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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I named today's FOTD image "Mandelbrot Mystery" because I'm not sure if it's a real fractal or some kind of artifact. But whatever it is, the image lies in the Seahorse Valley area of its parent fractal, which is a Mandelbrot set with lots of extra detail around the edges of the main bay and buds. The ridiculous real(p4) parameter of 10^(-45) seems far too small to produce such a change in a normal Seahorse Valley scene, but maybe that's the way the four-dimensional Hypercomplex Mandelbrot set is actually shaped. Changing this parameter to zero reduces the image to the expected Mandelbrot scene. Much of the coloring effect was achieved by rendering the scene with the outside set to 'summ', though the normal 'iter' setting gives almost as good a result. The rating of a 7-1/4 includes 1/4 point for the 5 minutes extra coloring time I put into the image. And the calculation time of under 2 minutes is quite nominal. As always, the finished image is posted for instant ecstasy on the FOTD web site at: Increasing clouds in the morning led to a cloudy afternoon and a cold evening rain here at Fractal Central on Monday, with a cold temperature of 37F 3C. The fractal cats were most disappointed with the lack of sun and got into a tussle when Cassie would not give up her spot on the scratching post by the warm radiator. After the spat, the duo sulked at each other for a half hour. My day was quite busy, and from the look of things tomorrow will be the same. But the next FOTD will be posted in 24 hours regardless. Until then, take care, and solve the Mandel-Mystery. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Mandelbrot_Mystery { ; time=0:02:50.00-SF5 on P4-2000
reset=2004 type=formula formulafile=basic.frm
formulaname=hypermandelbrot2 passes=1 float=y
center-mag=-0.749525773313297/+0.058824468328704/\
79121.91/1/85/0 params=0/0/0/0/0.32/0/1e-045/0
maxiter=3200 inside=0 outside=summ periodicity=0
colors=000kDrq9ur9vr8vz8wz8xz7xz7yz7yz8xz9wz9vuAuo\
AtkBsfCrcCq_Dp_DoXEnVFmSFlMGkBGjiHihIhgIgdnNapOZqP\
WsQTuRQvSNxTKyTJrXIk`HdcGYgGSkFLnEErD7vD1yF5wH9uJD\
tKHrMLpOPoPTmRXkT`jVdhWhfYle_pc`sbatcatdbtebufcufc\
ugdvhdvievjewjfwkfmlgcmgUngUncKj`KfYKbV7_W8ZX8ZY8Y\
Z8Y_8Y`9Xa9Xb9Xc9Wd9Wd9W`DQXHLTLGPPBLT6OR8QQASPCUO\
EXNGZMI`LKbKMdJOgIQiHSkGUmFWoEYmIXlLWjPViSUgWTfZSe\
aRceQbhP`lO_oNYsMXvLWyKYxN_mQ`cSbUVdKXe0_gwbiwdjwg\
lwinwlownmvokvpiuqhurzd0zm0zs0zzizzmzzz`qtbqqdpnep\
kgpiiofjocln`nnZonWqmTsmQtmOsjMrgKrdIqaGq_EiZLY_RV\
ZXOZbS`_WcY_fWcjTgmRkqPntNosQosTosWosZoszoszprzprz\
prmpzppzspzuqwsqsrqpqqlophlpbjoXhmTflOdjJciFbhCagD\
_gGZiHYjKXkLWhOWeOUcPSbPQdOOeONcNLgNJeNHgOFgOEhPLg\
RJfTHfVFeXEeYCfZAf_8g_7f_KgXXdRh`OeYNcVMaRL_OKYLJV\
HITEHRBGP8FN7IO6KO6NP5PP5RP4UQ4WQ3YQ2`R2bR1dR1gS0i\
S0kS6fWCbZIZaOUeUQh_MkeHo }
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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times.
