnY`iB4M89PDESIJUM\ OXRTZVXYWYXXZWYZRX`MXbIXdDXf9XhEWVJWHZW4ma5zgAzpFw\ sKryPhwUavZUucUuhUumUumUnhUgcz`ZzUUwNPSGKS9FS2ApNJ\ sWRUvZrvZgnfh0jtfnzcqpRhxE`x2TvBYuKbsTgr`kCATt9XlV\ UeoR`i_XchSYqOTzRSmTezoUPYcC_R0MG696BTMe_O_fQUlROz\ cSzcVzcZTVaOWeJXhEYl9Zo7_h6_a4_V3_O2_H7aFBcEFdCKfB\ Og9Si8Wj7UlAUnCUpEUrGZtIcuKNvThwamxjrydvz_wzVwzQzz\ LzzGzzBzz9zz7zz5zz3zz2zzb } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 05-02-09 (Venusian Landscape [8])
by Jim Muth 04 Feb '09

04 Feb '09

FOTD -- February 05, 2009 (Rating 8) Fractal visionaries and enthusiasts: The question of fractal reality sometimes arises to puzzle even the most devoted fractal fans, and sooner or later every fractal fan asks himself, "Are fractals real?" To begin, fractals must have some kind of reality. How else could we have pictures and animations of them? But it is obvious that fractals are not made of material. They appear to be more like mathematical abstractions, but abstractions have no shape, so how can fractals be abstractions? Mathematics is basically human thought processes stated in symbolic form, so could fractals be made of thought? Thoughts are usually considered to be less real than objective material objects. This is why we say, "ghosts are not real, they exist only in the mind." But sometimes thoughts can become almost real. In dreams, for instance, thoughts can appear quite as objectively real as any material object. So are fractals made of semi-materialised thought? If fractals are made of thought, we then wonder what thought is made of? A materialist would claim that thought is a by-product of the brain. So if fractals are made of thought, they are therefore created by the neural activity of the brain. But what is neural activity? Cognitive specialists tell us that neural activity consists mainly of electric and chemical interactions between neurons. Now it looks like fractals are made of electro- chemical interactions. I could continue by asking what are the interactions made of, but an endless regression is now becoming apparent. At the same time, an idealist, such as myself, would tell us that with thought we have reached the end of the line. Con- scious thought is the ultimate reality, and it is meaningless to ask what thought is made of. My conclusion is that fractals are made of thought, which can take many forms from total abstrac- tion to a rock-solid impression of objective material reality. Fractals are quite real, in fact they are as real as thought. Now let's end the philosophical fractal digression and say a few words about today's image. I named the image "Venusian Landscape" because something about it reminds me of the first pictures sent back from the surface of Venus. I rated it at an 8 because, unlike the surface of that planet, the image has a rather sunny feeling about it. The parent fractal is a cubic Mandelbrot set surrounded by seven spokes inside a circle that makes the set resemble the hub of a wheel. Today's image is located some distance to the northeast of the cubic Mandeloid. The calculation time of a zippy 1-1/4 minutes should bring happiness to every fractalist. Hard-to-please fractalists may find comfort on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for instant viewing. Lots of sun prevailed here at Fractal Central on Wednesday, though a morning low of 16F -9C made for quite a chilly start to the day. The high of 28F -2C was a little better. The fractal cats thoroughly enjoyed the sun. With the main computer back and up and running, my day was fair enough. The next FOTD will be posted in 24 hours. Until then, take care, and is the mind a by-product of the brain or are the things we call brains actually sense-produced images in the mind? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Venusian_Landscape { ; time=0:01:13.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 logmap=67 periodicity=10 center-mag=+0.9168008632085998/+1.217061671902639/\ 6.61573e+010/1/170.5/0 params=-6/11/0.001/0 float=y maxiter=1500 inside=0 passes=1 mathtolerance=0.05/1 colors=000_ZOkcPssMztJceGcZDcSBUL8UE5U72DzT6SEzi2j\ _1ZR1NI0B90czzRU0351230110nqzWXpOObGGQ88DunAlf8d_7\ XT5OL4GE2871wM6aH4SD3ZU9aOIwIRhCZfCddCjbCpaCubGscK\ qdNodRmeUkfYif`g`biWckQdmLeoGfqDXcANQ7ECJL9UR6dX3P\ eNAnfeFO`JMXNKSQIOUGKYEF`CBdA7g9BZJFQTIHaJIZJIWJJT\ JJQKJNKKKKKHKKFEPO8TX2Xe4`e5de6he7ke8oe9seAveJmVSd\ K_XAXSGUNMRISODYM8cPEmRKwNHsKFoHClEAhB7e85a53ZXSdx\ pjrekmVlgLlbAmY0mRGaLVQFiE9x2IvHRuWVnRZgNbaJeVEWBk\ VAjUAiTAiSAhR9gQ9fQ9eP9dO9dN8cM8bL8aK8`K7`J7_I7ZH7\ YG6XF6XE6WE6VD6UC5TB5SA5S95R84Q84P74O6Uz5UzmUz3Uz2\ UzmUz2Uz3UzmUz4Uz5UzmUz6UzmUz7UzmUz9czzczAczzczBcz\ zczDczzczEczzczFczzczGczzczIczzczzm7zz7zm6zz6zm5zz\ 5zm4zz4zm3zz3zm3zz4zm4zz4zm5zz5zw5zw5zw6zw6zw6zw6z\ w7zw7zw7zw7zw8zw8zw8zw8zw9zw9zw9zwAzwAzwAzwAzwBzwB\ zwBzwBzwCzwCzwCzwCzwDzwDzwDzzDzzEzzEzzEzzEzzDzzDzz\ DzzCzzCzzCzzCzzBzzBzzBzzB } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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Re: [Fractint] AOTD 2_3_09
by JackOfTradeZ＠comcast.net 04 Feb '09

04 Feb '09

. Fractal animation visionaries and enthusiasts: I have always been intrigued by fractals that exhibit extreme sensitivity to small parameter changes ("initial conditions"); as you all know this is one of the general concepts of chaos theory. Many Julias are like that, there are several examples on my site. This one, the "Critical Julia" (FOTD January 26, 2009) is no exception; the frames in this animation differ by only 0.0000001 in the P3 parameter. In all Julia morphs I have done up to now, the images always change (evolve) faster as you move towards the center. There is no way to "equalize" or balance it - the center is always changing too fast or the perimeter regions too slow. This one is the singular exception - the center region appears largely unchanged, or very slow, while most of the action occurs along the edges and perimeter. Why that is I do not know, but it's nice for a change. Another aspect of making animations is you never know exactly how they will turn out until it is finished and you look at it. Sometimes they are better than expected, like the recently posted "Darkness Descends". Sometimes they are not quite as good as the original test frames indicated. This one falls into the latter category, resembling a bad acid hit more than a fractal. But what the hey, it's still cool! I rate it a good 7, corresponding to two stars on my site. The rendering time of 3 days can be avoided by downloading the zipped viddie here: http://www.fractal-animation.net/vid/c_julia_x.zip The weather at fractal animation central has been sunny and mild - typical Colorado, in contrast to the NorthEast getting plastered by ice storms. My work day was better than average; the thrice per year liquid helium fill went without incident, as it fortunately has up till now. But always a day of some apprehension, as any who have witnessed the quenching of a superconducting magnet might testify. The wait for the next AOTD is ......... never can tell! My current CPU consuming project is a dive into the trench (REAL=-0.75 IMAG=0) and it should be done in a month or so. It is an interesting and unexplored region, and again, I don't know how the viddie will look till it's done and 4 months consumed! Until then, take care, and continue to believe in fractal miracles. .

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FOTD 04-02-09 (Smog [No Rating])
by Jim Muth 03 Feb '09

03 Feb '09

FOTD -- February 04, 2009 (No Rating) Fractal visionaries and enthusiasts: The main F.C. computer developed a problem on Tuesday, and left us using the old backup machine, which has been doing fractal duty for a couple years. The ailing unit is now in the shop, but trying to fix the problem left me with no time to complete the day's fractal. The day's image is actually only half finished. The colors obviously need a lot of work, but I decided to post it anyway. I named the muddy image "Smog". The reason is obvious. I gave it no rating. The calculation time of 8-3/4 minutes is too long for such an image, so I advise taking a trip to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Despite a forecast of snow, Tuesday turned into quite a pleasant day here at Fractal Central. The sun shone brightly, while the temperature reached a high of 39F 4C. The fractal cats took full advantage of the warm sun. With the main computer down, my day was very busy. But if all goes well, the next FOTD will be posted in 24 hours. Until then, take care, and relax. P.S. It's post time and I just got a call from the shop. They found a bad memory chip and replaced it. Things will be back to normal when I pick up the computer Wednesday. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Smog { ; time=0:08:45.36-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=t center-mag=-0.815142/0/5.882307/1.1571/-90/0 params=-3/1 float=y maxiter=1500 inside=zmag logmap=yes periodicity=10 colors=000g46g26g06d78aDA_JBXPDVVESaGPgINmJKsLIyMa\ rCuk2qi3ng3je4gd4db4``5Y_5VY5RW6OU6LT6HR7EP7BO7EO6\ HO6KO5NO5QO4TO4WO4XN3YN3ZM3_M3`M3aL3bL3cL3dK3eK2fK\ 2gJ2hJ2iJ2jI2kI2lI2mH2nH2oH1pG1qG1rG1sF1tF1uF1vE1w\ E1wE1qL3kS5eZ6_d8Uk9OrBIxCGwBEwBCwBBwB9vA7vA5vA4vA\ BuGHtMOtSUsY_rcfrilqorqtpnpnkmmiikffjcbha_gZWeXTcU\ QbRM`PJ_MFYJCXH8VE5UC2TB3SB4SB4RB5QB6QB6PB7PB7OB8N\ B9NB9MBALBBLBBKBCKBCJADIAEIAEHAFGAGGAGFAHFAHEAIDAJ\ DAJCAKBALBALAAMAAMBCLCELDGLEILFKKGMKHOKIQKJSKJTJ8A\ E9AFAAGBAHCAIDAJEAKFALGAMHANIAOJAPK9QMASOBUQCWSDZU\ EaWGdYIg_KjaMmcOpeQsgSviUvl`unfupmursunllkedgZXdSP\ `LHYE9V81W92XA2XA3YB3YC3ZC4ZD4MKHUKJUKLUKNUKPUKRUJ\ TUI`ULbROcOReLUfIXgF_iCbj9ek6hm3kn0no3pq5rr7ts6on6\ ji5ee5``4WX4RS3MO3JM2GN27L23I5BG7IIAPNCWTEbYFc_Fca\ GdcGdeHdgHeiHekIemIfoJfqJfsKguKgwKgyKizKkzKmzKozKp\ zpqHrrDZgVGYkKZgO_cS`_g76 } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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More thoughts on reality
by David M Fisher 03 Feb '09

03 Feb '09

Paddy Duncan wrote Madness is like exam results; the border is defined by social convention such that just the 'right' people are sane. And mimsy were the borogroves. Reality is what is.....sanity is measured by an individual's grasp of reality. Reality defined is what is real, regardless of whether something is known or not. Not knowing (thinking) something doesn't change anything except as pertains to the individual who is ignorant of whatever facet of reality they haven't discovered. Proof in point is mathematics, or better yet for this list, fractals. Fractals always were, but the discovery had to await the developement of computers. Fractals exist, are real and a part of reality. If some bushman in the Kalahari Desert doesn't know about them then his knowledge of/about reality is limited, but this doesn't negate anything, it only places limitations. and the insane are just heretics. I don't think so. Insanity is a measure against an individuals ability to "see" reality. Since we don't know everything reality (understanding) is constantly expanding and unfortunately there are some retards who can't accept this, but acceptance is not the basis for reality. The insane are mentally color-blind. An individual that can not see color(s) or hue(s) is defective......no other way to put it. Still, even so, color exists, and independent of the biological eye, too. IR and UV require special devices to be visible to the human eye, but nontheless are part of the spectrum at opposite ends. 'Nuff said.......shoot, Luke. David M Fisher

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FOTD 03-02-09 (Richly Decorated [7])
by Jim Muth 02 Feb '09

02 Feb '09

FOTD -- February 03, 2009 (Rating 7) Fractal visionaries and enthusiasts: The parent fractal of today's image is the most unusual parent of all time. Its main problem is that it is so small it's invisible at the default opening magnitude. But despite initial appearances, a tiny mandeloid lies at the center of the opening screen, and today's image proves it. When magnified a few hundred times, this mandeloid reveals itself to be splitting apart on its west side. Its Seahorse Valley has broadened into a double wedge, and deep in this wedge today's scene is found. The magnitude of 1.6*(10^12) is deceiving. When the parent fractal was shrunk, the decimal point of the coordinates shifted several places to the left, giving an illusory increase in precision. The rating of a 7 seems fair enough, though if I had had more time to work on the colors, I might have raised the rating to an 8. I'm not quite sure what the name "Richly Decorated" refers to. Most likely it's the areas of chaos. The calculation time of 14 minutes is admittedly slow, but nothing that a SOTA unit cannot handle with ease. (Unless the machine is over-qualified, that is!) Those with over-qualified units may see the image by hurrying to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and enjoying the finished image there. Early morning clouds, steadily falling temperatures, midday rain and late afternoon snow made a mess of Monday here at Fractal Central. The fractal cats agreed, and didn't even try to find a comfortable spot in their favorite window. My day was so busy with other things that I had little chance to be unhappy about the weather. The next FOTD will be posted in 24 hours. Until then, take care, and be ready for whatever. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Richly_Decorated { ; time=0:14:04.01-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 inside=0 center-mag=-0.00069807601274538/+0.000348635434926\ 36/1.609e+012/1/-26/0 params=2.0001/-0.9999 float=y maxiter=18000 periodicity=10 mathtolerance=0.05/1 colors=000o9vmBtlCrjEpiFogGmfIkdJicLgcMfcOdcPbcQ`c\ SZcTYcVWcWUcXScZQc_PcaNcbLcdJceHcfGchEciCckAcl8cm6\ cm7cl8cj8ch9ce9cbAc_AcXBhUBlQCqMCuIDyEDwACv9CtACsB\ CqBCpCCnDCmECkECjFChGCgHCeHCdICbJCaKC_LCZLCXMCWNCU\ OCTOCRPCQQCORCNRCLSCKTCIUCHUCIVEIWFIXGJYIJZJJ_KK`M\ KaNKbOKcPLdRLeSLfTMgVMhWMhXMiYNj_Nk`NlaOmcOndOoeOp\ fPqhPriPsjQtlQumQvnSyrQvoPpmOkkNhiLefKbdJ_bIY`HWZF\ UWESUDQSCOQAMN9JL8GJ7DH66B6BF6GJ6LM9PLBSLDVLFZLHaL\ JdLMhLOkLQnLSrLUuLWxLZrMamMchMfbMhYMkTMnNMpIMsDMu8\ Mq9On9PkAQhAReASaBTZBUWCVTCWQCXMDYJDZGE_DE`04_AEaJ\ NbSWc`eeinfqxirwgrvervcsuasu`stZstXtsVutTvuSwvQxwO\ yxMzyLzxJzwHzuFzsDyqCxoAwm8wl6wl5piFjgOdeXZbfT`oNZ\ xMYwMXvMWuLWtLVsLUsLUrKTqKSpKRoURoUQpUPqUPrUOsUNtU\ NuUMvULwUKxUKyUJzUKzULzULzUNvUMrUMmUNhUOcUQZUSUUTP\ WVKXUFYTEZSFZRH_QI`PJ`OLaNMbMNcLOcKQdJReISeHUfGVgF\ WhEXhDZiC_jB`jAbk9cl8dl8e } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] If only it were true.......alas
by JackOfTradeZ＠comcast.net 02 Feb '09

02 Feb '09

Alas .... Am I a man dreaming I am a world famous fractal animation artist? Or am I a world famous fractal artist dreaming I am a man? Animation of the critical julia is looking real strange now ... .

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FOTD 02-02-09 (Squarely Chaotic [2])
by Jim Muth 01 Feb '09

01 Feb '09

FOTD -- February 02, 2009 (Rating 2) Fractal visionaries and enthusiasts: All the 'reality' stuff on the Fractint list lately might indicate that the philofractal list may need to be brought to life again. I'm not going to say how I spent the day Sunday, but if I did, it would be no surprise. Due to a total lack of effort, today's image is hardly worth being called a fractal. I rated it at a 2 out of the kindness of my heart. And to make matters even worse, the image takes near 13 minutes to calculate. But it's still an image, and to see what kind of fractal I found with one eye on the TV, run the parameter file and indulge yourself in masochistic disappointment. The name "Squarely Chaotic" means little or nothing. The 13 minutes required to run the parameter file may be avoided by visiting the FOTD web site and viewing the finished image there. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Sunday turned out to be an unexpected gift here at Fractal Central, as total sun and a temperature of 50F 10C combined to make it seem almost like spring, despite the snow still covering the ground. The fractal cats agreed. They spent the entire afternoon soaking up the sunlight that blazed in through their favorite window. My day was occupied with other things. The next FOTD, a better one for sure, will be posted in 24 hours. Until then, take care, and if reality is what exists when no one is looking, how will we ever know what reality is without looking at it and thereby destroying it? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Squarely_Chaotic { ; time=0:12:47.54-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.22190505283/-5.50823873402/6.6e+007/\ 1/-150/0 params=-3.5/-1.1/-0.8/-5.9/0/0/0/0 float=y maxiter=5400 inside=0 outside=tdis periodicity=10 colors=000zzzAdaBdaCdbCebDecEecEfdFfdGgeGgeHgfIhfI\ hgJigKihKihLjiMjiOkzMjzKzzIhzGggEfzDefBde9cd7bd5ac\ 4ac5`a5``6`_6`Z7`Y7`X8`W8`V9`T9`SA`RA`QB`PB`OC`NC`\ MD`KD`JE`IE`HF`GF`FG`EG`DH_AG`CG`DG`EG`FF`HF`IF`JF\ `KF`LE`NE`OE`PE`QD`SD`TD`UD`VD`WC`YC`ZCa_Cb`CcaGdd\ JfgMhjQjmTqpWtrVsqUrpUsoTtoTtnStmRtlRtlQtkQtjPuiOu\ iOuhNugNufMufLueLsiKvmKtkJubIvaIv`Hv`Hv_GvZFvYFvYE\ vXEvWDvVDvVKqPZlKcg4gf5zf5zf6zf6zf7zf7ze8ze8ze9ze9\ zeAZeAXdAWdBVdBUdCSdCRdDQcDPcENcEMcFLcFLdEKcFKcGJb\ HJbIJbIIaJIaKIaLH`MH`MG_NG_OG_PFZQFZQFZREYSEYTEYUD\ XUDXVCWWCWXCWYBVYBVZBV_AU`zUazc0zUaUNXcGRm9Mz2Hm6J\ e9LcCMbFO`IQZLRYPTWSUUVWTYYR`ZPc`OfaPdbPcbQabQ`bRZ\ bRYcSWcSVcTTcTScUQcUPdVNdVMdWKdWJdXHdXGeYEeYDeZBeZ\ Ae_8e_7f`5f`4fa2fa1fa0fe5eh9dkEdnIcqNctRbwVbxVaxW_\ yWZyXYzXXzXWpaSgfOYjKPoGJr0GsCEsOCsZEtYFtXHtWItVJt\ VLtUMtTNtS7bZ8b_8b_9c`Ac` } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 01-02-09 (Ring of Snowflakes [8])
by Jim Muth 01 Feb '09

01 Feb '09

FOTD -- February 01, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's FOTD is late because on Saturday FL decided we should go on an antiquing expedition down to Hershey, and I agreed. The day was long, but despite the journey and late return, the hastily found fractal turned out to be an unusually attractive one, (at least in my opinion). The parent fractal is a shapeless thing created by combining various negative portions of Z^(-1.1) and Z^(-5.9). This parent fractal has a very large and prominent 'fan'. Today's image is located on the northwest edge of this fan. I named the image "Ring of Snowflakes" because it reminds me of a snowflake. I rated it at an 8 because I think it's pretty good. And the calculation time of under 2 minutes is brief enough to make running the included parameter file almost fun. As always, those who don't like fun may see the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But before checking the web site, give Paul a chance to calculate and post it. Sunny skies and a temperature of 25F -4C made for a chilly midwinter day here at Fractal Central on Saturday. The fractal cats enjoyed the conditions alone. Most of my day was occupied elsewhere. The next FOTD will be posted in 24 hours, but this is a probability not a promise. Until then, take care, and even if it's not real, who will know the difference? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ring_of_Snowflakes { ; time=0:01:50.08-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip center-mag=+1.160595246192642/+1.639648996209331/\ 1.410313e+009/1/42.5/0 params=-3.5/-1.1/-0.8/-5.9/\ 0/0/0/0 float=y maxiter=1000 inside=bof61 logmap=64 periodicity=10 mathtolerance=0.05/1 colors=000CPhCYRDLJD8CC0FBJHAKJAUL9KN8cP8QRL`PXTOh\ LMtDLzaGxgBqbDjcFcbGWXLPRQOQRNPTNOUFAKMMWLAKLKZKJK\ zzzzzzwvuuuttssrrsqprooqnmpllokjoiinhgmffledkcckba\ j``i_ZhYYgXBMVVfUTeSSdRQcPPcONbMMaLK``_EYXIWVLTSOR\ QSONVMLYZo1Ym3Xl4Xk6Wi7Wh9VgAUeCUdDTcEOx`04bF9hUEn\ hJtvOznQsgRl`TeUUZNWSGXLHTIHQGHNEIKCIHAIE8FEECEK9E\ PV_Gpu7y7SqhwTdY5`8JhMWpZYkYZfX_aX`XWaSVbNVcIUdEU`\ CWYAYV9_S7aP5cM4dd`EdcFeeGfgHfjIglJqs9gnJZjSQeaHaj\ 8YsLZlY_fpWei_`bcXWgTPkOIoKBsG4vC5mM5eV9dZCcbFbfJb\ jManP`rAbzS`uhZpyXkGnLQnJZnIhnGqnFznEwjFtfGqbHnZIo\ TIlVJjXJhZKf`KcbLadL_fMxbOYgM8lG7lKzlz5lzzhz5lzzzz\ 6zzzzzIzzzzzUzzzzzQzzzzzMzzzzzzzzzzCzzEzzFzzHzzIzz\ JzzLzzMzzJzzNzzRzzVzzZzzbzzfzzjzzmzznzznzznzznzznz\ znzznzzNzznzz`zzOzz0zzBzzLzzVczdcznuzDrzAoz7lz5az_\ bzVczRdzN_zLVzJRzHMzFrzMIzEKzFMzFOzGQzGQzCRzGRzKSz\ OSzSTzWTz_UzcUzgTzfAzjBze } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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If only it were true.......alas
by David M Fisher 01 Feb '09

01 Feb '09

Jim, you posted the following with the fotd 31 Jan 09: Until then, take care, and whatever it is, it's all in the mind. Does this mean if we change our mind(s) we change reality? Do we each have our own "reality" in our thoughts? If so, how then can there be any agreement about anything between two or more individuals about anything, not to even consider the fact that according to your statement, something not in my mind doesn't exist. Just asking.......... David M Fisher

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Re: [Fractint] Inauguration email
by Jim Muth 01 Feb '09

01 Feb '09

At 03:51 PM 1/19/09 -0700, Jack of TraDeZ wrote: > >On 2009-01-15 15:54, JimMuth wrote: >> **************Inauguration '09: Get complete >>coverage from the nation's capital. >>(http://www.aol.com?ncid=emlcntaolcom00000027) > >It's the beginning of the end for the country >I love(d) and grew up in. Thanx but no thanx. >I'd rather not watch. I agree entirely. I plan on totally missing the so-called 'big' event. IMO, the new president is not the beginning of the end, though he might hasten the decline. This once-great country began its decline years ago. And if anyone on the Fractint list thinks I actually wrote the above advertisement for AOL, they should turn in their fractals and resign from the list in disgrace. And if anyone wants to see some real debating on the list, get me started on liberal politics or conventional religion. Hmmm.... Maybe this is what we need to get a little life back into the list. Jim Muth

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FOTD 31-01-09 (Leaping Iterations [7.5])
by Jim Muth 30 Jan '09

30 Jan '09

FOTD -- January 31, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image lies in the parent fractal that resulted when I combined various negative portions of Z^(-2.1) and Z^(-9.2), then added (1/C). This parent fractal consists of a few large circular bays with a small satellite figure-8 shaped lake some distance to the east. The scene of today's image lies in a valley of this figure-8 thing. The general area has both critical and non-critical elements, so when I first checked it, I had little hope of finding an intact minibrot. I expected only dry valleys, but I stumbled upon the tiny minibrot at the center of the image almost by accident. To express my surprise, I named the image "Leaping Iterations", and then I gave it a rating of a 7-1/2, including a half-point reward for my coloring work. I would have preferred a shorter calculation time than 6-1/2 minutes, but this short wait may be avoided by hurrying out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Partly cloudy skies with occasional heavy snow squalls highlighted the weather here at Fractal Central on Friday. The fractal cats must not have considered such conditions a highlight, for they spent most of the day near the heat. My day was once again unacceptably busy. The next FOTD will be posted in 24 hours. Until then, take care, and whatever it is, it's all in the mind. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Leaping_Iterations { ; time=0:06:30.97-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.413306648958554/+0.0002551522349509/\ 1.291e+010/1/-15/0 params=-4/-2.1/-0.9/-9.2/0/0/0/0 float=y maxiter=3600 inside=0 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=000HLaEMcCNfAOh9Pf9Qd8Qb8Ra7S_7SY6TW6UV5UT5\ VR4WP4WO3XM3YK3YJ4_L5aN6cP7eR7fS8hU9jWAlYAmZBo`Cqb\ Dsdflrflpfkneklekjejhdjfdjddiaci_chYchWbhUbgSbgQbg\ O_dMXbKV_ISYHPWFNTDKRBIPAQGCY7ElWFi_NgcUdg`bkg`onz\ pkzqhzrfzrczs`ztZzuWzuTzvRzwOzwMzrRzmVSh_SccTZgTUl\ TPpTKtPOnLShHWbD_X9cR5fM6hP6jR6kT6mV6nX6pZ6ra6sz6u\ z6vz6xz6yzz42z64z76zL8zQ9zVBz_DzbFz_GzVIzQKzGUxHUu\ GSrGQoGOlFMiFLfFKcEK`EJYEJVCJSBIPAIM8HJ7HE7HL0GO8F\ Q6EQ9DP0CQ0CR0ES0GU0HW0JY0LY0MY0OX0PW0RU2TR4UP6WN8\ YKAZIC`GEaHFbIFbJEcJDcKCdLBdMAeMAeN9fO8fP7gP6gQ5hR\ 4hR4hQ5gQ6fQ6eQ7dQ8cQ8bQ9aPA`PA_PBZPCYPCXPDWPDWOHU\ NKTMNSMQRLPOLPMLPKURQaTViV`qXeyYjmWkbUlRSmGRmLWfQ`\ `VeU_jOdoHitBmx5dX8X5BUG8RR5O`3R_4UZ4XY4_X4bW4dW4g\ V4jU4mT4pS4rS4sVAtXFuZLv`QvbVwd`xfeyhkzjpzlusbsmUr\ fKp`BoV2nW4lW5kW6jX8hX9gXAfYBeYDcYEbZFaZG`ZIZ_JY_K\ X_LWYIUVGRTEPQGSOHULIXJJZ } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 30-01-09 (Buds Gone Crazy [No Rating])
by Jim Muth 29 Jan '09

29 Jan '09

FOTD -- January 30, 2009 (No Rating) Fractal visionaries and enthusiasts: As sometimes happens, Thursday turned super busy here at F.C. With help from FL, the unexpected job was finished on time, but not without sacrificing fractal time and quality. The image is something I dashed off automatically while I was taking a work break. The scene shows a few buds on the north shore of an almost-Mandelbrot set. But these buds must have had a bit too much liquid cheer, for they appear to have gone crazy at a festival of some sort. The name I chose for the madness is "Buds Gone Crazy". I gave the image no rating. If I had given one, it would have been around a miserable 2 or 3. The calculation time is a short 1-1/4 minutes, brief enough to cause no impatience. The image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Rather pleasant weather prevailed here at Fractal Central on Thursday, with lots of sun and a temperature of 34F +1C. The fractal cats enjoyed it to the fullest. As statd above, my day turned horrendously busy. The next FOTD will be posted in 24 hours. Until then, take care, and if you don't know it, believe it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Buds_Gone_Crazy { ; time=0:01:16.50-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=t maxiter=1500 center-mag=-0.316091/0.762459/4.419443/1/-15/0 params=-5/9/0.4/-13 float=y inside=0 periodicity=10 colors=000zw3zw4zw4zr5zm5zhAzcKvZPrUUmPZhLccIhZFmU\ ImPLmMOmJRmGTmDWmAZm7am4dm1fm4em6dm8cmBbmDamF`qI_t\ KZwMYzPYzRXzTWzWVzYUz_TzbSzdRzfQziRzhQzhPzhOzhNzhM\ zhLzhKzhKzhJzhIzhHzhGzhFzhEzhDzhDzhCzhBzhAzh9zh8zh\ 7zh7zgDzgIzgNzfTzfYzfczeczeczeczeczcczbcz`cz_czYcz\ XczVczUczSczRczQczOczNczLczKczIczHczFczEczCczBdzAd\ zH_zNWzTRzZNzdIzjEzpAzXFzZEzaDzcCzfBzhAzj9ziAMiBOh\ CRhDTgEWgFYgG`fHbfIeeJgeKjeLlfLlfKmgKmgKmhKmhKniKn\ iKnjJojJokJokJplJplJplJpkKokKokKojKojKojKniKniLniL\ niLnhLmhLmhLmgLmgMmgMlfMlfMlfMlfMleMkeNkeNkdNkdNkd\ NjcNjcNjcOjcOjbOjbOibOiaOiaOiaPi`Ph`Ph`Ph`Ph_Ph_Pg\ _QgZQgZQgZQgYQfYQfYQfYRfXRfWReXReXReWReWReWRevbwua\ vtavtausaus`ur`tr`tq`tp_sp_so_ro_rnZrnZqmZqmZqlYpk\ YpkYojYojXoiXniXnhXngWmgWmfWlfWleVleVkdVkdVkcUjbUj\ bUiaUiaTi`Th`Th_ThZSgZSgYSfYSfXRfXReWRee52d74d86c9\ 8cAAbBCbCEaDGaEI`FK`GM_HN } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 29-01-09 (Crouching Minibrot [No Rating])
by Jim Muth 28 Jan '09

28 Jan '09

FOTD -- January 29, 2009 (No Rating) Fractal visionaries and enthusiasts: Since today's image is more of an experiment than an effort at fractal art, I decided to give it no rating. The parent fractal is a grotesquely bloated Mandelbrot set with order-1000001 under- tones. Today's image lies in one of the elephant trunks in East Valley. I named the image "Crouching Minibrot" because part of it is occupied by a hidden minibrot. The black area at the right side of the image is the edge of a minibrot of order 1,000,001. This means it has exactly one-million similar bays around its peri- meter, which caused me to open my desktop calculator. Since only four bays appear in the image, this means that only 1/250,000 of the total circumference of the minibrot appears on the screen. On my screen the four bays extend over a distance of 30cm or one foot, which means that the total circumference of the minibrot must be 250,000 feet or 7,500,000cm. Dividing this distance by 3.14159 we determine that, at the same scale, the diameter of the minibrot whose edge appears at the right side of today's image must be near 2,400,000cm or 24km, which is near 15 miles. It's quite a minibrot. To see the entire circular minibrot, turn off the logmap and reduce the magnitude of the image to 1,000,000. Perhaps the most curious thing in the image lies in the peninsu- las that separate the bays, where the same pattern repeats, only very slowly changing from one peninsula to the next. I see much stuff for investigation here. Despite all the weirdness, the image calculates in only 1-3/4 minutes, about the time required to visit the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and appreciate the finished experiment there. Snow, sleet and freezing rain made for a most unpleasant day here at Fractal Central on Wednesday. The temperature of 30F -1C only added to the unpleasantness. But strangely, the fractal cats seemed to enjoy the day, watching the neighborhood snow removal activities from their window shelf, with obvious fascination. My day would have been pleasant had it not been for the task of clearing the fractal sidewalks. Five inches of sleet is quite heavy to move around. If nothing worse happens, the next FOTD will be posted in 24 hours. Until then, take care, and I wonder what the world is really made of. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Crouching_Minibrot { ; time=0:01:43.64-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=t center-mag=+26.0517371691385/-0.177380788769248/\ 1.700493e+011/1/80.7/0 params=1000001/100 float=y maxiter=1500 inside=0 logmap=126 periodicity=10 mathtolerance=0.05/1 colors=000hgsghofikdkgclcbwVbrYbm_biabdcb`ecWgeRig\ NkjImiEqi9sh1ue3ub5s_7qX9oUAmRCkOEjLGhIHfFJdCLb9N`\ 4Kb6O_8RY9UVBXTC_QEbOFeLHhJJtIIkHIcHIYHHUHHSHIQFHO\ HGMIFKJFILEKMDNNDRPCUQBXRB`TAcU9fV9jX8mY7pZ7s_9rKA\ t0Br4Cp8DnBElFFjJFhMGfQHeTIcXJa`J_cKYgLWkMUnNSrNRu\ PTsQUqRVoSWnTXlVYjWZiX_gYaeZbd`cbad`be_cfYdgWk`phd\ eehVblK`q6_pAZpEYoIXoMWnQVnTUmXTm`SldRlhQklNosQkoT\ hlWehZbea_bdXZgUWjRSmOPoLMjMKeMI`NHWNFRODMOCHPACP8\ 8P7JKLUFYdAje9ge8ef8bf7`g7Yg6Wg6Uh5Rh4Pi4Mi3Kj3Hj2\ Fj2Ej2DmIIoNMqTQs_UzdfzlhxqwyqoyleyfXwaNvXEwRJvMNv\ HStBTr6Un1TjAScKRUU2K`6JfAIgEGlBHjEHhHHgJHeMHdOIbR\ IaTI_WIZYIX`IWbKY`L__MaZNcXOeWPgVQiURjSSlRTnQUpPVr\ NWtMXvLYwK`qIblHdgFfbEiXDkSBmNAoI9uZEznImqH`tGOwFC\ yEKiQRUaYEmDb`GeZJgYMiXPkW8PXD_VHjTLtRJTfH2v_V_NMk\ ADvBEpCFjDGdDGZN9BSQbfMguJkfLbSNUEPLM9fTOT_bFfp1RF\ 3uHBsLHqPNoTTmXZk`didjjew } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 28-01-09 (Peek-a-Brot [8.5])
by Jim Muth 27 Jan '09

27 Jan '09

FOTD -- January 28, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: Today's lively little image came about when one part of Z^3 was subtracted from three parts of Z^2. The resulting parent fractal is a slightly under-sized Mandelbrot set located just beyond the left edge of the opening frame and rotated 180 degrees so that its negative spike is now a positive spike, (at least it's pointing in a positive direction), and its East Valley is now a West Valley. There is little out of the ordinary about the details of the parent fractal except for a scattering of disconnected extra stuff beyond both the positive (negative) spike and West (East) Valley. Today's image is a scene deep in the most distant bit of debris in the scattering of debris west of West (East) Valley. When rendered in the 'normal' manner, with the 'normal' equal- iteration bands, the scene is dull indeed, but when rendered with the outside set to 'fmod', the scene really comes to life. The entire image has been rotated 180 degrees to return the parent fractal and the minibrot at the center of the image to the normal position, with the spike pointing west. This is a self-imposed rule that I usually follow. I rated the image at an 8-1/2 which includes a half-point reward for the coloring, which gets something from nothing. To see the 'nothing' change the outside from 'fmod' to 'iter'. The name "Peek-a-Brot" must have some significance, but at the moment I can see very little reason for it. The very brief calculation time of 18 seconds can be made even briefer by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Still proud of catching the mouse on Monday, the fractal cats stood tall here at Fractal Central on Tuesday. The lack of sun, the threat of snow, and the temperature of 27F -3C, didn't worry them a bit. My day was about average. The next FOTD will be posted in 24 hours, which is the average time between FOTD postings. Until then, take care, and never stop searching for the ultimate fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Peek-a-Brot { ; time=0:00:18.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=ident center-mag=-2.524958827887493/0/2.880577e+011/1/180 params=3/2/-1/3/0/0/0/0 float=y maxiter=290 inside=0 proximity=1 outside=fmod logmap=28 symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=000zzz0vz0rz0mz0hz0cz0Zz0Uz0Pz0Kq0Kh0Kf0Lj0\ Fn0AqLCnPEkTGhWIf`KZdKRhKKlKCpK5oK0oK0nKAnKEmKImKA\ lK3oLFmMKmNKmOKmPKmQKmRKgSKaTKWUFQV8KW1CXJ4Y`JZVY_\ Ql`LkaGjbBic6hd2geRefMcgJahH_iFYjDWkBUl9Sm7Qk5Oh6N\ e6Lb6K_6IX6HU6FR6EO6CL6BI69G68C6696556426545665674\ 7947A38C38D29F29G2CH2FH2II2LI2OJ2RJ2TJ2UK2UK2UK2VK\ 2WK2XK2YK2_K6`KA`JDaIHbHLcGOcFNcENcCNcAJc9Fb9Ba98`\ DB_GEZJH_MK`QNaTQbWTcZWd_`e_dg_hh`mk`qnamqaitaewaa\ y`Yz_ThU5mc5xUAwQAwOAvOAvMAuMAuPAtRStUOsWKsYGr`Crb\ 8X7jaEaeLUjSLnZDnNFnULoVJoWIpXGpYFpZDq_Cq`Aqa9rb7r\ c6h`OiaMjaLjaKkaJlbIlbGmbFmbEncDocCocApc9qd8qd7rd6\ zi0yh1xh1xg2wg2vf3vf3uf3te4te4sd5rd5zcdyc_xcWwcRvc\ NucItcEsb9FekJdfNdbRdZVdUZdQbdMfdHjdDnd9lclmcimcfn\ ccnc`ncYocVocSpcPpcMpcJqcGqcDraArc7_cdacabcZdcWecT\ gcRhcOjcLkcImcGncDpcAqc7UluWkpYjl_jhaidch`ehXggTig\ PkfLmeHoeDqd9gBamQL68GABF } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 27-01-09 (Cradle of Infinity [7])
by Jim Muth 26 Jan '09

26 Jan '09

FOTD -- January 27, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes yesterday's image to the limit. I named it "Cradle of Infinity" because somewhere in the vicinity of the value of the real(p3) parameter, the Julia set expands to infinity before collapsing back on itself. With the limited mathematical precision available, I came as close as possible to the point of infinity, close enough for today's image to give a pretty good idea of what that ideal fractal must look like. The zig-zag boundaries are a result of rendering the fractal with the inside set to 'zmag'. I have no idea how the rather lurid color scheme came about. If I had put a little more effort into the coloring, the rating of a 7 might have been a bit higher. The calculation time of 3-1/2 minutes should bring little hardship. And even this may be eliminated by dashing out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Monday featured partly cloudy skies and a temperature of 28F -2C here at Fractal Central. But the fractal cats did not waste time complaining about the weather, they spent the day celebrat- ing their glorious victory. An annoying mouse has been darting around the fractal kitchen the past few days. Monday morning the intrepid mouse darted out once too often. Both cats were on kitchen patrol when the mouse dashed across the room. Nicholas, the large but clumsy black british shorthair, pounced first but missed. All was not lost however, for he chased the mouse right toward small but agile Cassie, who pounced and easily caught the mouse. Not a cruel cat, Cassie dispatched the mouse quickly and offered it to FL. Both fractal cats were rewarded generously. I did not see the mighty victory, but FL, who was on the scene, gave complete details . . . once she settled down, that is. The rest of my day was notably average. The next in the ongoing series of gorgeous fractals will be posted in 24 hours. Until then, take care, and even a mouse deserves a break. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Cradle_of_Infinity { ; time=0:03:32.83-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6Julia center-mag=0/0/0.0002\ 046932 params=-4/8/0.1/0/-0.72008749000115/1.128295 float=y maxiter=1500 inside=zmag logmap=yes symmetry=origin periodicity=0 colors=000D57IE7ON7UW6Zd6dm6jw5cpJXiXPakQabR`US_KW\ aN`cQeeTjhXoj_tlbynezqitfct_etUftNhtHitAkpRgkWfg_e\ bdcYibUmaPr`KwZPscOtgNukUY`_BTaLScWReeQhpPVkYKqeKl\ `JfVJ`PIWJIQDHK7GE1cHCzLOuLPoKQiJRcISYITSHUMGVGFWF\ EUDDRBCP9BMLIKYPHjWEwcBn`9dY6VV4LS1mAGmAGmAHmAImAI\ fHG_OEUVCNaAGi7Hh8Hg9IgAIfBJfCJeDKeEKdFLdGLcHLbIMb\ JMaKNaLN`MO`NO_OP_PPZQPYRQYSQXTRXURWVSWWSVXTVYTUZV\ `eUXaTUZSQWRNSQKPPGMODIN9FM6CK28L39M39N49O49P59Q59\ R59S69T69T79U79V89W89X89Y9AZ9A_AA`AA`AFaBLaCRbDXbD\ acEgcFmdGstKiyfQpIelG`gEXcBS_9OV7JR5FM2AL6CKBEJFGI\ KIGPLTlBTZKTLTS6adNbqdcSCZRJWRPTQWPPVJQZPPaPPePOhP\ OkPNoOQdPTXPVPPYIP_APb2OlMUzZZtV`mQcfMf_HiTCl_MhTL\ jMKlFJn7IpwPoEMgDP_CTSBWKAZC9b4CRRDLZEFec9zcBzcDzk\ FzvItdSuYexWYXmmzmmzzrhmmzbDaaCfqmzjmzqmzCmzqmz8mz\ qmzCmzqmzGmzqmzKmzqmzOmzqmzeGhe8Zl0UpJSzVLzVLyWKwX\ KzeJzZIxTJmPHeLFYHDN00055 } frm:DivideBrot6Julia { ; Jim Muth z=pixel, c=(p3), a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 26-01-09 (Critical Julia [8])
by Jim Muth 26 Jan '09

26 Jan '09

FOTD -- January 26, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's scene is a Julia set very close to the one that appeared in yesterday's image. The difference is a very slight but very significant change in the the (p3) parameters. To see why I named today's image "Critical Julia", tweak the (p3) parameters a bit. The slightest change totally changes the appearance of the image. I find it very curious that the Julia set in the image has no Mandelbrot-set characteristics at all in it, even though the parent Mandeloid consists of a very obvious Mandelbrot-set shape. It's kind of a whole new world, which I must further investigate.. I rated the image at a slightly inflated 8. It probably does not deserve quite this high a rating. Its calculation time of 3-1/3 minutes, though still relatively brief, is about 10 times as long as the time of yesterday's image, due mostly to the lack of obvious periodicity. The image may be seen and enjoyed by running the included parameter file, or by visiting the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing it there. Clouds and cold weather kept the fractal cats at Fractal Central close to the heat on Sunday. When light snow began late in the afternoon, they curled even closer. My day was about average. The average wait for the next FOTD is twelve hours. I can see no reason why it should not appear on schedule. Until then, take care, and what ever happened to all the fractal miracles? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Critical_Julia { ; time=0:03:40.03-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=dividebrot6julia center-mag=0/0/0.06672 params=-4/8/0.1/0/-0.720085/1.128295 maxiter=1500 float=y inside=zmag symmetry=origin periodicity=0 colors=000zzDzMCzSBzXAUaMUeYUiiWkgXzeYzcZzb_z``zZa\ zXbzWemVgfUj_TlTSzMRqFQs9QvNWx``zmeyf`z`XxUTxOOwHK\ wBGw5CeFLPOTgXmzYLO_QM`VKa_HbcFchDdmBeqFdjIcdzbZPa\ TS`MW_GzZAaY4_Z7YZ9WZBUZDTZFUYKVXOWWSWVWMPTCJQ3EO5\ IQ7LS9OUARWAUYAW_AZaA`cAbdD`cF_bIYbKXaNV`PU`Cie8`f\ 4TgCQZJOQKQMKSIKTFLVBLW8LY4KU0LZ1Mb2zf3Nk4Oo5Nr2Os\ 6PtAQuERvHzwLTxPTxSQmWOb_CNjMTbVYWccPlhIumBnfJg`Q`\ VXUPc2LiNJjfHkzFkgLWQRGN_HKgIHoJFwKDtRzrYBoc9mj8jq\ 7hwY`txTqoUigVaZWVRXNIYFAZ8LXHVVQeTZoRg`MZMzzzwtzu\ szsrzqqyopxmovjntgmrdlqakpZjlWigThbQgYNeSKcQHaOE_M\ CYJAWFAUCAP8AK0AFzAA0AA0AA0AA8YF7XE6XD5XC4XB3WA2W9\ zW8GHRFIPzJODKNCLMBMLANK9OJ8PI8PG7QF6RE5TDOVC3YBAZ\ ASZ9WYS_XR_QRZHRZHRZHQYIQzIQXIQXIQXIPzIPWJPWJPVJPV\ JOUJOUJOUKOzKOzKNzKNzKNSKNXUPzRR`OTrKVbLVIAZNMVRYS\ WiPzzRztMzzIzsDzz9zr5zzCzmIzzPWiVagageguoslcmcTgWI\ azHbdGczFdb7ud3tz0te4FzAE } frm:DivideBrot6Julia { ; Jim Muth z=pixel, c=(p3), a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 25-01-09 (Circular Ringers [7])
by Jim Muth 25 Jan '09

25 Jan '09

FOTD -- January 25, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal is late because I had no chance to write it at the scheduled time. But the image is still a pretty good one -- better late than never. It's actually an entire Julia set of the distant outskirts of a Mandelbrot set whose surroundings are starting to break up. The name "Circular Ringers" refers to the circular objects that are arranged in a kind of square. The rating of a 7 might be optimistic, but that's what I think the image is worth. The calculation time of just under 20 seconds could hardly faster. And for even more convenience the image soon will be posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Due to the unusual hour of this posting, give Paul a few hours to get the image calculated and posted. Morning clouds and afternoon sun kept the fractal cats happy here at Fractal Central on Saturday. The morning temperature of 41F 5C dropped steadily during the day to 21F -6C by night- fall, while the cats moved to a warmer location. My day was unexpectedly very busy. The next fotd will (hopefully) be posted in around 12 hours. Until then, take care, and knock on fractal wood. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Circular_Ringers { ; time=0:00:19.80-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6Julia center-mag=0/0/0.3 params=-4/8/0.1/0/-0.6157/1.2948 float=y maxiter=1500 inside=bof60 periodicity=10 colors=000zmzzzMkzzjsfjqfiofimeikehiehgegddgbdg`df\ ZcfXcfVceTceQbdObdMbdKacIacGacEadF_eFYfGXgGVhGTiHS\ jHQkIOlINmILnJJoJIpKGqKErKDtMAuO7vQ4kW8a`CReGHjK7o\ O8qL9rI9sFGgRNXbOUbORbOObOLbRK`TIZVJXXKVZLT`MRaNWa\ O_bPdbQlbRscRzcTvcNzXKwRFnKEaEDU7CMGCME9MC7M95M73N\ 51O75P90QB0RC0SE0TG0UI0VJ0WL0XL0YPilQioOijMifKjbIj\ YGjUEkQCkMAkH8lD6l94l55m65m75m76m86m86m96mA7nA7nB7\ nB7nC8nD8nD8nE8nETZ`VXaWVbXTcYScZQd_Oe`MeaLfbJgcHg\ dFheEifCigAjh8ki7kjAhkDelGbmI_nLXoOUpQRqTPrWMsYJt`\ GucDveAwh7xk4ym2pXLhHbjI`kJZlJYmKWnKUoLTpLRrMPsMOt\ NMuNKvOJwOHxPFyPExNIxMMxLQxJUxIYwH`wGdwEhwDlwCpwBs\ uScshPqxARU56R6UtuVpqWlmXhiYdeZ`a_XYdzuhsokljneerZ\ `uSWwKUxLRxMOyNLyOIyOFqQBiR7kNGlKOmHWnDcoAkp7slAni\ CjeFebHa_JYWMTTOPQQLYPSeOZmNetNkrMfqMbpLZoLVnLQmKM\ lKIkKEgMRcNb_PnWQzduNYlMSdLLWKFOJ9GI8KG8OF7SE7WD4l\ IGfPRaWaXaeWYhWUlWQ_debhf } frm:DivideBrot6Julia { ; Jim Muth z=pixel, c=(p3), a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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No FOTD for January 24
by Jim Muth 23 Jan '09

23 Jan '09

Fractal visionaries and enthusiasts: The subject says it all. Due to an overwhelming load of work, I have no time to write an FOTD for January 24. But with the work out of the way, there should be no trouble posting the FOTD for January 25 on schedule. Jim Muth

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FOTD 23-01-09 (Straight Edge [7])
by Jim Muth 23 Jan '09

23 Jan '09

FOTD -- January 23, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's oversized parent fractal appears to have a problem with anemia. It is no doubt a Mandeloid, but its main bay is shaped like a teardrop rather than a heart, and its buds shrink and vanish into the land of extreme periodicity well before reaching the area where East Valley should be. In fact, no hint at all of an East Valley appears in the parent fractal. I named the image "Straight Edge" because it lies on the edge of the main bay of its parent fractal in an area of such high peri- odicity that the buds have shriveled to invisibility and the edge appears as a straight line. I rated the scene at a 7. It is no surprise that the elements of the image have an itera- tion count well into the thousands. The maxiter of 150,000 might be a bit excessive, but with the logmap turned off, it makes little diference. Such a high iteration count makes the image a very slow one however, taking a full 43 minutes to finish on the fastest machines. But salvation is at hand on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where I have sent the image on ahead to save Paul the calcula- tion time. But as always, I still suggest a wait of an hour or two to give him a chance to post the image. Brilliant sun and a temperature of 37F 3C here at Fractal Central on Thursday not only gave the fractal cats a pleasant day in the sunny window, but it also melted the frozen drain. My day was rather busy but still within reason. The next FOTD will be posted in 24 hours. Until then, take care, and stay alert. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Straight_Edge { ; time=0:43:21.44-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 inside=0 periodicity=10 center-mag=+47.43645771417901/-2.558486870943088/\ 1353819/1/32.5/0 params=1/50 float=y maxiter=150000 colors=000aBfeAfhAfl9fp9fs9fpDgmGgjJhgNhdQiaTiZXjX\ _jUbkRfkOilLllIpmFsmDvmFtlGrlIqlJokLnkMlkNkkPijQhj\ SfjTejVciWbiX`iZ_i_YhaXhbVhccicZhcUhcPgcKgcGgdLeeQ\ cfVbg_`d`Whc_kecnggqijtknwmrzourjnjfgcb`WZUOUNHQG9\ M91K12L23M33N44O54P65Q75R86S96TA7UB7VC8WD9XE9YFAZG\ A_HBaIBbJCcKCdLDfMDgNEhOFgLEiPEjTElWEm_DobDpfDriDs\ mAusDtpGsnIrlLqiNqgQpeTobVn`YmZ_mWblUekSgjPjiNogDl\ iLjkToxlhm`abPcLDWSEOZFGeG9lGAjIAiKAhMAgOAfQAeSAdU\ AbWAaYA`_A_aAZcAYeAXgAWiFUfJScNR`SPZWOW_NTeLSjLQnJ\ Pp3NqFMpLJoPFnTCnX9l_FjbLidRgfWehadkgbnmdpuapr_mpX\ jmVgkSdhQafNYcLVaISZGPXDMUBJS9GQBFRCFRDFSEFSFFTHFT\ IFTJFUKFULFVMFVOFVPFWQFWRFXSFXUFXVFYWFYXFZYFZVQu_D\ _ZFZZHYYJYYLXXNXXPWWRVWTVVVUVXUUZTU`TUbSTdRTfRShQS\ jQRlPRnOQpOQrNPtNPvMNyLPxMRwNTvNVvOXuOYtP_tPasQcrQ\ eqRgqRhpSjoSloTnnTpmUssXrpVqmUqjTphSpeRobPn_OnYNmV\ MmSLlPJkNIkKHjHGtC7oEBjFF } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 22-01-09 (Gills [7])
by Jim Muth 21 Jan '09

21 Jan '09

FOTD -- January 22, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image lies in the northeast suburbs of its parent Mandelbrot set, in an area where nothing would normally be expected. But the DivideBrot6 formula does not draw normal M-sets, it draws M-sets with a difference. The difference in today's parent M-set is that it doesn't know when to stop. It is surrounded by an apparently limitless series of concentric rings. Today's scene lies in one of these extra rings, just beyond the point where the northern filament terminates. I rated the image at a 7, which seems about right. Then I named it "Gills". For some reason I thought of gills when I studied it. The calculation time of under 3 minutes may be cut to zero by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies and a temperature of 25F -4C made a rather pleasant winter day here at Fractal Central . . . at least the fractal cats thought so, since most of the sunny intervals came during the afternoon. My day was busy but not rushed. The next FOTD will be posted in 24 hours. Until then, take care, and keep your fractal side up. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Gills { ; time=0:02:56.34-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 center-mag=+0.002\ 16727635394304/+1.049158677727557/4.856e+011/1/-12\ 4/0 params=-53/57/0/0 float=y maxiter=1500 inside=0 logmap=101 periodicity=10 mathtolerance=0.05/1 colors=000F00I00L00O00S00Y00cG0i_0ti0zy0zyQzyXzzfw\ zzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzrisr0sr0sr0k\ r0frXZrLUrBNr3Ir0De0DM08708004004000C00e00r00r00r0\ 0r00r00r00r0sr0sr0sr0sr0sr0sr0sr0sr00r00r00r00r00e\ 00C_00_00_00_00_40_40_40_40_40_80_80_80_D0_D0_D00I\ H0Ie0Ir0I3_07_07_07_07_0C_0C_0C_0C_0H_0H_0H_0H00M3\ 0M70MB0MG4TLDTQNTXZTafYiUeiIjn8rn0rn0rv0rv0rv0rv0r\ v0rv0rv0rv0rv0rv0rv0rv0rv0rv0rv0rv0rv0rn0ra0rX0rL0\ rB0r30r04r0Ir0Zr0sr0sr0sr0sr0sr0sr0sr0sr0sr0sr0sr0\ sr0sr0sr0sr0sr0kr0fr0Uj0Nj0De08Y04T00M00H00C00C007\ 0030000000000000s00s00s00s00s00s00s000000000r00r00\ r00r00r00r00r00r00r00r00r00r00e00e00r00r00r00r00r0\ 0r00r00r00r00r00r00r70rL0ri0evzCvz0vz0vz0vz0vzrvzr\ vzrvzrvzrvzrvzrvzrvzrvzrvzrvzrvzrvzrvzrvzrvzrvzrvz\ rvzrvzrvzrvzrvzrvzrvzrvzrvzrvzrvzrvz0vz0vz0vz0vz0v\ z0vz0vz0vz0vz0vz0vz0vz7vz } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 21-01-09 (A New Beginning [Rating Optimistic])
by Jim Muth 20 Jan '09

20 Jan '09

FOTD -- January 21, 2009 (Rating Optimistic) Fractal and political visionaries and enthusiasts: When I posted yesterday's FOTD, I was feeling irritated because of the frozen sink drain. Then when I read the e-mail claiming that I had directed the members of the list to an AOL web site about the inauguration, I wrote a hasty reply and struck the send button before counting to 10. Actually, AOL itself adds these little perks at the bottom of all its overpriced e-mails. But I was rather surprised by some of the replies to my hasty response, especially those that expressed disappointment with my opinion of what the new administration might achieve. For one thing, I fail to see the connection between the search for beauty and my opinion of the ability of the new administra- tion to solve the country's problems. (If I am wrong, and I could easily be wrong, and the hoped-for miracles actually are brought about, I will be the first to admit my mistake.) I believe I have amply shown my appreciation of fractal beauty in the thousands of fractals I have posted to this list over the past almost 12 years. And I have shown my appreciation of the beauty of nature in my careful observations of the FC sky and my continuing reports of the FC weather. And at least most of the time, but not always, I also appreciate cats! Now on to the fractal business before I get scolded by the all- seeing god of the Fractint list. Today's image has a kind of beauty about it. The beauty might be a bit hard to recognize, but it is there, waiting for some intrepid fractalist to discover and enjoy it. The image is a scene on the main spike of its oversized parent Mandelbrot set, in the area of the East Valley of the large minibrot. A quick glance gives the impression of discontinuities, though none actually exist in the image, where everything blends smoothly together without breaks. The optimistic rating and the name "A New Beginning" reflect the national mood of the day. I'll not speculate on what the mood might be in a year or two. But regardless of moods, the calcula- tion time of only 45 seconds will give no problems. If other problems should arise however, the finished image may be seen on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Tuesday began with clear skies and a temperature of 5F -15C here at Fractal Central. But at noon the clouds moved in and the fractal cats turned cranky. The afternoon high of 27F -3C left them cold. Their biggest thrill came during the middle of the night, when a noisy cat fight broke out nearby. Another thrill came in the afternoon, when a mouse darted across the kitchen floor, barely escaping Cassie's pounce. My day was filled with work, and to keep FL happy I joined her to watch the inaugural festivities on TV. To my surprise, I actually enjoyed the ceremonies. The next FOTD will be posted on schedule in 24 hours. Until then, take care, and wait for the sunrise. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_New_Beginning { ; time=0:00:45.89-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=t center-mag=-34.92\ 9072151/-0.000006934429/174000/1/9.5/0 params=53/20 float=y maxiter=2750 inside=255 symmetry=xaxis periodicity=10 mathtolerance=0.05/1 colors=000LdbLfaLh`Lj_LlZLnYLpXLrWLtWSjcYajdTrjKyk\ MxlOwmWvmVunUtoVsoWrpXrqYqqZpr_osanscmtelsgkrijrjh\ okelkbij_fiXchU`gRYfOVeLSdIPcFMbCJa9G`6D_3AZ0BY8BX\ FBWMBVTBU_BTfBSmBRtGQqLPnQOkVPiZRfcXchaamgZrlWvqUr\ nWnkYkhZge`cba`_cXXdTUfQRgMOiFLkJMjNNiROiVPhZQhbRg\ fSfjTfnUepTfqVeqXdrYdr_cr`bsbbscaseatg`th_uj_ukZum\ YvnYvpXzs`vqXrpUooQknNglJdkG`jCXi9Uh6SiCQiHPiNNiSM\ iYKibIihHimFisEixDhvCgtCgrBfpBfoAemAek9di8cg8cf7bd\ 7bb6a`6a_AbVDcQHcMKdHMh8NdDN`HOXLOTPPPT98rPMXhT9dZ\ C`dFXjIRuGToKVjNXeQZ`T_WWd_UicSngQskOqiPogQneRlcRj\ aSi_TgYUfWUhXXjX_kXbmXeoXhpXkrXntXqwYtuXssWsqVspUr\ nUrlTrkSriRqgQqeQqdPpbOp`NpZ_z_Npd4l_AfVF`RKVMQPHV\ JBlID_DEN9FA5KH4ON3SU2X_1`f0dl0bl4al8_lBZlFXlIWlMU\ lQTlTRlXQl_7U39V6BV9DWCEWFGXHIXKJYNLYQNZTILiOZVUlG\ _z2at6co9eiCgdGiZJkUMmOQoJTqDWs8ZpAXmCWjDVgFUdHTaI\ SZKRWMPTNOQPNNRMKSLHUK00L } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Back to the topic, please
by Tim Wegner 20 Jan '09

20 Jan '09

This is not a response to any particular message (I certainly haven't read them all), just a request to end off topic responses about the inaguration (or anything else). Even correct observations that the other threads are off topic are themselves off topic, except those written by me, the benevolent list dictator (the delicious self reference in that almost makes it ON topic). I personally don't care what political or religious views people on this list have, but of course this list isn't the right place to discuss those views. The topic is fractint and fractals. Tim

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FOTD 20-01-09 (Seven Times Seven [No Rating])
by Jim Muth 19 Jan '09

19 Jan '09

FOTD -- January 20, 2009 (No Rating) Fractal visionaries and enthusiasts: Today's image earns no rating. After studying it for several minutes, I decided it is simply too much of the same thing to be worth a rating. But it's still an 'interesting' image. This is what I say about something when I don't want to admit that I see little of worth in it. The name "Seven Times Seven" refers to the multiple layers of 7-part symmetry surrounding the minibrot at the center. The parent fractal is a Mandelbrot set that has started to come apart at the seams. Today's image is located in the western part of the large minibrot on the main spike of the parent fractal. This large minibrot is coming apart even faster than its parent. The calculation time of 1-1/2 minutes is mercifully brief. The virtual trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image is just as brief, and even more fun. A balmy temperature of 26F -4C, with just enough sun to warm the shelf by the window, kept the fractal cats happy here at Fractal Central on Monday. Less work than expected kept me reasonably happy, but FL is unhappy because the drain of the kitchen sink is still frozen. To avoid tearing out a brick wall however, it looks like the pipe will stay frozen until it melts naturally. Until a thaw, the laundry tub in the next room will have to do. The next FOTD will be posted in 24 hours. If all goes well, it will be an image to warm the heart, if not, it will still be cool. Take care, and walk in the sun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seven_Times_Seven { ; time=0:01:30.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 center-mag=-14.26149982104\ 061000/+0.00298104454086101/4.265755e+011/1/-47.3/0 params=7/8 float=y maxiter=1500 inside=0 logmap=197 periodicity=10 mathtolerance=0.05/1 colors=000WPXWOWWNVWMUWLTWKSWJRVIQVHPUGOTFNTEMSCKR\ BJQAIP9GO7FO6EP5CQ4BR3AWCB_KCcSDg_EkgFnoGqwGksHfoH\ `kHWgHQcIL_IFWIASI5PI7OK8NL9MMALNCKPDJQEIRFHSHGUIF\ VJEWKDXMCZNB_OA`P9aQ9bRAcRBcRCcSDdSDdSEdTFeTGeTHeU\ HfUIfUJfVKgVLgVLgUKcYJ`YIXZHUZGQ_FN`EJbDGcCCeB9f96\ cBAaDDZFGXGIUIKRKNNNPKPRGSUDWXAZ_B_`B_`B_`C``CWaC`\ aDaaDaaDaaCXaBSaANa9Ja8Ea7B`68`CCbIGcOJdTLeZNfdPgi\ QhzmhimhzmhimhzmhimhzmhimhzmhimhzmhimhzmhiOhzcziOh\ zcziOhzcziOhzcziNhzczichzcziNhzczjNizczjmijMijmijM\ ijmijMijmijMijmijMijmizmijmizLijmizLizLizLizLizKiz\ KijKizKijKizKijKizKid4Yz6_f8`z9agBbgCchEeiGfiHgjJh\ buzXwzYvzYuzYtzZszZrzZqz_pe_oe_nf`mf`lf`kfajfaifai\ fbhfbgfbfgcegcdgccgdbgdagd`ge_geZheYhf`hfchfhhgmhg\ rhgvhhzhhzihziiziiziizijzijzijzikz7jz8jz9jzAjzBjzC\ jzDjzEjzFjzFjzGjzHjzIjzJjzKjzLjzMjzNjzNjzOjzPjzQjz\ RRzgSzfTzeUzdVzcWzbXzaYza } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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(no subject)
by JimMuth＠aol.com 19 Jan '09

19 Jan '09

**************Inauguration '09: Get complete coverage from the nation's capital.(http://www.aol.com?ncid=emlcntaolcom00000027)

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FOTD 19-01-09 (High and Mighty [6])
by Jim Muth 18 Jan '09

18 Jan '09

FOTD -- January 19, 2009 (Rating 6) Fractal visionaries and enthusiasts: The name of today's image, "High and Mighty", refers not to an airplane adventure but to the magnitude of today's image, which at 1.7*(10^13) is one of the largest ever. But a very large magnitude does not necessarily mean a great fractal, and after a bit of pondering I rated today's image at an unimpressive 6. The preponderance of greens lowered the final rating. The image shows a tiny order-7 minibrot with some order-2 genes in its background. The minibrot itself is beyond resolution, but what the heck. All order-7 minibrots look pretty much alike. The calculation time of under 4 minutes means relief for those with no time to waste. Even more relief may be found at the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the completed image is posted for instant viewing. Heavy clouds and warmer temperatures prevailed here at Fractal Central on Sunday. But a temperature of 24F -5C is warmer only when compared to -11F -24C, and the occasional periods of snow totaling about 2-in 5-cm did nothing to help create a feeling of warmth. Feeling totally chilly, the fractal cats passed the day lounging near the heat source. I passed the day trying to figure how to thaw the frozen drain pipe, which is inside an outside wall, making applying heat impractical, and has become an annoyance for FL. The next FOTD will be posted in 24 hours. Until then, take care, and fly with angels. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= High_and_Mighty { ; time=0:03:56.05-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 periodicity=10 center-mag=+2.823839870185858/-0.6690400717071375/\ 1.714889e+013/1/-37.5/0 params=7/8 float=y inside=0 maxiter=3200 logmap=463 mathtolerance=0.05/1 colors=000IbVLcXOdZRe`UfbXgd_hfbihejjhklklnnmpqnrt\ otwpvyqxvnvtltrjrphpnfnldljbjh`hfZfdXebYcaZa`___`Y\ ZaWYbUXcSWdQVeOUfMSgLRhJQiHPjFOkDNlBMm9Ln7Ko5Jp3Iq\ 2Hm7GjBGgFFcKE`OEYSDUXCR`COdEPbGQaHR`JSZKTYMUXNVVP\ WUQXTSYRTZQV_PW`NYaMZbL`cJadIceHdfGeeFeeFfeEfdEgdD\ gdDjzYhyVfxSdwQbvN`vKZuIXtFVsCUsAIgT7WkCVlGVlLVmPV\ mTVmUYfV``WcVWfPXiIYlCZo6Zr0_q1`p1ap1bo2cn2dn2dm2e\ l3fl3gk3hk3ij4ii4ji4kh4lg5mg5nf5nf5PhN0id2hc3gb5ga\ 6f`7f_9eZAeYCdXDdWEcVGcUHbTIbSJcUJdVJdWJeYJfZJf_Kg\ aKgbKhcKieKifKjgLjiLkjLlkLlmLmnLmoKlmKkkJjiJigIheI\ gcHfaHf_GeYGdWFcUFbSEaQE`OD`MD_KCZICYGBXEBWCAVAAV9\ CTDERGGPKINNJLQLJUNHXPF`RDcSCfVHcXMaZRZ`WXb_UedSgi\ PinNksKmwICkKFiLHhMKgNMfOPdPRcQUbRWaSZ`T`ZUcYVeXWh\ WXjVYlWVmXSnYPoZMpZJq_Gr`DsaAtb7ub5rX8pRBmMDkGGhAJ\ f5LdAOcERbJUaNX`S__WbZ`eYdhXikWmnYooZqo_so`uoawpbx\ pcypczpczrczvczzczzczzczz } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 18-01-09 (Aquamarine Fantasy [6])
by Jim Muth 17 Jan '09

17 Jan '09

FOTD -- January 18, 2009 (Rating 6) Fractal visionaries and enthusiasts: I spent most of the day Saturday trying to thaw a frozen pipe, which, together with a bit of real work, left little time for fractal fun. Today's image shows a Minibrot of order 7 with order-2 tendencies. The name "Aquamarine Fantasy" refers to the blue-green border surrounding the Minibrot. The rating of a 6 implies that I consider the image merely average. The calculation time of under 1-1/2 minutes is pretty good, but viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> is even better. Saturday started with a frigid temperature of -11F -24C here at Fractal Central, and rose to a balmy high of 16F -9C. When the ice-fog cleared out at 9am, the rest of the morning was sunny. But clouds moved in during the afternoon and snow flurries began by 7pm. The fractal cats huddled by the heat most of the day. My day was occupied by trying to thaw the drain pipe of the fractal kitchen sink, which froze solid overnight Friday. As of press time, with a temperature of 12F -11C, the pipe was still frozen. The next FOTD will be posted in 24 hours. Until then, take care, and look lively. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Aquamarine_Fantasy { ; time=0:01:24.96-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 periodicity=10 center-mag=-28.44863797978338/+0.1223338687689399/\ 1.368564e+011/1/1.75/0 params=7/16 float=y inside=0 maxiter=1500 logmap=122 mathtolerance=0.05/1 colors=000QGMSHNUIOWJPYKQ_LRaMScNTeOUgPViQWjRXkSYl\ TZmU_nY_nb`sgaumawrbzvbqqajmachaWZaPUaHGVIOZI`eJjm\ JuwOzzJuzEmrHHjDVd9g_CcYE`XGYWIVULSTNPSPMQRJPOCQQE\ PRFOTGOUHNVIMXKMYLLZML`NKbOJeQJgRIiSHlTHnUGsZ5rX9q\ WDoVGmUKjTNhSRfRUdQYjQXfPZbP`_PaWPcTPdPPfGQgIPgKPg\ MPgOPgQOgSTzUYzMjzQbzTRzWOgZMcaJ_dHWgFSYQWP__Gjc7t\ fHfbRUZ`GVj3Ri7ShBSgFTfITeMTdQUcUUbXVa`V`dV_hWZkWY\ oXXsXWwWXvXYvXZvY_vY_uZ`uZauZbu_cu_ct`dt`ztaztazrn\ zsizseztaztYztUzuQzuMzxGzwHzvIzuIztJztKisKgrLfqLdq\ MbpNaoN_nO`sM_pNZnOYkPYiQXgRWdSVbTV`UUYVTWWSQTTSUT\ TVTUWUVXUWXUXYUYZV__V``Va`WbaWcbWdcTheWecZbba_`cX_\ fVYiSXkPVnMUqJSjEMmFOpGPsHREn4TbCgSKvHSsMXqR`oWem`\ ikemijrgovetzduycuycuybuybuyauxaux`ux_vx_vxZvyZvzY\ vzYvzXvzXvzWuzWuzWvzWwzWxzVyzVzzVzzVzzVzzUzzUzzUzz\ UzzRzzUzzWzzYzz_zzazzczzezzgzzizzkzzmzzozzozzozzoz\ z9zzBzzEzzGzzJzzLzzOzzRzz } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 17-01-09 (Alex in Blunderland [8])
by Jim Muth 16 Jan '09

16 Jan '09

FOTD -- January 17, 2009 (Rating 8) Fractal visionaries and enthusiasts: I named today's scene in the Hypercomplex Mandelbrot set "Alex in Blunderland" because I'm not sure if the stuff filling the Seahorse-Valley-type minibrot at the center is real or just an artifact of imprecision. But whatever this stuff is, the image rates an honest 8, thanks to a significant degree to the expert coloring created accidentally by Fractint and tweaked by myself. There is not much more to be said about the image, which speaks for itself almost like one of those cute greeting cards with a built in vocal greeting. To hear the silent words, copy this email into your fractint directory in text format with a .par extension and run it like any other parameter file. Or zip on over to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and listen to the silent words there. The sky was sunny here at Fractal Central on Friday, but when the day dawned with a temperature of 5F -15C and brisk winds, I knew the fractal cats would be cranky, as indeed they were. The afternoon high of 12F -11C and the forecast of a low tonight of -2F -19C cheered them not a bit. It took an extra treat of tuna to ease their dissatisfaction. For me the day was busy enough to leave little time to enjoy the cold. The fractal, which turned out above average, added to the indoor warmth. The next FOTD will be posted in 24 hours. Until then, take care, and stay alert. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Alex_InBlunderland { ; time=0:01:28.70-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=-0.7492030151/+0.0759589135/37209/1/80/0 params=0/0/0/0/-4.7/0/0/1e-120 maxiter=1400 inside=0 logmap=-123 periodicity=0 colors=000QAKRAMSAOTAQUASVAUWAWXAYYB__BaaBcdBbfBai\ B`kB_nBZpBYrBYtHWuKUvKTwKRxKPyKOwKQuKRsKTqHUoAWm4X\ l9WkEVkJUjOUjTTiXSiaRhfRhkQgpPgqPdoOakOZgOWcOT_NQW\ NNSNKONHKNEGMBCM88M54M30MA3LG6KM9KTBJZEJdHIjJIiNNi\ RSzXWzcczfksggsceiabjWbjVajUakT`kS`kR_lQ_lPZlOZmNY\ mMYmLYkKWiKVgJUeJTcJSaIR_IQZIPXHNVHMTGLRGKPGJNFILF\ HKFGYXDkmAjkBjiBjgCzeCjmDzaDi_EiYEiWFiVFjSEjQEjODj\ MDjKCjICjGBjEBjCAjAAj89j69j48j28j08TGNCWa9XU6XNB`L\ FdJKgHOkFToDXrBiBB_EJRGRSxaTE2XLzTKsPJlLIeQJsNIlKI\ e9UyCy_BoKBe5FkFJqONvXUjU_ZSfNPlBNTCG9CAHACO8DW6Fb\ 5G`AcX9LSCQNFVM3`gB4VFKKKpJJjIIdEcbFYaGT`HN_rSk_Nd\ GO3TAtPDlLGeH6vOoczsIc`R6JKLMvJKjladQhqMVgpz3i5f_A\ cRE`ipNRjPhZzW6bXAVPEXmlzbapSSg62xA8oEDfhjU_SxRNYq\ cXhYYtTYRNZOYkMSfKNbJYzImZIEZ5CtAElEGeIcY9KKe6V_cW\ UCXOFYtKBjJH`JNRITtgCj`I`VOROUw6tl9nbCiSFcnGvOnoMe\ jLYfJQbSY6OSGLNQniIicNdYS } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD -- 16-01-09 (Never-Ever Land [5])
by Jim Muth 15 Jan '09

15 Jan '09

FOTD -- January 16, 2009 (Rating 5) Fractal visionaries and enthusiasts: Another too-busy day on Thursday left too little time for a full fractal search. I had to settle for a hasty scene in the Hyper- Mandelbrot set. The image I found is another picture of a minibrot in trouble. This minibrot is located close to the northwest shore line of the main bay of the four-dimensional Hypercomplex Mandelbrot set, which consists basically of two overlapping Mandelbrot sets. The image rates a 5. The name "Never-Ever Land" is a whim of the moment. The calculation time of just under 5 minutes can be avoided by viewing the already-calculated image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The partly cloudy skies and temperature of 18F -3C at Fractal Central on Thursday were too harsh for the fractal cats, who spent most of the day by the heat, while I spent most of my time getting the real work out of the way. The next FOTD is due to be posted in 24 hours, and if all goes well, it actually might be posted on schedule. Until next time, take care, and be of cool demeanor. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Never-Ever_Land { ; time=0:04:55.64-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 passes=1 center-mag=-0.6683561954880116/+0.320647858085555/\ 2.64492e+008 params=0/0/0/0/0.11/0/1e-090/0 float=y maxiter=5000 inside=0 logmap=400 periodicity=0 colors=000TAJSAJR9JQ9JP8JO8JN7JM7JPAHSDFUGDXIB_L9a\ O7dR5gT3iW1lZ0m_0n`0oa0pb2qc4rd6se8tfAugCvhEwiGzlG\ xjHwiIvhJugJtfKsdLrcLpbMoaNn`Om_OlYPkXQjWQhVRgUSfS\ TeRTdQUcPVbOV`NW_LXZKYYJYXIZWH_XH`VG_UGZTFYSFXREWQ\ EVPDUNDTMCSLCRKBRJBQIAPHAOF9NE9MD8LC8KB7JA7I96H86H\ BBKEGNHLQJQSMVVP_YRd_UibXne_rfbthZsgWpeSmdPjcLgaHd\ `EaZAZY4S_7WXAZUCaSFdPIhMKkKNnHRuDQsEPqFPoFOmGOkHN\ iHNgIMeILcJLaKK_KKYLJWMJUMISNHQNHOOGMPGKPFIQJEIHGM\ FHQDIUBKY9La3Gj6Jg8MdAPaCSZEVXGYUI`RKcOMfLOiJQlGSo\ DUrAWu79yJMxCYx5`u9csDeqHhnLjlPmjSpgWre_uccw`gzZkz\ XnzWoyWoxVowVovVouUnuUnuTmtTmsTlqSlpSkoSknRklRkjQk\ iQkhQkfPkePkcOkaOk`Ok_NkZNkZOnYNkXMhWMfVLcVK`UKZTJ\ WSJUSIRRHPQHOPGMPGLNEJLDGKCDIBAG97HA8HB9HCAHDBHECH\ FDHGEHHFHIGIJHIKIILJIMKIMLINMIONIPOIQPJRQJSRJTSJUT\ JVUJWVJXWJYXFbbJYYMUTPPOzLJzXJzXNzaNzfNzVIXLPZNR_S\ T_VVb`XdfZfkahpfjuklyopzs } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD -- 15-01-09 (Something is Wrong [5])
by Jim Muth 15 Jan '09

15 Jan '09

FOTD -- January 15, 2009 (Rating 5) Fractal visionaries and enthusiasts: Once again on Wednesday, too much work meant too little time for the FOTD. Today's image shows a minibrot that appears to have something wrong with it. The minibrot is located on a filament in the eastern suburbs of the large minibrot on the main stem of the four-dimensional HyperMandelbrot set. Everything is normal until we approach the boundary of the minibrot, where instead of a sharp fractal edge, we find a fade- off to a circular area of smoothness. This might be an artifact of imprecision, but if so, it is the most precise imprecision I have ever come upon. I rated the over-hurried image at a 5, and named it "Something is Wrong". The calculation time of 26 seconds makes up for any lack of quality or lack of interest. And as always, the finished image may be viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Wednesday at Fractal Central featured morning sun, afternoon clouds and evening snow, with a temperature of 18F -8C. The fractal cats forgot the drafty window and found the heat. My day was unfairly busy, but who ever said that life was fair? Due to the lateness of today's FOTD, the next FOTD could be posted in about 12 hours. Until then, take care, and unfairness reigns supreme. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Something_is_Wrong { ; time=0:00:26.37-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=HyperMandelbrot2 float=y center-mag=-1.742567447895688/+0.005947579792857/\ 3.93563e+007/1/-2.5/0 params=0/0/0/0/0.2/0/1e-090/0 maxiter=2300 inside=0 logmap=65 periodicity=0 colors=000SLoPKlMJhJIcDH_KGXRFUYERcDPjCMq6Jw0Horck\ iYhaTdTOaLI_CDX4B_BIbHPcOUfUai`hlfosQnWES836D5DI7K\ N9RSBYXDdaFkfHrkIygNsdSm`WhY`bVeXRiSOnMLrHNpOPoURn\ _TlfVklXjrYixZli_nV`pGZmMXkRViXTfaRdgPblN`qMQeLFUL\ 5IJCEHJBiYRdWO_TMUQJPOHKLEFJCHMEJPFLSGNUHBghMUoXHv\ VOmTUeR_YQeQThMWkIZnF`qBct8fw4hz1cs7_lDWeJS_OWufSY\ POB8PGDPKHPOMPSQPWVP_ZPcbLhcHldDqe9ufKqZUmRcjJelOg\ mSioXjp`lrensiotmbfbRUTFHJ3496QECWFH`GNfHSkIXpJWqI\ WqHVrGUsFUsETtDDbzFdvGerHgnIhjKifLkbMl_NnWPoSQpORr\ KSsG9YtB_qC`nDblEciFdgHfdIgaJh_KjXLkVMlSOnPPoNQpKR\ rISsFul8fpBP9vQLjRX_ShOcfbbg`ahZ`iX`jW_kUZlSYmQYnP\ XoNWpLVqJVrIUsGTtEUeETjDToDSZgT_eT`dTacTbaTc`Td_Te\ YTfXTgWThVTiTTiSTjRTkPTlOTmNTnMToKTpJTqITrGTsFTtE0\ bnAhaKnP1rM3sL5sK7sK9sJBsJDsIFsHGtHItGKtGMtFOtEQtE\ StDp7cVBv`9vf7vk6vfVUbs2`r4Zr6Yq8Wq9UqBTpDRpFQpG4q\ U9sYEtaJudOvhUwlzxrzyzzzz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================

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FOTD -- January 15, 2009 (Something is Wrong [5])
by JimMuth＠aol.com 15 Jan '09

15 Jan '09

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Re: [Fractint] Question on Fractint Image Resolution
by Paul.N.Lee＠Worldnet.att.net 15 Jan '09

15 Jan '09

"Tim Wegner" replied to a [Fractdev] posting: > > Rich or anyone, can you remind me where Rich's > FractInt for Windows executable and source is? > For many years, one could easily download the executable, the source, or both. Each was in a single "compressed" file format (tarball, zip, arc, etc.) and made accessible to the public. Now, this "FREEWARE" software seems to be getting away from allowing others access, not only the information about it (Spanky server being down and out) but to the source code. No longer can anyone retrieve the current working versions' source with a single download, nor are there any instructions for doing so on the web sites that are still functioning. An executable for Rich's Windows version is at: http://www.nahee.com/Software/FractInt_Setup_21-00_beta-5.msi And most of the older versions (both executable and source) may be found at the following: http://www.nahee.com/Software/+FractInt_(OLD)/ I would also have a copy of the Spanky site, but have yet to get RSYNC to acquire what is at: lin27.triumf.ca::spanky even though Noel said it was setup for me to retrieve to my IP address. I was hoping to have a full mirror for Spanky available. Sincerely, P.N.L.

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FOTD 14-01-09 (Less Than Nothing [7])
by Jim Muth 13 Jan '09

13 Jan '09

FOTD -- January 14, 2009 (Rating 7) Fractal visionaries and enthusiasts: An unexpected last-minute change on a job we thought was already finished left little time for fractal diversion on Tuesday. But the MandAutoCritInZ formula makes interesting fractals almost automatically, and using it, I found an emergency image in a few minutes. The parent fractal is one of those double minus things with a prominent fan extending east from the origin. Today's image is located in a small valley at the edge of the fan. I named the image "Less Than Nothing", which probably refers to the effort I put into it. The rating of a 7 seems fair. The calculation time of 9 minutes may be avoided by surfing to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Cloudy skies, a temperature of freezing and occasional periods of snow kept the fractal cats in poor spirits here at Fractal Central on Tuesday. The changes to a supposedly finished job kept me in poor spirits. The next FOTD will be posted in 24 hours. Until then, take care, and choose wisely. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Less_Than_Nothing { ; time=0:09:00.04-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+3.586569974821439/-0.00067185136372234\ /8.07787e+008/1/102.5/0 params=-5/-1.25/-0.5/-7.3/\ 0/0/0/0 float=y maxiter=4200 inside=0 logmap=700 periodicity=10 colors=000KHK5J`FWn_HzgpGZhLR`PITTAMXNCRZ3Mw42cG8L\ SE2cJ9WOFOSMGXS8`Y0dM6nBCxPJcbQKpW0feEXnSNwdMubMs`\ MqZMoXMmVQ_WUNXXAYTI`PPcMWfIbiFilBpo8wqFvnLvkSuiYu\ fdtdjtapt_b_WQGTNLQLQNIVKG_HDdEBiB9n8FkALhCReEXcFb\ `HhYJmWK5wJ4rM4mP4iS3dV3`Y0MW3Sczzzauibpjclldgmebn\ fZpgUqgQrcOs_NtXLuTKvPJwMHxIGyFFyLDwRCuXBsbAqh9on8\ mt7ky6ir5ll4nf4p`3rU2tO2vI1xC1zG5uK8pOBkSEfWHa_KXc\ NTdKUdHUeEUeCUf9Vf6Vg3Vg1Vb3_Z5cU7gQ9kLBoHDsDEwAuW\ 2wT3xS3xR3xQ3xQ3xP3xO3xOLjYaXgrJpkPjdVeZ`_SfVLlPFq\ KRsObtSnvWzwZyq`ykbyedy`fAnAIiMQeXY`heXs0m`1kb1jd1\ hf1gh2ej2dl2bn2ap9TnLdASgE_jHnmLzpOzsRzrQzrQzrQzrP\ zqPzqPzqOzqOzpOmzNmzNlzNkzMkzMjzMRmDiominmhnmgnmfn\ mfmmemmdmmdmmclmblmalmalm`km_km_lHZkGYjGYjGXjFWjFV\ iFViKUiPTiUThZShcRhhbimajrakvalzamz`nz`oz`pz`qz`rz\ _sz_tz_uz_vz_wzZxzZyzZzzZzzYzzYzzYzzYzzYzzXzzXzzXz\ zXzzXzzWzzWzzWzzWzzVzzVzz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 13-01-09 (The Missing Stem [8])
by Jim Muth 12 Jan '09

12 Jan '09

FOTD -- January 13, 2009 (Rating 8) Fractal visionaries and enthusiasts: This month is January, not July. To atone for the error I made yesterday, we have a fractal that can not only be considered different, but is also one of the smoothest colored of all time. Unfortunately, with a palette of only 256 colors and only half the colors actually appearing in the image, the bands are still visible, but they are subtle enough that they almost disappear. The image consists totally of 'inside' stuff made visible by the 'bof60' inside fill. Changing the 'bof60' to 'numb' or 'maxiter' results in a totally blank screen with only a few tiny left-over dots of 'outside' stuff. The other active inside fills also give interesting effects, and are worth a try. The name "The Missing Stem" refers to the figure at the center, which is a true Mandelbrot set with only its main stem missing. The rating of an 8 includes a reward of a full point for the hour of tweaking I did to get the colors as smooth as possible. The calculation time of 21 seconds is brief enough to cause no frustration. The finished image is posted on the FOTD web site to make it even simpler to see the image. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies and a temperature of freezing made Monday about average here at Fractal Central. The fractal cats, who prefer things better than average, did not appreciate the periods when the sun was obscured. My day was slow enough to give me time for the extra coloring effort on the image. The next FOTD will appear in 24 hours, and this time I'll get the date right. Until then, take care, and be at one with whatever you decide to be at one with. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Missing_Stem { ; time=0:00:20.58-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 float=y center-mag=0/0/0.76 params=-204/208/0/1600 logmap=yes maxiter=1000 inside=bof60 passes=1 symmetry=xaxis periodicity=10 colors=000zzzvzutzqrzlpxinuhlrgjofhlefiddfcadcZbcW\ `cTZcQYcPXcNWcMVcLUcKTbJSaIS`HR`GR`FR`ERaDRbCRcBRc\ AQd7Qd6Pe5Pe4Oe3Of2Nf1Mf2Mf2Mf2Lf2Kg2Kh2Kh2Kh2Kh3K\ h4Kh5Kh6Kh7Kg8Kg9KgAKeBKeDKeFKeHKeIKeJKeKKdKKdKKdK\ KdKKdKKdKKcKKbKKaKK`KK_KKZKKYLKXLKWMJVNJUOITPISPIR\ PIQPIPQIORINRIMRILRHKRHJQGIPFHOEGNDFMCELBDUvvUwuVv\ tWutXttYstYrtZqtZpt_ot_nt`mtaltaktbjtbitchtcgtdftd\ etedtectfbtgatg`th_thZtiYtiXtjWtjVtkUtkTtlSqkSojSm\ iSkhRigRgfQeeQcdPacP_bPYaOW`OU_OSZOQYNOXNMWNKVMIUM\ GULETLCTKDSKESJERJFRIFQIGQHHPHHPGIPGIOFJOFKOFKOFLO\ FLOFMOFNjfNjfOjeOjdPjdQicQicRibRiaSiaTi`Ti_Ui_UhZV\ hZWhYWhXXhXXhWYhVZgVZgU_gU_gT`gSagSagRbgRbiQcjPckO\ clNdmMdnLdoKepJeqIerHesGftFfuEfvDgwCgxBgyBgxCfxCfx\ CewCewCdwDdvDcvDcvDbuDbuEauEauE`tE`tE_tF_sFZsFZsFY\ rFYrGXrGXqGWqGWqGVqHVpHUpHUpHToHToISoISnIRnIRnIQnI\ QmJSlKUkKWjLYiL_hMagMcfNe } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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Corrected date -- FOTD 12-01-09 (Julia Starburst [7.5])
by Jim Muth 11 Jan '09

11 Jan '09

FOTD -- January 12, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's image is the first one created with a new formula, the DivideBrot6Julia, which draws the Julia aspects of the strange near-Mandelbrot set created by the DivideBrot6 formula. And speaking of near-Mandelbrot sets, today's image is the Julia set of a point in the East Valley of a small minibrot on the main spike of one of these strange things. And yes, I realize it looks nothing at all like a Julia set of the main spike of the Mandelbrot set, but what good would fractals be if they always did the expected. I have lost track of the shortest calculation time in FOTD history. The 8 seconds of today's image must be close to the record however. The name "Julia Starburst" accurately describes the image. The rating of a 7-1/2 seems about right for an image that took about a little less than no effort to create. If the calculation time of 8 seconds is still too slow, the finished image may be viewed at leisure on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cloudy skies and a temperature of 28F -2C on Sunday made clearing the 6 inches, 15cm, of snow from the Fractal Central pavements a task of sorts, but with the fractal cats offering encouragement from the windows, and two hot coffees courtesy of FL, I finished the job with minimum discomfort. The next FOTD will be posted in 24 hours. Until then, take care, and I can see no end in sight. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Starburst { ; time=0:00:08.09-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6Julia center-mag=0/0/0.22366 params=-16/20/0.0002/-11.5/-1.7/0 float=y maxiter=1500 symmetry=xyaxis periodicity=10 colors=000ZcczoIzzZTp54g4Gd3Ri3af3lj3wj3tr5qy7ptBp\ pFolIohMndQn`TlUPjNLhHHfADz4zzzzORZWbdcnzjzz`xzSrz\ JkzAri9tZ9kP8fF8a59XB9OH9KN9BTACUBCUBDVCDVDDWDEWEE\ XEEXEEXEEXEEXEEXEEXEEXDEXDEXDEXDEXDEXDEXDEXCEXCEXC\ EXCEXCEXCEXCEXCEXDDYEDZED_FD_FC`GCaGCaHCbHCcIBcIBd\ JBeJBeKBfLAgLAhMAhMAiNAjN9jO9kO9lP9lP9mQ8nQ8nR8oS8\ pS8qT7qT7rU7sU7sV7tV6uW6uW6vX6wX6waDYeJ8kIHpHPuGYz\ FexEdwEdvEcuEctEbsEbrEbqDapDanD`mD`lD_kD_D9NjD_iDZ\ hCZgCYfCYdCXcCXbCXaCW`BW_BVZBVYBVXBUVBUUBTTBTSASRA\ SQASPAROARNAQLAQK9PJ9PI9PH9OG9OF9NE9NjAZi9Yh9Yg9Xf\ 9Xe9Xd9Wc9Wb9Wa9V`9V_9VZ9UY9UX9UW9TV9TU9TT9SS9SR9R\ Q9RP9RO9QN9QM9QL9PK9PJ9PI9OImLIrGTkJbdMmYPwSSoVThX\ T`ZTU`TNbTFdT8fT1hT5cS8_RCWQFSQINPMJOPFNSBNQANNANK\ ANI9NF9N1pd2oc2nc2mb3lb3kb3ja3ia4h`4g`4f`4e_5d_5c_\ 5bZ5aZ6aY6`Y6_YIFhHEiGEjFDlECmDBnCAoBApA9q98r87s77\ t88s88r88qJV0MQIPLZRHoYTc } frm:DivideBrot6Julia { ; Jim Muth z=pixel, c=(p3), a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 12-01-09 (Julia Starburst [7.5])
by Jim Muth 11 Jan '09

11 Jan '09

FOTD -- July 12, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: NEW FORMULA ALERT! Today's image is the first one created with a new formula, the DivideBrot6Julia, which draws the Julia aspects of the strange near-Mandelbrot set created by the DivideBrot6 formula. And speaking of near-Mandelbrot sets, today's image is the Julia set of a point in the East Valley of a small minibrot on the main spike of one of these strange things. And yes, I realize it looks nothing at all like a Julia set of the main spike of the Mandelbrot set, but what good would fractals be if they always did the expected. I have lost track of the shortest calculation time in FOTD history. The 8 seconds of today's image must be close to the record however. The name "Julia Starburst" accurately describes the image. The rating of a 7-1/2 seems about right for an image that took about a little less than no effort to create. If the calculation time of 8 seconds is still too slow, the finished image may be viewed at leisure on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cloudy skies and a temperature of 28F -2C on Sunday made clearing the 6 inches, 15cm, of snow from the Fractal Central pavements a task of sorts, but with the fractal cats offering encouragement from the windows, and two hot coffees courtesy of FL, I finished the job with minimum discomfort. The next FOTD will be posted in 24 hours. Until then, take care, and I can see no end in sight. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Julia_Starburst { ; time=0:00:08.09-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6Julia center-mag=0/0/0.22366 params=-16/20/0.0002/-11.5/-1.7/0 float=y maxiter=1500 symmetry=xyaxis periodicity=10 colors=000ZcczoIzzZTp54g4Gd3Ri3af3lj3wj3tr5qy7ptBp\ pFolIohMndQn`TlUPjNLhHHfADz4zzzzORZWbdcnzjzz`xzSrz\ JkzAri9tZ9kP8fF8a59XB9OH9KN9BTACUBCUBDVCDVDDWDEWEE\ XEEXEEXEEXEEXEEXEEXEEXDEXDEXDEXDEXDEXDEXDEXCEXCEXC\ EXCEXCEXCEXCEXCEXDDYEDZED_FD_FC`GCaGCaHCbHCcIBcIBd\ JBeJBeKBfLAgLAhMAhMAiNAjN9jO9kO9lP9lP9mQ8nQ8nR8oS8\ pS8qT7qT7rU7sU7sV7tV6uW6uW6vX6wX6waDYeJ8kIHpHPuGYz\ FexEdwEdvEcuEctEbsEbrEbqDapDanD`mD`lD_kD_D9NjD_iDZ\ hCZgCYfCYdCXcCXbCXaCW`BW_BVZBVYBVXBUVBUUBTTBTSASRA\ SQASPAROARNAQLAQK9PJ9PI9PH9OG9OF9NE9NjAZi9Yh9Yg9Xf\ 9Xe9Xd9Wc9Wb9Wa9V`9V_9VZ9UY9UX9UW9TV9TU9TT9SS9SR9R\ Q9RP9RO9QN9QM9QL9PK9PJ9PI9OImLIrGTkJbdMmYPwSSoVThX\ T`ZTU`TNbTFdT8fT1hT5cS8_RCWQFSQINPMJOPFNSBNQANNANK\ ANI9NF9N1pd2oc2nc2mb3lb3kb3ja3ia4h`4g`4f`4e_5d_5c_\ 5bZ5aZ6aY6`Y6_YIFhHEiGEjFDlECmDBnCAoBApA9q98r87s77\ t88s88r88qJV0MQIPLZRHoYTc } frm:DivideBrot6Julia { ; Jim Muth z=pixel, c=(p3), a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FW: [Fractdev] Question on Fractint Image Resolution
by Hal Lane 11 Jan '09

11 Jan '09

----------- Daniele Corradetti said ---------------------- > > ...I would need some fractals in higher resolution (more then > > 2048x2048). ... Is there any way to avoid this limit? Daniele, Tim, Rich Thompson's 'Fractint for Windows' and the current DOS Fractint version can both overcome the limit of 2048 pixels by using a configuration file to allow the creation process of fractals to use disk files and or RAM instead of the screen. (This statement is technically a bit too simple -- but let's keep it simple.) The configuration file is named: FRACTINT.CFG and is located in the directory (folder) where 'Fractint for Windows' or Fractint for DOS is installed. Fractint's configuration file data layout is pretty understandable -- just duplicate one of the existing Disk Video entries and change the "x" and "y" values -- and remove any duplicate key bindings. This works in both versions. I recommend that you don't modify any of the existing specifications in the file -- just add any resolutions you need. If you do make changes to your FRACTINT.CFG file, make a backup copy before you begin making your changes. (I'm a lazy file backup person -- I just right click the file and choose 'Copy'; then I right click 'white space' in the same folder (where there is no file name) and choose 'Paste'.) If you are not familiar with the Fractint configuration file concept, here is what the program does: - For images that fit on the screen, Fractint will display the image while it is being calculated. - For fractals that are too large to be displayed while they are being calculated, Fractint creates the image using RAM and/or hard disk drive space on your computer. The line number of the current line of pixels being generated is displayed during the image calculation (remember, there is no image being displayed.) You still must save your image after the image is completed. - Resolutions calculated using RAM and/or hard disk drive are identified in 'Fractint for Windows' beta 5's file as: "Win32 Disk Video". The DOS version of the program lists these resolutions as: "Disk/RAM 'Video'" Notes: - You don't need to specify a key binding (1st entry on the line) for your new resolutions. - Don't specify duplicate key bindings. - There is an additional entry on each line in the 'Fractint for Windows' format of FRACTINT.CFG compared to the DOS FRACTINT.CFG file format. Appended to the end of each 'Fractint for Windows' line is either: ",disk" or ",gdi" (the driver). - Order in the file is not important. However, the order of lines in the file is the order that the resolution choices will be presented to you when you press the <del> key in Fractint. - Don't use the <tab> character in the file. - Remember, images of resolutions that are *not* shown in the list of Video Mode choices as "Disk Video" *cannot* be read back into Fractint and displayed on the screen. (Sorry for the double negative above -- the positive version: Only images of resolutions that *are* shown in the list of Video Mode choices as Disk Video can be read back into Fractint and displayed correctly.) - Use a general purpose image viewer to see your Fractint images that are not of Fractint screen-viewable resolutions. - In 'Fractint for Windows' sometimes comments (next to the last field on the line) that you enter into the file do not appear in the list of resolutions displayed by the program. - I don't know what the limit on the maximum x and or y pixel dimensions are in Disk Video mode in 'Fractint for Windows' or DOS Fractint. - I have successfully calculated images of 8192 x 8192 pixels in 'Fractint for Windows' and 5120 x 4096 -- which is (1280 x 1024) x 4 pixels in DOS Fractint. I re-sized the 5120 x 4096 image in an image viewing program using a built-in smoothing algorithm and got an anti-aliased image of 1280 x 1024 pixels as the result. This image has greatly reduced 'pixilation'. Example of adding lines to FRACTINT.CFG: (with a bunch of spaces removed so the lines won't wrap around during emailing.) Original line from *Fractint for Windows* FRACTINT.CFG file: ------------------------------------------------------------ CF5 ,Win32 Disk Video,0,0,0,0, 19, 8192, 8192,256,,disk Lines added to *Fractint for Windows* FRACTINT.CFG file: ------------------------------------------------------- ,Win32 Disk Video,0,0,0,0, 19, 512, 512,256,,disk ,Win32 Disk Video,0,0,0,0, 19, 640, 640,256,,disk ,Win32 Disk Video,0,0,0,0, 19, 1300, 1000,256,,disk For the DOS format of the FRACTINT.CFG file remove ",disk" from the end of each line. I successfully created images using all 3 of the above resolutions that I added to my 'Fractint for Windows' FRACTINT.CFG file. - Hal Lane ######################### # hallane(a)earthlink.net <mailto:hallane@earthlink.net> # ######################### > -----Original Message----- > From: fractdev-bounces(a)mailman.xmission.com > [mailto:fractdev-bounces@mailman.xmission.com]On Behalf Of Tim Wegner > Sent: Sunday, January 11, 2009 1:09 PM > To: Daniele Corradetti > Cc: fractdev(a)mailman.xmission.com; Jonathan Osuch > Subject: Re: [Fractdev] Question on Fractint Image Resolution > > > Daniele, the original DOS version of Fractint had a resolution limit > of 2048 pixels. However it also has a means of generating multiple > images and piecing them together, see the documentation. I believe > this effectively overcomes the limit. (Sorry for not being more > specific, it's been a while since I looked at this.) > > Rich Thompson has created a Windows version that may overcome that > limit. > > You didn't mention which version you are using. I am cc'ing both > Jonathan Osuch, who has been mainting the current version, and Rich. > However my suggestion would be to join the mailing list at: > > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint > > since there are many people who could help you better than I can. > > Tim > > > > Dear Tim Wegner, > > I'm a mathematician from Pisa, Italy. Let me tell you > > how glad I am finding a new update of FractInt for Windows Vista. > > Indeed this program means a lot for me since I was just a kid when it > > was released and I grew up with its fractal. Most of my love for > > mathematics probably came from it. > > > > Anyway, I got a problem with the maximum resolution of Fractint. > > Indeed I would need some fractals in higher resolution (more then > > 2048x2048). I saw in some post of yours that the max resolution 2048 > > is crucial. Is there any way to avoid this limit? > > > > Thank you for your answer > > Best Kinds > > > > Daniele > > > > ----------------------------------------------- > > Dr. Daniele Corradetti > > via Pellas 34 > > 50141 > > Firenze > > Italia > > tel.: +39 3497896073 > > email.: d.corradetti(a)gmail.com > > skype: d.corradetti > > ---------------------------------------------- > > > > > > _______________________________________________ > Fractdev mailing list > Fractdev(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractdev

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FOTD 11-01-09 (Threads of Passion [?])
by Jim Muth 10 Jan '09

10 Jan '09

FOTD -- January 11, 2009 (Rating ?) Fractal visionaries and enthusiasts: I don't know quite what to make of today's image, which gives me a rather queasy feeling. I named it "Threads of Passion" which has nothing at all to do with a suggestive outfit. Not knowing what to make of the image, I could not decide how to rate it. The question mark leaves it to the individual viewer to decide a rating. The image is just different enough to qualify as an FOTD, and its calculation time of an incredibly fast 22 seconds makes running the included parameter file not only a breeze, but a full-blown typhoon. Those who dislike high winds may view the image, already calculated, on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A temperature of 27F -3C and an all day snow spoiled the planned events in the Fractal Central area of the Susquehanna Valley on Saturday, but the forecast foot (30cm) of snow failed to pile up, leaving us with a not very impressive 5 inches (12cm). The fractal cats wondered why the outside world looked so different. My day was occupied by graphics work and thoughts about clearing the sidewalk, which I will put off until tomorrow, when the next FOTD will appear in a blaze of glory. Until then, take care, and do it right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Threads_of_Passion { ; time=0:00:22.35-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 center-mag=-0.1202642055100029/+1.135069928224513/\ 1985/1/30/0 params=-98/102/0/-12.5 float=y maxiter=265 inside=0 logmap=10 periodicity=10 colors=000hQ0TR0ZM0000000000000MGQUfajkzgmwiJpjizz\ gczSYzVSzYLz`Fzb9fm6Ux3`jHfYVlLhr8vjDnbIfWNZORRHWJ\ 9`B2d49Z9FTDzNIzIMzLKzNIzQGzSEaVCcXAe_8ga6bQIZFUVL\ QRQNOVJz_GzdCzi9zn5zs2zq8zpEzoKRnQWmW`laWg`Sc`N__J\ V_ERZANZEOTHONKOIOPCRP6UP1gnhiicje_k`WlXSkTPjPNiLL\ hIIgEGfAEe7CXIPPTaHcn9mz8np7ofzoXzpNzqDzq3ziLzzazz\ rzzjzzczzXzzQzzJzzNzzRzzVzzZzzbzzfzzhzzjzzkzzmzzoz\ zpzzrzzszzozzlzzizzfzzczz`zzYzzZzzRzzKzzCzzszz_zzK\ zzVzzJzz7zzhzzlzzozzszzbzzZzzWzzSzzjzzozz_zzUzzOzz\ HzzWzzLzzBzz0zzYzzhzzlzzpzzXzzNzzDzzmtzuWzfKzg8zi_\ zRRzCezibzn_zsXzxUziGzm1zqQzyfzhezkdznbzSYzEIziAzW\ YzhNzlCzpSzUgzZgzSgzLhzEfzhezkczofzjezprz4bzaYzKSz\ 1SzKSzbTzvbztlzqozjrzcuzXyzQxzWwzbvzhtzomzQazWZzMV\ zCRz2YzBdzLkzV_zXOzZRzUUzPXzK_zEczmHzFRzKazPlzUfzG\ nzzYzYOzQEzI4zAdzZ`zSYzLUzDlz`qzVgzegzdgzdgzcgzegz\ egzefzekzfpzh_zcjzprztqzg } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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spanky fractal database problems
by Noel Giffin 09 Jan '09

09 Jan '09

There were several bad power-bumps on site over the Christmas break and it took a toll. After about spinning almost continuously for 20 years, the system disk is showing a hardware failure. I'm not sure what this means in the long term, as I may be able to build another, but it won't happen anytime soon. I'll be away from the site until February. It may be time to retire the system. All things must pass! Noel Giffin

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FOTD 10-01-09 (From the Abyss [7.5])
by Jim Muth 09 Jan '09

09 Jan '09

FOTD -- January 10, 2009 (Rating 7.5) Fractal visionaries and enthusiasts: Today's fractal is a simple Julia set of the East Valley area of the large minibrot on the infinitely divided main stem of the Z^(2.003)+C Mandeloid. The corresponding Mandelbrot point is at the edge of one of those curious rectangles that I occasionally mention. Yes, the rectangles also exist in the Mandelbrot aspect of the Z^2.003 fractal. In fact, today's image is filled with tiny rectangles. Today's image is extremely sensitive to very small changes of some parameters, while other parameters may be changed to any value with no effect on the image. I named the image "From the Abyss", probably thinking of one of those great old sci-fi movies, where creatures like Godzilla emerge from abysses. I rated it at a 7.5 because I can see nothing in it worth more. The fast calculation time of 1-1/2 minutes will leave lots of time for non-fractal activities. As always, the finished image is or soon will be posted for instant viewing bliss on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies, a temperature of 30F -1C and a biting northwest wind made the outdoors unpleasant here at Fractal Central on Saturday. The fractal cats do not go outdoors however, and there was enough afternoon sun to keep them happy. But we'll see how they take to the foot or so of snow forecast for the FC area tomorrow. My day was too busy to be pleasant. The next FOTD will be posted in 24 hours. Until then, take care, and be careful of the creatures in the abyss. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= From_the_Abyss { ; time=0:01:33.55-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/0/920/1/-37.5/0 params=90/90/90/90/-1.743488082976184/3.2412432010\ 25422e-007/0/0/2.003/0 float=y maxiter=800 inside=0 logmap=226 periodicity=10 colors=000JFFKEKLDPMCTOBYQ9bS8fT7kT6pR5tW0v`3tc2rf\ 1pi0nlAmmCmnEmoGmpImqKmqMmqOmqQmqSmqUmqWmrYmramsem\ thnulnvpnvsnvrlvrjvrivqgvqfvqdvpbvpavp_vpZnkYgfY`a\ XTXXMSWFNW8IWAKZCMaEOdFQgHSjJTlLVoMXrOZuQ`xRazYLWY\ 42_96`E9aJCdOFgSIjXLmaOrfRvkUzoXzrVzrTzrRznPzkOvgM\ rfKmeIhdGccFZaDW`BY_9_Z7`Y6bW8cUAdSCeQEgOFhMHiKJjI\ LkGMbLLVPLNTKFXK7`KA_PDZTGYXJXaLWeOViRUnUTrXSvZRzj\ UoZZqObrCgt1ku4gu6du8auAZuCWuFTuHQuJNuLKuNHuLHrKHo\ JHlHHiGHgFHdEHaCHZBHWAHU8HR7HO6HL5HJAMOERTIVYMUbRU\ fVUkZUpbUufUyjWfU6OU7QU7RUCTUHUUMVUQWjVXg_YgZWecZc\ g`acb_cdYcf_cgWchTciQcjNckKllGilDfmAdn7ao4Zp1Xp4Yn\ 7YmAYlDZjGZiJZhMZgO_eR_dU_cX_b_``b`_e`ZeXZg`YidXkh\ WmkVooUqsTrvSprTnnTmjTkfTjcTh_UfWUeSUcOUbLUZRWVWXS\ `ZOf_KkaHpzMXYRkTzzzzuzzzzTkURlWQnZOp`NrcLseKuhIwj\ HxlJtmKqnLnoNjpOgqPdrR`sSYtTVuUSuyPIrSPkVVdY`Y`gRc\ mLhrKfsKesKdtJ55U99cDCmHF } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 09-01-09 (Square Rectangles [7])
by Jim Muth 08 Jan '09

08 Jan '09

FOTD -- January 09, 2009 (Rating 7) Fractal visionaries and enthusiasts: Due to the continuing rush here at FC, the image that was intended to be the FOTD for January 8 now appears as the FOTD for January 9. There will be no FOTD for January 8. The image is actually a study in the hidden patterns brought out by the broad color palette. When a color palette with narrow bands is applied to the image, the pattern totally vanishes. I named the image "Square Rectangles" because of the obvious square surrounding the central minibrot and the curious rectangles that lie at the corners of the square. These rectangles are of the same family as the ones in the Julia set of the Z^(2.003)+C Mandeloid, with a C value of -1.7435,0. I rated the image at a 7 when I found nothing in it worth more. The calculation time of under 4 minutes will pass like lightning for true fractalists. The trip to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will pass like lightning for those true fractalists frustrated by DOS-challenged machines. Partly cloudy skies, brisk winds, flurries of snow, a maximum temperature of freezing and a forecast of heavy snow on Saturday made for a day of variable contentment for the fractal cats here at Fractal Central on Thursday. My day was very busy. Luckily, I have developed an instinct for fractals that enables me to find them with almost no effort. The next FOTD will be posted in 24 hours. Until then, take care, and don't ask questions whose answers raise more unanswered questions. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Square_Rectangles { ; time=0:03:54.62-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 center-mag=-0.044068177284054/+0.0000027835075896/\ 2.038602e+010/1/152.5/0 params=2.003/-4/0.025/0 float=y maxiter=2000 inside=0 outside=summ periodicity=10 mathtolerance=0.05/1 colors=000czz_zzJzzNzzPzzTzzVzz_zzazzezzgtzjnzlizn\ ezlazl_zlXzlVzlTzlRzlPzlNzlLzlJzlHxlFvjDrjBpj9nj7l\ j5jj3ij1gj0ej0cj0aj0_j0Xe0_a0_X0_T00P00L00H00B0070\ 030000000000000000030090PH0JP0DV09c03j00p00x00z00z\ 00z00z00z30z70zB0zD0xH0rL0lP0iR0cV3X_7RcBNeFHiJBlN\ 5pR1rV0v_0zc0zg0zi0zc0tX0nR0jL0eH3_B7V5BU0FU0Jc0NU\ 0Rc0XK0TU0Rc0Nc0L_0Hj0Fv0Dz0TU0RU0RU0PU0PU0Nc0NK0L\ K0LU0LU0rU0zn0zp0zp1zp3zp7zp9zpDzpFvpJtpNpzPzzTzzV\ zz_zzazzezzizzjzznzzpzztzzzzzvzzXDzi5zr0zz0zz0zz0z\ z1zz7zzDztHtpNtlRtiXtecr_grVlrRprNvrHzrDzr9zr5zr1z\ r1zr0rr0jr0cr0Tr0Lr0Dr05r00r00r00n01j05g1Bc5Fa7LX9\ PTDVPF_LHeJLiFNnBPr7Tx3Vz1Xz0az0cz0ez0gz0_z0Rr1Li5\ D_95PD0FH05L00P00N00L00L00J00H00H11F51F91DD3BH3BL3\ 9P39T57X55a55e73i73l71p90t90x90z90zPFleVVtjF0zJ0zL\ 0zN0xP0xP00z00z03z05z09z0Bz0Fz0Hz0Lz0Nz0Rz3Tz5Xz9a\ zBczFgzHizLlzNnzRrzTtzXxz } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 07-01-09 (Intricate Tapestry [8])
by Jim Muth 08 Jan '09

08 Jan '09

FOTD -- January 07, 2009 (Rating 8) Fractal visionaries and enthusiasts: Sorry for the lateness. Due to unforseen circumstances, today's FOTD is posted without comment. But this does not mean it is worth little. It is in fact worth an 8. I strongly recommend taking 3-1/2 minutes to run the included parameter file or taking a couple minutes to hustle over to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to see why I named the image "Intricate Tapestry". Tuesday dawned clear here at Fractal Central. Clouds moved in by 9am. Light snow arrived at 3pm. It changed to freezing rain at sunset. The temperature of 30F -1C was not too chilly, but it was chilly enough for ice. The fractal cats meowed their disapproval. My day was quite busy. The next Fotd, the one for January 8, will likely be late again. Until the next time, take care, and if we ever found how to create life from its basic elements in a test tube, would it show that God is not necessary for life to develop, or that an outside intelligence is necessary? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Intricate_Tapestry { ; time=0:03:29.95-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 center-mag=-3.866658236653685/0/1.615e+010/1/90/0 params=3/3 float=y maxiter=1900 inside=0 logmap=340 periodicity=10 mathtolerance=0.05/1 colors=000J_SzgRvePrbOm`MhaLcbJZcIUdHPeJMfLJgNOhPT\ iQYjSblUgnWlpYmqZmoXjmWgkUciT`gRYdQVaORZNOWLLTKIQI\ ENHBKF8HE3EC5CD7BE9CEADFCEGEFGGGHHIIJKILMJNOKOQKQR\ LSSMUTMVUNXVOZWO`XP`XQaYPaYPbZPbZPc_Pc_Pc`Od`OdaOe\ aOebOebOfbNfcNgcNgdNhdNheNheMifMifMjgMjgMlgPjgMhYJ\ zOGzEDz4Bz5Dz6Ez7Gz8Hv9JrAKmBMhCNcDOcEQcFRcGTcHUcI\ WcJXcKZcL_cM`cN_dzzdvzdrzdmzehvecre`meXhfUcfYZf`Uf\ fPgmKhsGmwCrzAvzBzzCzzCzwDzrDzoEzoEzoFzlFziGziGzhH\ vhIrhImgJhgJcgKZfKUfLQfLPeMOeMNeNMdOLdOKcPJcPIcQHb\ QGbRGbRFaSEaSDaTC`UB`UA`V9_V8_W7_W6ZX5ZX4ZY3YY2YZ1\ ZY2YZ3Y_4Y_5X`6Xa7Xa8Wb9WcAWcAVdBVdCVeDUfEUfFUgGTh\ HThITiITiJUgJVfJWeJXcKYbKZaK_`K`ZLaYLbXLcWLdULbTMa\ SMbRMcPMizNjzNkzNlzNmzNnzOozOpzOqzOrzPszPtvPurPvmO\ uhPvcQvZQvURvPSvKSvETvFUvGZvIcvJhvKmvMrvNvwOzwQzwR\ zwSzwUzwVzwWzwYzwZzw_zwazwbzxbzwczwczwdzwdzwezzfzz\ ezzczzbzz`zz_zzYzzXzzVzzU } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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Re: [Fractint] AOTD
by JackOfTradeZ＠comcast.net 07 Jan '09

07 Jan '09

. Animation of Jim Muth FOTD (Dawn of the Stars) December 29, 2008 is posted: http://www.fractal-animation.net/vid/dark.zip 20 Meg download These complex formulas are interesting. Start out looking like a regular Mandelbrot, then get weird as you go in. This one even has a Cantor Strip (I think that's what it is - it doesn't change if you zoom in to it). A queshun for The Maestro if I may: When you post these moderately deep ones (e+12 etc) do you find it at that depth or start with the parent and zoom in until you find something good? .

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Re: [Fractint] Fractint Digest, Vol 71, Issue 2
by JackOfTradeZ＠comcast.net 07 Jan '09

07 Jan '09

Jim Muth ponders: ""and if we ever found how to create life from its basic elements in a test tube, would it show that God is not necessary for life to develop, or that an outside intelligence is necessary?"" It only delays the question, because then who/what created US that we could then create the test tube life? And who/what created THEM that created us? If we are the result of alien genetic tampering on pre-human apes (an idea I don't necessarily discredit), how did the aliens get to where they are? At some point there must be a beginning. .

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FOTD 06-01-09 (Real Gone Minibrot [8.5])
by Jim Muth 05 Jan '09

05 Jan '09

FOTD -- January 06, 2009 (Rating 8.5) Fractal visionaries and enthusiasts: With an unexpected load of work to finish, I have little time to write a discussion. The image lies on the main spike of a perturbed Mandeloid. In my opinion, it is worth a rating of 8-1/2. The half point is a reward for the bit of extra effort I put into the coloring. The name "Real Gone Minibrot" refers to a minibrot that once was there but now is gone. The calculation time of 2-1/4 minutes brings relief to the time challenged. A trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the already-calculated image brings relief to all. A mixture of sun and clouds here at Fractal Central on Monday kept the fractal cats confused; the temperature of 43F 6C kept the heating bill down. My day was very busy; tomorrow will be the same. The next FOTD has a 75-percent chance of being posted in 24 hours. Until then, take care, and the real truth will confuse skeptics and believers alike. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Real_Gone_Minibrot { ; time=0:02:15.21-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=-3.711918934\ 869418/0/2.319291e+011/1.0829/90/0 logmap=408 params=0/0/0/0/0/0/-0.81/0/5/2 float=y maxiter=1200 inside=255 periodicity=10 mathtolerance=0.05/1 colors=000AAKAAKAAOAASAAWAA_AAbAAfAAjAAnA9qABrACsB\ DtBEuBFvAGwAHxAIyCJzEJzGJzIJzKJzMJzOJzQJzZV6VQ9RMC\ NHFJDHNCGQBGUAFX9F`8Ec7Ef6Dj5Dm4Cq3Ct2Bw1BYC68M2BO\ 6DPAGREISIKULNVPPXTSYXU_`W`cZbg`ckceoefsggvedrdanb\ _jaXg_VcZS_XPXWNTUKPTIMKJdBKwDOvFSuGVuIZtzzzzzzzzz\ zzzzzzzzzzzlzzXzvYzrZznWziVzfQzdOvbNr_MmXLjTKeQJ`N\ IWJHRGGLDFF9EA6D63C000U10dA0mK0sU0u`0wh0zo1zv9dXHV\ dPLlXPiZTg_Xe``bad`bgZckXdoUesSfwQgzOhAo`BpbCpdDpe\ EqgFqiGqjHrlLrnProUsqZsscsthtvmsshtmcuhZvcUwZZvUiu\ blukprtlqrgopcmn_klWijTghPefLcdHabD_`9YZ6WYBUVGSTL\ QQQNOVLLZJJZGGYDDYBBUEERHKONUKUcU`mZfrcmvhtzmzzkzz\ izzfzvczr`zmZyhXxfVwgUuhPsiKqj9ohCmfFkdJibMf`PcZT`\ XWYWZVUbSSePQhMOlJMoGKrDJsAIsBHsDHsFGsHGsJFsMFsOEs\ QEsSDsUDsWCsYChhRZseXrdWrcUqcTqbRpbQpaOoaNo`Mn_Kn_\ JmZHmZGlYElYDkXCkXJbTPUQVLNWMLWNKXOJXPIYQGYRFZSEZT\ D_UB_VA`W9`X8aY6aZ5b_4b_3 } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 05-01-09 (A Golden Oldie [4])
by Jim Muth 04 Jan '09

04 Jan '09

FOTD -- January 05, 2009 (Rating 4) Fractal visionaries and enthusiasts: With almost the entire day spent at a nearby antique emporium, I was left with no time to find a new image on Sunday, so I worked up a new view of an old image -- the image from Dec 3, 2008, which was named "Golden Nonabrot". The formula behind the image, the DivideJulibrot, appears rather awesome on the surface. But it does draw any Julibrot angle of any scene calculated by the DivideBrot5 formula. That image was an everyday Mandelbrot view of the scene, while today's view of the same area is an oblique view through the Julibrot. Most of the image is a repeat of the earlier image, including the same color palette. The main difference is the shape of the minibrot at the center, which instead of an 8-lobed Mandelbrot midget, now appears as a narrow slit. Because the image holds very little that is new, I could rate it no higher than a sub-standard 4. The name "A Golden Oldie" refers back to the original image, which appeared a month ago. The calculation time of under 4 minutes might be a bit too much to ask for an image that is a virtual repeat. The better choice may be to hop on out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the pre-calculated image there. Clear skies in the morning gave way to afternoon clouds and light evening rain here at Fractal Central on Sunday, while the temperature reached 37F 3C for the third consecutive day. The fractal cats were unhappy about the clouds that moved in and hid the sun in the afternoon. I spent the day with FL, looking at the stuff other people threw out, yet still managing to find the time for a FOTD when we returned after dark. The next glorious fractal image will be posted in 24 hours. Until then, take care, and be unbounded yet finite. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Golden_Oldie { ; time=0:03:56.45-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideJulibrot center-mag=0/0/\ 4.266495e+009/0.0131/88.53859228715406/-89.1361541\ 431742808 params=-92/189.6/-26.6/58/-442.137773374\ 8792/0.1697133339657901/-442.1377733748792/0.16971\ 33339657901/9/250 float=y maxiter=60000 inside=0 periodicity=10 sound=off mathtolerance=0.05/1 colors=000neSlbUk`WiZZgX`fVbdTddQkcRfcRbcRZcRVbSRb\ SNbSJbSF`OAbSBdVBfZBhaCjdClhCnkDpoDrrDsuDpsCnrClqC\ joBhnBfmBdkAbjA`iAZg9Xf9Ve9Xl0Vh5Td9S`DQXHOTLNPQLL\ UJHYIDaG9eF5iQNZYeP_dO`cNacMcbLdbLeaKgaJh`Ixb0i`IV\ ZZ8VzHYoP_dXaUdcJpb2nd5le8jfAhhDfiFdjIblK`mNZnPXpS\ VqUTrXTuZRsZPrZNpZLoZJmZCpcIlZOhVUeQ_aMeYHkVDqR8Lk\ uc_VvO4rP6oQ7lR8iSAfTBcUC_VEXWFUXGRYIOZJL_KWObh8ue\ CtcFs`IrZLrXOqURpSUoQXoN_nLbmIelGhlEkkBnj9qi7tiArl\ CqnEpqGosInvKmxSamZzbfzSmzIdzHWzGNzFzzEzzDzzBzzAzz\ 5zqhzzMzwRzgKJzDBz6zQECoY9YM6zBMefzzSzzEzzBzz8zz5z\ z2ztENeAGS79z3RsK5rG4dC4z83z4GzV`C6zz3zzCzz9zz6zz3\ zz4zz3zz9zz1PFeO`CZSHhKLrBPz3TbcEWPdXL`WNWVPRURMUT\ IRahiShyUJWE9ORkHHWA8GWKNOEHa9BA05s3Re2KT0DG06U0dN\ 0UG0K94Alnz`ajQPVECFMkECN7knHXXBm_YjYVhWSXUPYOLZPJ\ _QGaSKcVNfYRi`UlbYoe`rhdukfwmezodzncyocxpcwqcwrczs\ cztczuczvhzwmzxrzyvzzzogQ } frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), aa=-(real(p5)-2), bb=(imag(p5)+0.00000000000000000000001), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)/(z^(aa)+bb)+c |z|< 1000000 } END PARAMETER FILE=========================================

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FOTD 04-01-09 (Filament Abundance [6.5])
by Jim Muth 03 Jan '09

03 Jan '09

FOTD -- January 04, 2009 (Rating 6.5) Fractal visionaries and enthusiasts: Today's quickly-found image returns us to the MandelbrotBC3 formula and the fractal that is formed when the expression Z^(1.5)+C is iterated 22.15 levels up the logarithmic hyper- ladder with no function applied. This parent fractal doesn't look like much at first glance, but it has an interesting area near the southeast shore line of its main bay. Today's image is located on a filament extending from a larger minibrot in this area. I rated the image at a 6-1/2, with the extra half-point added by my modest coloring efforts. The name "Filament Abundance" gives away the appearance of the image even before it is calculated. The calculation time of 8-1/4 minutes borders on slowness. To avoid all chance of impatience, I recommend surfing out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the already-calculated image there. Near full sun and a temperature of 37F 3C kept the fractal cats on their best behavior here at Fractal Central on Saturday. I am almost always on my best behavior, so nothing more need be said. The next FOTD will in all likelihood be posted in 24 hours. Until then, take care, and keep taking care until there is no more care to be taken. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Filament_Abundance { ; time=0:08:15.24-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.778594649890781/+0.04565415904501465\ /3.0825e+009/1/-27.5/0 params=1.5/0/22.15/0 float=y maxiter=6000 inside=0 logmap=825 periodicity=10 colors=000KKcKKcKKcKKcKKcKKcKKcKKcKLcKMbKNbKObKPbL\ QbMRbRKhTKhVKhXKhVKhUKhWKhYKjZHlXKjWPgUPeSPcRPaPPf\ NJjLRnKQrJPwIOvHNuHMuGKtFItFHtEGtDJtDMtCPtBStBVtAY\ t9`t9ct8ft7it5rx7lt8gp9alAXiCSeDMaEHYEDXFCWFCVFCUG\ CTGCSGBRHBQHBPHBOIBMIAKIAIJAEJAAJAAL9AJAAIAAGBAFBA\ DCACCABCA9DA8DA6EA5EA3FA2FA0DA1FA2GA3HA4IA5JA6KB7L\ C8MD9NEAOFAPGESFIVFMXFQ_FUbFYdFahFemFirFmvFzzFzzFz\ zGzvFztFzrFzpFznFzkFziFzgFzeFvcFr`FmZFhXFfVFeTFpfo\ menjemgeledlbdk_djXcjVciSchPbhMbgKbfHafEaeBad5ig9a\ dCVbFN_JHWIGYIG_IG`HGbHFcHFeGFfGFhGEjFEkFEmFEnEDpE\ DqEDsF9sEDtEGuDLvDOwDRxCWyCZzBczBfzBjzAnzArzAuzZkf\ zgSzcTz`UvXVrUWmPThRWcSYZT`UUbQVeRWgTXiVYlXZnZ_q``\ sbcxaaza_z`Yz`Wz_Uz_SzZQzcSzaPzcNzeLzgIziGzkGNmEOo\ DOqCPsAPu9zw8zz6zz5zzczzczzczzczzzzzczzczzVJzzJzUK\ zUKzUzzUKzzLzULzUzzTMzzLzRLzQLzzLzOKzNzzMKzzKzKJzJ\ zzzJzHJzFzzLLzzMzXOzaPzzR } 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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FOTD 03-01-09 (Octal Regeneration [7])
by Jim Muth 02 Jan '09

02 Jan '09

FOTD -- January 03, 2009 (Rating 7) Fractal visionaries and enthusiasts: Today's image is a bit deceiving. The name "Octal Regeneration" implies that the Z^(8.0000001)+C Mandeloid is involved, while actually it's the Z^(10.0000001)+C Mandeloid. Once again the image lies on the infinitely-divided main stem, deep in the East Valley area of the large minibrot. I rated the image at a 7 because I was surprised at what I found in such a high-order fractal. The unexpectedly fast calculation time of 2-1/4 minutes makes the image well worth the effort of running the included parameter file. At this point words become useless, and the image must be seen with one's own eyes. This glorious vision is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> without the task of calculation. Friday began with clouds here at Fractal Central. Things looked bleak for the fractal cats, but just after noon the clouds blew off to the east, giving the cats a full afternoon in the sun- shine of the southwest window. My day was average, with all that this implies. The next FOTD will be posted in 24 hours. Until then, take care, and do not be deceived. The year is most certainly 2009, not 2008 Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Octal_Regeneration { ; time=0:02:13.28-SF5 on P4-2000 reset=2004 type=manzpower passes=1 float=y center-mag=-1.071297808532068/+0.00000003671007264\ /5.799985e+012/1/-60/0 params=0/0/10.0000001/0 maxiter=2200 bailout=16 inside=0 logmap=137 periodicity=10 mathtolerance=0.05/1 colors=000EACCAFAAI8AL6AO2AR5AU8AXBA_DAbKKfUUicdoh\ iuprzzzzASYAKPACGA47APWAA0mXpjWqgWrdVsaUtZUuWTvTTw\ QVsOXoMYkJ_gfViiWfkXdmXaoY_qZXsZVj`UbaTVbSMdREeQ6f\ QGhMQjJ_lGZiKZfNYdQYaTY_WXX_XUbWSeWPhWNkVPmURoTTqS\ VrRXtQZvP`xOayFmk6xZ7pX8hV9`T9TRAWWBZ_CacCdhDglEjp\ EmtLosRqrXsrbuqhwqnyptzprsmpmkngil`gjVehPcgJacN__R\ ZWVYSZXObWKfVGjUCnT8qS7nQ6lO6jN5gLAeKFcIKaHPZFUXEZ\ VCcTBhUEmVGrWJvXLzYNzZQz_Sz`VzaXzbZzcazdcyefxfhwfj\ s`glWdgRa`MZUHWNCTG7QF6PG6PH6PI6PJ6PJ6PK6PL6PM5PO5\ PP5PR5PT5PV5PX5PY5PaDRdKSgRTjYVmdWokXtrgrniqkjphkn\ elmbmlZokWpiTqhQrgNsfJudGvcDwbAxa7yX8wT9rPAmLBhGCc\ CDZ8EU4FU0AUCAUOAU_Aqkit_jvPkwDlyAmzKmvUmrcmnmmjwm\ fzmbzm_zmWzmSzmOzmKzmGzmDzmITmMQmROmVLm_JmcGmhEmlB\ nq9ou7py9qpBrhCs`EtTGuLHvDGwBGxAGy8Gz7Gz5Gz4Gz2Gz1\ DzDAzP7z`4zl2zw9zvFzvLzvRzuXzubzuhzujzmkzflz_mzSnz\ LozEpz7kz8gz8cz9_z9VzARzA } END PARAMETER FILE=========================================

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FOTD 02-01-09 (Belated Decorations [6.5])
by Jim Muth 01 Jan '09

01 Jan '09

FOTD -- January 02, 2008 (Rating 6.5) Fractal visionaries and enthusiasts: When I posted yesterday's FOTD image I had decided to make that image the last one of the series. Since then however, I found an interesting scene very deep in the corresponding area of the Z^(8.0000001)+C Mandeloid. I named the image "Belated Decorations" when I noticed that the eight yellowish features surrounding the central order-8 minibrot resemble the candy canes still hanging on the F.C. solstice tree. In my opinion, the overall worth of the image was compromised by its similarity to the most recent images, resulting in a rating of a 6-1/2, which probably is overly conservative. The calculation time of under 2 minutes is brief enough to make running the included parameter file almost a pleasure. A trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the completed image there would be a literal pleasure. Lots of sun and lighter winds here at Fractal Central on Thursday made the temperature of 23F -5C feel pretty good, good enough at least to satisfy the fractal cats, who spent most of the afternoon in the sunny southwest window. My day was notably uneventful. The next FOTD will be posted in 24 hours. Until then, take care, and seek the elusive fractal. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= BelatedDecorations { ; time=0:01:52.74-SF5 on P4-2000 reset=2004 type=manzpower center-mag=-1.0945128360\ 42731/+0.00000004679414411/4.087013e+012/1/-82.5/0 params=0/0/8.0000001/0 float=y maxiter=2000 bailout=16 inside=0 outside=tdis periodicity=10 mathtolerance=0.05/1 colors=000NbQfJpiQklXgocbrjZuzUzzQzzUzwXzw_zwbzwez\ whzk_z_SwB8pE7iI6bM5WQ4PU3JY2Lb1Ng1Pl1SkAUkIWkQZjZ\ `ifbendeve_ufVtgQthLsiGsjBrk6rXKvIXzj81k58k2Ek0K7w\ _BocFggI_jMSnQKrTCuQHsOMrLRpJVoG_mEdlChkLloUorhWUw\ C5vwLtsIspGqlEpiBne9mb7l_5ad4Sh4Im48q4El8KgCQbGVZK\ `UOfPSlKWqGZCwYBxZAx_9y`8yaDvcHtdLrePpfGpX8pN0pE1k\ H2fJ3aM4XO8YPCZQF_RJ`SMaTQbUTcVNfUHiTBkT8`S5QR2GQ8\ JOEMMKPKQSIWVHRNKMFNH7PLDIPICTN6_WAfdEmmIsuLnpTik`\ dgh_bpWZxVQqU6WT9OSGXRCQQ9JN0GKCEHEBFF9KFKOFKSFmWN\ z_Pzc_zg`zaazXaxRbsMbmHcgBcb6dY1dTB`RLXPVTPdPOnLOh\ ITbGYXDbRBgL9lTOn`bpgqrhmqhiqhephapiYoiUoiQniNnfRp\ cVq`ZrYbtVfuSjvQmwPkuOisNgrNfpMdnLbmK`kK_jFYbAWW5U\ P1SI2QG2OF2MD2KC2IB3JC3JC3JC3JC4JD4JD4JD4JD9TEEaEJ\ kFNtFRqLUnQXkV`h_cedfciiZflVcoQ`qMYkLUeKR_JNUIKOIH\ LOLJTPHYTFbWCh_Amc8rg6wjAqZEkOIeCM_1OX7QUCRRITPNUM\ TWJYXHb_GuZLuYPuVTmSWeQ_Y } END PARAMETER FILE=========================================

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FOTD 01-01-09 (Happy New Fractal [6])
by Jim Muth 31 Dec '08

31 Dec '08

FOTD -- January 01, 2009 (Rating 6) Fractal visionaries and enthusiasts: For the first FOTD of the new year we conclude the current theme of minibrots on the edge of infinitely divided main spikes in the East Valley of the large minibrot. Today we check one of the 5 main spikes of the Z^(6.0000001)+C Mandeloid, and find much the same stuff that we found in the past 3 day's images. Since I am getting bored with this theme, I rated the image at a 6, which is not too bad, but still below FOTD standards. The most interesting feature of the image is the series of thin slices of order-6 minibrots at the center. I have not counted how many individual minibrots are merged into the sausage-shaped assemblage, but it must be in the dozens. The name "Happy New Fractal" is self-explanatory. My only comment might be to add that today's fractal is not very new. The fast calculation time of 2-1/4 minutes will cause little discomfort, and the finished image is or soon will be posted for even less viewing discomfort on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The day started with a snow squall here at Fractal Central on Wednesday, and continued with high winds, clouds, occasional snow flurries and dropping temperatures, which reached 25F -4C by sunset. The fractal cats did not like these conditions and comforted themselves by the warmest radiator. My day was only moderately busy. The next FOTD will be posted in 24 hours. Until then, take care, and enjoy a fractally happy year in 2009. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Happy_New_Fractal { ; time=0:02:15.58-SF5 on P4-2000 reset=2004 type=manzpower center-mag=-1.1325337816\ 87138/+0.00000007422384354/3.024243e+011/1/117/0 params=0/0/6.0000001/0 float=y maxiter=2000 inside=0 logmap=268 periodicity=10 mathtolerance=0.05/1 colors=000SqESqDSqCQmBOiAMfAKb9JZ8HW8FS7DO6BL6AH58\ D46A4463333A8AGCHMGNSKUYO`cSfiWmo_smYokXkiWggUceT_\ cSWaQS_POYOL_MM`KNaINbGOdEPeCPfAQg8Rh6Rg8SfATeCUeE\ VdGWcIXbKYbMYdNVeNSgNQhNNjNLkOImOGnODpOBqO8rO6nP9k\ PChPFePHbPK_PNXPQUPSQQVNQYKQ`HQbEQeBQh8Qk5QmCNkILj\ OIiUGh`DffBel8dr6cp9dnCemFfkIgjLhhOifRjeUkcXlb_m`b\ n_engVhoLcwBZsC`pCbmDdjDfgDhcEj`ElYEnVFpSFrPFtpyzn\ uzmqvlnrkjmjfhicch_ZgXUfTPePKdMFcIAbF7hCBn9Ft6Jy3N\ s5Om7Og9OaBOWCPQEPKGPEIP8JPCLMGNJKPHORESTBWV9_X6bY\ 4a_5aa6ac7`e8`g9`i9RCHTMEVVCXdAifqfhecjV`lJl6lhHae\ SSabI8a`9aQnNCf`AuvoiqUa5v`Ke_ZPakq`le_lVZmJdNFbUD\ a`B_g9IS5`IhEQAGTAHWAJZALaANdAPgAQjAKi7Eh49g2Di4Hk\ 6Ll8PnAzpCzqDzrCzsCztCzuCzvCzwBzxBzyBzzBzzBzzBzzAz\ zAzzAKzzPzzUzzYzzTzzPzzLzzHzzDzz9zz5zz6zz7zz8zz9zz\ 9zzAzzBzzCzzDzzDzzEzzFzzGzzHz_Hz_GzaFzbEzdDzeCzgBz\ hAzj9zk8zm7zn6zpSzHSzGSzF } END PARAMETER FILE=========================================

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FOTD 31-12-08 (Double Your Pleasure [7])
by Jim Muth 30 Dec '08

30 Dec '08

FOTD -- December 31, 2008 (Rating 7) Fractal visionaries and enthusiasts: Today's image, the last of this year, continues the exploration of the theme of the past two days, but with the exponent of Z raised from 2.0000001 to 4.0000001. Much the same type of elements exist in today's image, which lies at the edge of the divided main spike in the area of the East Valley of the large minibrot. Since the theme is growing stale, I could rate the image at only a 7. The name "Double Your Pleasure" refers not to chewing gum, but to the doubling of the exponent from 2.0000001 to 4.0000001. Unfortunately, the worth of the image failed to double with the exponent. The calculation time of 3-1/4 minutes is about average. The minute or so it will take to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> remains, as always, a minute or so. Total sun and a temperature of 43F 6C made the fractal cats' afternoon in the sunny southwest window a pleasure here at Fractal Central on Tuesday. The blustery winds that blew outdoors did not disturb the inside comfort. My day was busier than I would have liked, but with a bit of extra effort we finished the work by mid-afternoon. The next FOTD, the first of the new year, will be posted in 24 hours. Until then, take care, and be aware of the hidden dangers lying in fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= DoubleYourPleasure { ; time=0:03:17.12-SF5 on P4-2000 reset=2004 type=manzpower inside=0 logmap=511 center-mag=-1.223414419566392/+0.000000122803008/\ 3.15e+011/1/155/0 params=0/0/4.0000001/0 float=y maxiter=5000 periodicity=10 mathtolerance=0.05/1 colors=000Y7CW7DU7ES7FQ8GO8HM8IK8JI9JG9IE9IC9MA9QG\ FUMLWSQcXWhbbmhgrnnvssznmrjejf_abUPZPIWdLUsNNO9MNA\ LNAKNAJMAIMAHMBGLBFLBELBDLBCJCBIDAHE9GF8FF7EG7DH6B\ I5AJ49J38K27L16M15M29N3DO4HO5KP6OQ6SQ7WR8ZS9bSAfTA\ iTDcXFY`HSbKMUMGUOAUSBZVCcYCe`DicEjgEjjFkmGlpGmsHm\ vHmmFdmEXmYPz_HpuAsoCuiExcGzYIpgCfq6Xz1Vw8UsFToMSk\ TRg_OeiQdeRcbSb_TaWU`TPbNV_Q`YTeWWkTZqRayQfvPcsP`p\ OYmOWjNTgNQdMOaMLZLIWLGTKDQKAOK8QODRRISUNTXSU_XVba\ UdgWefXffZfe_ge`gdbhdciceicfjblpYgjbcdfZZkYXqVUoTS\ mRQkOOjMMhKKfHIeFGcDEa79eBC`FEXJGSMIOUKJ_JFbIAjH0e\ H6aH7ZGFWFM_FUdE`hEgiHfjKfkNelPemSdnVdoYcp_cqbbreb\ ybmrgbklTdqIlz8zz0PmCO_QNMcM8qOAoPBmQDkSEiTFhUHfWI\ dXKbYLa_M_zOYzPWzQVzogzjbzfZzaVzzRzzNzzJzzFzzFzzEz\ zEzzDzzDzzGzzIzzKzzMzzOzzQzzSTzUVzWYzY_z_jzhbzadzc\ gzeizgwzNvzPuzQuzRtzTszUszVrzWqzYqzZpz_ozaozbnzcmz\ dmzflzgkzhSz0Tz0Uz2_zB`zA } END PARAMETER FILE=========================================

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FOTD 30-12-08 (Edge of Eternity [8.5])
by Jim Muth 30 Dec '08

30 Dec '08

FOTD -- December 30, 2008 (Rating 8.5) Fractal visionaries and enthusiasts: The extra float=y in yesterday's parameter file was inserted by me. I often edit the parameter files to simplify them, and I failed to remove the second float=y entry. The idea for today's image sprang directly from yesterday's image. Today, I used the manzpower formula to examine the main spike of the Z^(2.0000001)+C Mandeloid in the East Valley area of the largest minibrot. Once again I checked the edge of the infinitely divided spike, where I found today's image a short way inside a rudimentary spiral. The image is notable in that the usual minibrot at the center actually consists of two overlapping minibrots, which are a result of a prominent discontinuity running through the center of the frame. I named the image "Edge of Eternity"; I don't know why. Then I rated it at an 8.5 because I kind of like it. The calculation time of 4-3/4 minutes will cause difficulty to no one, unless their machine can't do DOS. And even those with DOS-challenged machines can see the image by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Brilliant sun and a temperature of 46F 8C brought out the best in the fractal cats here at Fractal Central on Monday. My day was quite busy. The next FOTD, the last of 2008, will be posted in 24 hours. Until then, take care, speak softly and carry a toothpick. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Edge_of_Eternity { ; time=0:04:44.99-SF5 on P4-2000 reset=2004 type=manzpower bailout=16 inside=0 center-mag=-1.74973734800525/+0.00000049270129877/\ 2.96469e+011/1/-10/0 params=0/0/2.0000001/0 float=y maxiter=17500 periodicity=10 mathtolerance=0.05/1 colors=000pDzqCzm0zsCzyYzzstzzmzzhzzfzzczu_yqXwmUu\ hRsdOq_KpWFmRCkM7jH3hC0f50d00c00a00Y00W10S50PC0MH0\ JK0FP0CS07X03a10d30h50m70p90tC0z00y50wC0tH0sM0pR0o\ W0oX0m_0jX0gU0dS0aP0YM0WJ0SH0PD0M90J50F30C00700300\ 000500900D00H01K03P05S07W09Y0Ca0Df0Fh0Hk0Jo0Kq0Pz0\ Ow0Mt0Kq0Jo0Jk0Hh3Ff7DcCD_DCXH9UK7RO5OR5KS3HW1DY09\ a00d03c05c57cD9aJDaOFaUH_YJ_cM_gO_mPYqRYuUYzWXzXXz\ YXz_X00a00d00g01j15k19o3Fq3Jt5Mu5Py7Sz7Xz9_z9czCfz\ 0iz0kzCmzMnzWozTpzcqzcrzcszctzcuzcvzcwzcxzcyzcwzaw\ zawzavzarzamzahzaczaZzaUzaPzaMz_MzYOzXRzWSzUUzUXzS\ YzR_zPczOdyMfuMhtKjqJkpHomFpkDqhDtgCud9wc7z_5zY0zX\ 5zX9zXDyXHwXKuXPsXSqXWoXYmXakXfhXhgXkdXocXsXYqaXpd\ XogWojWmmUkpUjsSptXmuUjuSguPduOWHMaCJeAHh5FlCCoF9q\ J5sM3tP0tS0uW0wY0ya0zd0zg0zj0sf0ka0cX0WS1MO5DJ91DF\ 07J01M07J0CH0HF0KC0P90S70W30_10c00g00j00m00j03g79d\ DFaKKYPPWWUSaYPfcMkgJpkFu } END PARAMETER FILE=========================================

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FOTD 29-12-08 (Dawn of the Stars [7.5])
by Jim Muth 28 Dec '08

28 Dec '08

FOTD -- December 29, 2008 (Rating 7.5) Fractal visionaries and enthusiasts: Today's parent fractal is a virtually perfect Mandelbrot set. But virtual is not identical to literal, and in today's case, the difference lies along the main spike, which when examined very closely turns out to be infinitely divided. Today's scene lies deep in the East Valley of the large minibrot on the main spike of the parent fractal, at the edge of the northernmost division of the spike. I gave the image the rather poetic name "Dawn of the Stars", referring to the stars in the sky, and not the stars on TV. I rated it at 7.5, which seems about right. The calculation time of 9-1/2 minutes is a bit slow, but nothing that a dedicated fractalist cannot handle. But even dedicated fractalists sometimes need to save time, so the finished image is posted for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Morning clouds gave way to afternoon sun and a temperature of 55F 13C here at Fractal Central on Sunday. The fractal cats enjoyed the sun and endured the rest. My day was busier than expected. The next FOTD will be posted in 24 hours. Until then, take care, and the only thing certainly real is experience itself, not the images we experience. . . . I guess. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Dawn_of_the_Stars { ; time=0:09:29.71-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 periodicity=10 float=y center-mag=-1.749943991834191/+0.00000000268939668\ /4.858328e+012/1/135/0 params=-1.1/5.1/1e-009/0 float=y maxiter=16000 inside=0 mathtolerance=0.05/1 colors=000XNdVOdSPeQQeOSeLTfJUfHVgEXgCYhAZh8_hPHmR\ JkSLjTNiUPhVRgWSeXUdYWcZYb__a```XXWTTSPPOLLJHHKDDP\ AAUCCZDEcEGdFHeGJfHLgINhJOiKQjLSkMUmNVoOXqPZsQ`uRa\ wZ_xfYxlVxjTrfQmbOhZLcVIZRGUNDPKBKKFNLJPPMRUQUZUWc\ XYg``idbkgdlibmj`nkZolXqmVsnTuoRwpPzqNzrLzsJztHmuF\ ovDqwBrxAcmRQcgCUxEXrF_lGbfHeaJhWKkQLnKMpFQjOUeXX`\ dVedSkeQqfOvfLgSJTDOWITZMYaQ_cQUhROlSIqSCuT2zX7yTC\ yQHxNMxKQxHPfRF`1Fb2Fd3Fe3Fg4Fi5Gk6Gl6Gn7Gp8Gr9Gs9\ GkBGcDGXFGPHGIJLLNPNRUPVYSZbUafWekZio`msbpq4tq8rqC\ qqGoqKnqNlqRkqViqZhqbfqeeqicqmbqq`wu_zzZpnboefnWjm\ NnlEqeLoZRmTYkMciFjg9peDk`HfWLaSPXNTSIXNE`I9cD5gP3\ j_2mj1ng7oeCpbIq`NrYTsWYsUbpPamK`jF_gBZfDYeFXdHWcJ\ WbLVaNU`PT_RTZTSYVRXXQXZQRVRLRRGOSAKS5HSAFZEEeJClN\ BrPEsRGtSItULuVNuXPvYSv_Uw`WwbXqdYkfYehZ_jZUl_On`I\ p`Cra6sa0eaDSaPEha0hzBYhLMWWFOe7Fo07m38l59k8AjABiC\ CgFDfHEeJFdMGcOHbQHaKcZLc } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 28-12-08 (Web of Misfortune [8])
by Jim Muth 28 Dec '08

28 Dec '08

FOTD -- December 28, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image is late because I let myself get dragged to an antique mall again on Saturday, where FL and I spent the after- noon looking at the stuff other people had the sense to throw out. Oh well, it wasn't all that bad, but it cut short the time available for the fractal search, and FL found a fresh supply of mystery novels. Despite the limited fractal time, I found a rather interesting image, which lies in the parent fractal that results when a Z^2 Mandelbrot set is starting to morph into a Z^(-16) Mandeloid. This parent is basically a Mandelbrot set inside an embryonic Z^(-16) Mandeloid, with 17 points and a series of fractal rings circling the M-set. Today's scene is located in a filamentary fractal bridge between two of these rings. The whole image is unique enough to rate an 8. The name "Web of Misfortune" might have been inspired by the half-dozen or so mystery novels we found. The calculation time of a fireball- fast 38 seconds is what the impatient fractalist likes to see. As always, those with machines that are fully tricked out yet can't do DOS may see the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But due to the unusual time of this posting, give Paul a chance to calculate and post the image before surfing there. Heavy clouds and fog prevailed in the Fractal Central area on Saturday. The temperature reached a mild 41F 5C, but the fractal cats must have been disappointed by our absence, for they gave us a lively scolding when we returned. The next FOTD will be posted in 24 hours. Until then, take care, and if women hate violence, why do they read so many murder mysteries? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Web_of_Misfortune { ; time=0:00:38.22-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 center-mag=-1.199554685788041/+0.7506726841627577/\ 1.577859e+010/1/-135/0 params=-16/20/-1e-007/-5 float=y maxiter=600 inside=0 logmap=63 periodicity=10 mathtolerance=0.05/1 colors=000JDIKCDQB9WB5AJDeRKLZRzfYXndzzkhhhQLXL3QJ\ AaHHmFOyVX`zdCzqDzbEzaEz`Fz_Ge_GON_7ArGgzJmvLLzOIz\ QFzTUzV9eY6b_4_WCXTJVPQTMYRIdPFzNGzNGzMGzMGlMGlLga\ oeav_dlUgcOjUImLSkYaijkhv7A1BH0FN0IT0MZ0Qd0Tj0Yd5b\ _AgVElQJpLNhQK`VHT_FLdCDiABaC9UE8MG6EI56JE9KNBKVDK\ cFLlHLtJLoIMkINfIObIOeGThEYkCanAfq9jh8i_8iR8iz7iz7\ iz7iz9fzBczCazEZzGWzHUu56lB6cH6VN6MT6DZ64d6zc7zc8z\ c9zc9zzAzzBzzCzzCzzFzzIzzLzzOzzRzzUzzXzz_`zePzkDzq\ 2zv8zgEzTKzFzf7zf7zf7zf7ze8ze9zeAzdBzdBzzCzzDzzEzz\ EzzFzzGzzHzzIHzIHzJGzKGzLFzLFzMEzNEzODzPDzPCzQCzRB\ zSBzSAzTAzU9zV9zW8zW8zX7zY7zZ6zZ6z_5z`5za4zb4zb3zc\ 3zd2ze2ze1zf1zg0Rh0Rh1Sf2Te3Ud4Vc4Wb5Xa6Y`7Z_7_Y8`\ X9aWAbVAcUBdTInNCeSDfREgQEhOFiNGjMHkLHlKImJJnIKoHI\ vWJuVJuVJuVJuUJuUJuUJuUJuTJuTJuTJtTJtSJtSJtSJtSJtR\ JtRJtRJtRJtQJtQJsQJsQJsPJsPJsPJsPJsOJsOJsOJsOKrNKr\ NKrNKrNKrMKrMKrMKrMKrLKrL } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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FOTD 27-12-08 (Double Feature [8])
by Jim Muth 27 Dec '08

27 Dec '08

FOTD -- December 27, 2008 (Rating 8) Fractal visionaries and enthusiasts: Today's image rates an 8, which means I like it quite a bit with its almost layered look. I have nothing against fractals that appear to have several layers as long as the layers are part of a single fractal, as today's layers are. The scene lies in a bit of debris between the two branches of the Seahorse Valley of a Mandelbrot set that has been rotated 180 degrees and is starting to morph into a Z^(6)+C Mandeloid. Most of the image consists of inside stuff made visible by the bof61 inside fill. Since there are two nearly identical mini- brots in the image, I named it "Double Feature". I was thinking of the old Saturday afternoon matinees at the movies, where an action-oriented youngster could see two third-rate cowboy movies for the price of one. The calculation time of 11-3/4 minutes is slower than I would have liked, but still well within reason. Those with a different definition of reason may view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> One of this year's presents was a new-age book about spiritual reality. As I was browsing through it Thursday evening, FL innocently asked me if I considered myself a materialist. She knows better than to ask such questions, because this kind of stuff always causes me to start pondering, and she gets more reply than she expected. "Materialists consider the material world to be the ultimate reality,", I began. "But I'm not even sure that such a thing as an ultimate reality exists, much less that the material world is real. All I experience are ever-changing images in my aware- ness. Rational people claim but cannot prove that these images correspond to something that is really out there, whatever 'out there' means." I finally settled the discussion by declaring that, in my opinion, the material world is every bit as real as a fractal, no more and no less. An unobserved material object is in the same state that the Mandelbrot set was in before it was discov- ered. I guess this makes me an idealist type of a materialist. After an ice-storm on Wednesday and a pleasant Christmas, clouds and sun mixed together here at Fractal Central on Friday to produce a perfectly average winter day, with a temperature of 36F 2C. The fractal cats enjoyed the sun and tried to ignore the clouds. My day was occupied by trying to break in a new king-size coffee mug. The next FOTD will likely appear in 24 hours. Until then, take care, and when reality turns bad, make imagination real. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Double_Feature { ; time=0:11:43.29-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 passes=1 symmetry=none center-mag=+3.035409692250254/-0.020872200758093/\ 67367/1/-167.5/0 params=6/-4 float=y maxiter=1500 inside=bof60 logmap=yes periodicity=10 colors=000zgzweztczqbwmWtjRpgMpcOq_UrVYsPatKdvJfzI\ ezJdxKbvL_uMXtNUsORrPOqQMpRKpSKpTKpUKpULpUMpUNpUOp\ VPpVQpVRpWTp_VpcYpgapkeqpjtupwwuztsvnnrgipaepZapXY\ pWVpWSpWQpWPpWOpWNpWMpVb6Vb6Ua6Ta7Sa8Ra8P`9O`AN`BM\ _BL_CK_DJ_DGbIDdMBgR8iV7k`6kZ2hT5eV4bT4_R3YQ3VO2SM\ 1PK1MI0KH0HF0ED0BB0890680970B71D62G62J53M56P4BS4HV\ 3MY3R`2Yb2`e0Wb1RY2LU3EQ4AM56H42D40941C44F36I38L3B\ O3DR3GU2IX2L_2Nb2Rf3Pe2Ne1Le0Ke0Ie0Ge0Ed0Dd0Bd09d0\ 7d04c06d07d08d09d0Ad0Bd0Cd0De0Ee0Fe0Ge0He0Ie0Je0Bk\ WKe0BU96X12JJ03i05d06`07X29T3AP4BL6DH7ED8208928F98\ LG8RN8XU0ko3hg8b`DXTHWEISMJOTKK`KHgJJdJLaJMZJOXIQU\ IRRITOIUMHWJHYGHZDH`BGb8Gc5Ge2Kj0Ih0Gf0Ed4Cb8BaC9_\ G7YK5WP3UT2TX0R`0Pd0Nh0LlH1a5Bi0Kp0NY0QF0T00U10V50\ V93WD6XH9XLCYPFZTIZXL_`O_d0MQ0II0E9AGp5EZ0CINbb390\ 0A0E5l87X29H0ko0aZ0OIZ1XP4PF6H589SFMHDF6B800VdbbQT\ QBJD0k00dT0PF0c80kT0VFR20 } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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FOTD 24-12-08 (Something From Nothing [No Rating])
by Jim Muth 23 Dec '08

23 Dec '08

FOTD -- December 24, 2008 (No Rating) Fractal visionaries and enthusiasts: Because of the rush there will be no FOTD for December 25 and 26. The next FOTD will be posted as scheduled on December 27. Today's image is a quick but harmless thing that I named "Something From Nothing". It is hardly more than a bright spot and a filament tree. Since I spent all of 3 minutes on it, I gave it no rating. The image calculates in 20 seconds. Those who would rather not calculate may view the image in finished form on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Cloudy skies and a temperature of 21F -6C kept the fractal cats near the heat here at Fractal Central on Tuesday, while the things that needed to be done kept me on the run. Due to the holidays, the next FOTD will appear in 3 days on December 27. Until 72 hours have passed, take care, and whatever you cele- brate at this time of year, may it be a happy one. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= SomethinFromNothin { ; time=0:00:19.92-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot5 center-mag=-42.89826087481\ 042/+13.3327877730677/1.4e+009/1/-7.5/0 params=5/50 float=y maxiter=1500 inside=0 periodicity=10 colors=000lGuiIsgJqdKobLm_MkYNiVOgTPeQQcORbPPcQNcR\ MdTKdUIeVGeWEfXCfYAgZ8g_6h`5h_4gZ4fZ4fY4eY4dX4dX4c\ `TRWPX`RSeSOjUKmTCnVGoWJpYNqZQr_UsaZtbcudhvemzhrwf\ vcmzbmzamz`mz_mzZgzzzzfjzadzZ`zWWyTSxSOwRMvQKuPItO\ GsNGqMFoLEmKDkJBiICgH9eG8cF7aE8_E8YE9WE9VE9UEATEAS\ DARDBQDBPDBODCNDCMDCLHIKLNIPTGTYCXc6`h2dzncm2T`GJO\ T3Cf9BeEBdJBcPBbUBbZBadB`iB_nBZu8`sBZrEYqHXoKVnNUm\ QTlTRjVQiYPh`NgcMefLdiJclIbnHdnKenMgnOhnQinTknVlnX\ mnZonapncrnesngtnjvnlwnnxnpummrmkomillfildglbdk_ak\ YZkWWjTTjRRjPTkRUkTWlVXlXZmY_m_`nabnccoeeoffphhpji\ qljqmhpkfoidogbne`ncZmaXm_WlYUlWSkUQkSOjQMjOKiMAha\ JiKKgOLeRLcUMaXM__NYbNWeOUhOSkPQnPOqQMtRIyQKwQLuQM\ sQNqQOoPPmPQkPRiPSgPTePUdRRcTPbVMaXK`ZI``F_bDZdAYf\ 8Xg6XfBYfGZfKZfP_eT`eY`ebaefbdkbdocdtddxdhkYkZSnML\ qAFmCJjDNgERcFV`GZYHbXHdVIeTJfSJgQKhOLiNLiQKjSKkUJ\ lWJmYIn_IobIpdHqfHrhGsjGt } frm:DivideBrot5 { ; Jim Muth z=(0,0), c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================

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R: Re: Jacopo
by jakovll＠libero.it 23 Dec '08

23 Dec '08

ok thanks! jacopo ----Messaggio originale----Da: JackOfTradeZ(a)comcast.netData: 23/12/2008 7.47A: <fractint(a)mailman.xmission.com>Ogg: Re: [Fractint] Jacopo.Jacopo - I haven't been in Rome since the empire fell so I don't know much about what's there now. But for fractals - try the internet! Google for "fractal", "mandelbrot", etc. there is MUCH information there. When Al Gore invented the "information superhighway" he wasn't kidding!.

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Re: [Fractint] Jacopo
by JackOfTradeZ＠comcast.net 22 Dec '08

22 Dec '08

. Jacopo - I haven't been in Rome since the empire fell so I don't know much about what's there now. But for fractals - try the internet! Google for "fractal", "mandelbrot", etc. there is MUCH information there. When Al Gore invented the "information superhighway" he wasn't kidding! .

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Re: [Fractint] AOTD
by JackOfTradeZ＠comcast.net 22 Dec '08

22 Dec '08

Animation of Jim Muth FOTD -- December 14, 2008 (superspiral) is posted, 20 Meg download: http://www.fractal-animation.net/vid/tohu va-vohu.zip This is an unusual fractal, very complex. With respect, I would opine that the originally posted FOTD image does not do it justice. There doesn't appear to be a "parent" fractal in the usual sense. If you back out you see a roughly circular complex "thing" which might be called the parent. But it is set on a diagonal stripe across the screen. (with a little imagination you may see one of the moons of Jupiter against a backdrop of the planet). And if you back out from that, the "parent" eventually vanishes to a point and disappears but the stripe never changes! Whatsup with that!? Also, there look to be many interesting areas worth exploring you can see in the early part of the viddie - the highly colored areas, just before entering the spiral. I changed the colors and gave it a cool name from a DVD lecture series on chaos theory I am now watching. Stay amazed JoTz .

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FOTD 23-12-08 (Why? Why? Why? [6])
by Jim Muth 22 Dec '08

22 Dec '08

FOTD -- December 23, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image is closely related to the strange near-rectangle that exists in a Julia set of the East Valley area of the large split minibrot on the infinitely divided main spike of the Z^(2.003)+C Mandeloid. Today's image is a Mandelbrot scene however, and contains no obvious rectangles. But I would not be surprised if rectangles exist hidden somewhere in the scene. I named the image "Why? Why? Why?", and why not? There certainly are enough shapes resembling the letter 'Y' surrounding the central minibrot. Perhaps I was a bit conservative in the rating of 6, but the deed is done and the rating will remain. The calculation time of 2-1/2 minutes is about average. If this is too slow, time may be saved by viewing the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> There was ample sun here at Fractal Central on Monday, but the day started with a temperature of 9F -13C, which never rose above 21F -6C. The chill displeased the fractal cats, who turned sulky and sought a warmer spot. My day was busy with last minute preparations, etc. If all goes well, the next FOTD will be posted in 24 hours. If no FOTD appears, do not be surprised or concerned. You will know I was too busy. Until next time, take care, and the only true reality is what every person wants it to be. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Why?_Why?_Why? { ; time=0:02:27.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basic.frm formulaname=DivideBrot6 passes=1 float=y center-mag=-1.742160389291465/+0.0000386113589347/\ 5.827869e+009/1/141.5/0 params=-2.5/6.5/-0.001/0 maxiter=1900 inside=0 logmap=220 periodicity=10 colors=000KAJKAKKALKAMKANKBOKCPKDPKEQKFRKGSKHTKIUK\ JUKKUKKUKKUKKVKKWLKXMKYNKZOK_PK`QKaQKbQKcQKdQKeQKf\ QLgPMgONgTSaYWXa`RfdMkhGomBtq5xu0yq2xk4xf6xb8v_AvX\ CrUDmSFhOHcLJcHLcDNZAOKDQKFRKISKKUKMVPPWPRYJUZEW_9\ Y`FX`KX`QX`VW``W`eW`erFeqJeqmepmepmeomeom_jYVfSQzN\ KzHFzBAz69z98zC7zFflIrrKrqLiiMfXMJNNNENQBOT7OW3PZ0\ PaUGXTLTSQPRVLR_HQdDPi9On5OrAQnFRjJSfOUbTVZXWWaYSf\ ZOz_KzaGzbCzc9zbAzaAz`Az_AzZBvYBrXBmWBiVCgUCzcCdTC\ `UGYVKUWORWRNXVKYZGZbDZeH`cKbbNdaQe`Ug_XiZ_jXblWfn\ VioUlzTosSrtR_XgHAwJBtLCqMDnOEkQFhRGeTHbUH`q9NpDOo\ HOnLOnPOmTOlWOk_OkcOjgOikOinOfiNdeNbaM`XMZczWPzUKK\ SGKQCJO8JTDHXIGaNFeSEjXDnaCreBk`AdWAYR9RS9KT8DU8rV\ vqWrpXoo_lnbinefmhclk`knYjqVjtSiwzhwzgwzgwzdzzazzZ\ zzXzzUzzRzzOzzMzzJzMGzNEzNWzKlzIlzImzHmzHnzGnzGozF\ ozFozFhzIbzLXzORzRKzUEzX8z_2zb1zc1zc1zc1zc1zd1zd1z\ d1zd1zd1ze1ze1ze1ze1zf1zf } frm:DivideBrot6 { ; Jim Muth z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2, d=real(p2)+0.00000000000000000001, f=imag(p2)+16: z=z^(a)/(z^(-b)+d)+c |z| < f } END PARAMETER FILE=========================================

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