FOTD -- July 05, 2008 (Rating 6) Fractal visionaries and enthusiasts: With today's image I introduce the ultimate, final, absolutely last version of the DivideBrot series of formulas -- version number 5. It draws the same images as version 4, but with two minor changes. I have added a value of 0.00000000000000000001, or 10^-20, to the imag(p1) parameter. This insignificant addition avoids a blank screen when the parameter is set to zero, and has no effect on the calculation time or image. I have also elimina- ted the real(p2) parameter and inserted a hard-coded bailout radius of 1,000,000, which eliminates the need to raise the bailout as the imag(p1) parameter is increased. The result is a simpler formula with less chances for mistakes. I named today's image "Pancake With Syrup". (The syrup is blueberry flavored.) I rated it at a 6, which indicates that I do not consider it anything out of the ordinary. The magnitude of the image is large enough to make the math- tolerance entry necessary. This assures that the parameter file calculates at the correct magnitude. The parent fractal is another almost-Mandelbrot set, with today's image located on a spike on the northeast shoreline of the main bay of the large midget on the negative spike of the parent M-set. As is true of many almost M-sets, the main bay as well as the buds are filled with tiny bits of debris, which prove to be entire universes when enlarged. The calculation time of only 42 seconds exceeds the speed of light, showing that the theory of relativity is flawed. The completed GIF image is available on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> While we were relaxing in our lawn chairs this afternoon, FL casually asked me whether I believed in science or religion. Not being in the mood for philosophical rambling, I replied that I believe in both of them, since both science and religion are real. This reply saved a lot of words, but I'm not sure what I would have said if she had worded the question differently and asked me whether I consider faith or reason to be the the better path to ultimate truth. The question brought my philosophical muse to life however, so expect some enlightening or not so enlightening words about faith and reason before long. Heavy clouds and threatening rain made Friday less than ideal at Fractal Central. And the temperature of 73F 23C hardly felt like Independence Day, which is usually as hot as a firecracker. But it stayed dry, the neighborhood cookouts were a success, and the fractal cats made the most of the marginal conditions. The next FOTD will be posted in 24 hours. Until then, take care, and watch for runaway fractals. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Pancake_With_Syrup { ; time=0:00:42.81-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=DivideBrot5 center-mag=-10.45034361189\ 851/+0.00241713891946783/2.225036e+012/1.001 params=6/6 float=y maxiter=1500 inside=0 logmap=105 periodicity=10 mathtolerance=0.05/1 colors=0009MUDMUHMULMUPMUTLUWLUYLV_LWaLYcK_eL`bQa`\ VaZZbXcbUhcSlcQqdOudPtfPtgPtiPtjPtlPtmUsjYshasffsc\ jsans_rnYpjUofQm`MiWIgSEgPAfM6eJ3b00A`zDYqGVhIZjLc\ lOgnRlpTprZeedVTjKGpA3qC5qD7rF9rGBsIDsJFsKGlMbfOyb\ Io_DeW8WT3NS5KR7IQ9GPBEODCNFANG8IEFDDL8CR4BXDJUMQR\ O_IQi9Sr1LpVEowGrlHuaIwSMvUPuVStWVsYYrZ`q_cp`9VhWW\ `qXUoZXm`Zka`icbgddagfWigQliLnjFql9sm4unHneUhYfbQr\ XIiXL`XNSXQJXSBXUEVWGTYIR_KPaMNcOLeQJgSHiPQaMZVKgO\ HpHFyAIiIKUQMEYPKVRPSTUPWZMYcJ_hH_YC_N8_D4VrF_ubcw\ ycCffIhhOikTkmZlocmsSQvG2vJ8vLEvNKvPPvRVvT`vUfvYko\ amiencioYmpSqqMurGxsAztFzqJznNzkRzhVzzZzzbzzazz`zz\ _zzZzzYzzzzzzzizzizzizzizzXzzazzetzfozgkzggzhbzhZz\ i`ze_zf_zfZzfZzg8z0Dz7IzDNzKSzQXzXazbezhXzdPz`GzX8\ zUCzTGzSJzRNzRRzQUzPYzO`zOezQizRmzSbzWTz_Jzc9zfNz6\ TzIYzUUzPRzKOzGLzBIz6Fz2JzBNzKRzTVzaZzjMzjOzhQzeSz\ bUz_WzYazUgzR8zb4zd0ze5zb } frm:DivideBrot5 { ; Jim Muth z=0, c=pixel, a=real(p1)-2, b=imag(p1)+0.00000000000000000001: z=sqr(z)/(z^(-a)+b)+c |z| < 1000000 } END PARAMETER FILE=========================================