|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: With today's image we return to the classic Mandelbrot set, but we return to it in a special way. The M-set comes in many versions, determined in one aspect by the bailout value. The bailout has a great effect on the outer bands, but as long as the bailout value is 4 or greater, the differences in the basic inner detail are small. However, with a bailout of less than 4, strange things start to happen. To start, the M-set is simply not all there. The tip of the negative stem is the first to be cut off. As the bailout is further reduced, more and more of the set becomes cut off, and the part that remains becomes ever more distorted. The closer to the bailout radius a feature lies, the more that feature is distorted. The distortion is of the type seen around midgets that lie near -2 on the negative stem when the bailout value is 4. This effect of fingers pointing inward toward the midget is not an inherent characteristic of midgets far out on the negative stem; it is due entirely to the closeness of the midgets to the bailout radius. This same finger effect appears in nearly all parts of the M-set when those parts lie very near the escape radius, and sometimes it takes most interesting variations. The midget in today's image, which lies on the filament extending from the north bud, is very near the cutoff point, giving the appearance of a midget on the negative stem. Because the scene contains so many areas of flat color, I named it "Patches of Color". I rendered the scene with classic outside equal-iteration bands after trying the other outside options, and discovering that the result was pretty much the same. I rated the image a 7, which, considering the simplicity of the scene, is perhaps a bit optimistic. But it's a pleasant thing to view, and worth its rating. Since the magnitude of the image is in the arbitrary precision range, the parameter file is a slow one, taking all of 1/2 hour to render on my tired old Pentium 200mhz machine. It will render in far less time on one of the speedier newer models. (No, I am not trying to sell computers. This is simply a statement of fact.) For those who decide not to run the parameter file, the GIF image will soon be available on the Web at: The fractal weather today was sunny and pleasant enough, though a bit chilly for May. The fractal cats approved of the 73F (23C) temperature by passing the afternoon in the grass of the yard. It's now 10am and time to get busy on other things. But I'll return tomorrow with a most unusual scene that Lee Skinner found in my "Pooped-Out" image. Until then, take care, and if fractals didn't exist, someone would have to invent them. Jim Muth jamth@mindspring.com |
START 20.0 PARAMETER FILE =================================
Patches_of_Color { ; time=0:34:50.52--SF5 on a p200
reset=2001 type=mandel passes=b
center-mag=-0.016866288292003691049311636513915874\
/1.00548061034188650807845045625051303/6.126022e+0\
31/1/-82.499 params=0/0 float=y maxiter=3200
bailout=2 inside=255 logmap=802 periodicity=10
colors=000H4KyWzvYztZyq_wAw34w0Rz0lf7zrDhuMLlV0db0\
MAFPKYRSpU`zVhzN_qHS_9L_3DR05L0IF0U80d20p00z74tG9l\
QFdZKZhPRqUKzYDwQ7vI0mA0v4Vw0zv7uuDmuLftRZrYRzzKqk\
Czz4yyIYiWPfhMZ`KSVHLNFFHC8APZdIbfCdfK`dRYcZUcfQbm\
NbqSduYgybhzgkzklvlplmrbnvSpyIqz8rz0rzUqzwqzvWziby\
YguLmq8rmHilP`lWSlSUhQVfNWbKY_HZWF_UC_RFUQGNPHHPKC\
NL5NM0MN0MV0I`4Gg9DbGNZLWVRdQWmMbvIgzNnwSupYzh`zbV\
zZPtWKlUDdR7YP2RM9YRGcWNi`UndZRKb30Z84WD8SIDQNHMSM\
KYQIbMHgIFlFDqACv7Az39z0Cz4Du8FnDGiHIdLKZQLUUMNZPI\
bQDfR7kS2nU0rV4tWCtYKtZQt_Yt`dt`ktZirYiqVipNiiUipR\
inQimRywQvuQvtQmrPpqPfpPkn0zK4zP8zSCuYFq`InfMlizVK\
zWMzYPwZRt_Up`WlbZic_fdbbfdZggVhiRilwKmrNmmRmhVmcZ\
mZbmUfm2PM4RP5SR8UU9WVAYYDZ_F``HbcIcfKfgMgiNhlR7NQ\
LWPYdm0Kk3Mi5Nh8QgCRdFUcHVbLY`NZZQ`YUbWWdVZfSbhRdi\
Qgl0wW0vY2uZ4t_5r`8rb9qcCpdDnfGmgHmhKliLkkNilk`0hb\
0fc4cd9`dG_fLYgRVgYShb000
}
END 20.0 PARAMETER FILE ===================================
|
times.
