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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image really turned out well, so well in fact that I rated it at a lofty 9. The parent fractal, which was created by combining 2 negative parts of Z^(1.5) with 2 positive parts of Z^(2.5) and adding straight C, is a distortion of the Mandelbrot set, with many extra bays and other goodies to explore. Today's image is located in one of these extra goodies -- a tiny, almost invisible valley that sprouts from nowhere and goes nowhere. This tiny valley is located just outside of the much larger seahorse-type valley that sets off the period-2 bud on the northwest shoreline of the main bay. (There is a second period-2 bud and a second tiny valley on the symmetrical southwest shoreline.) The image is made by its coloring, which is a refreshing change from the usual and often too-intense colors of most FOTD images. I named the image "Emerald Iterations". The green is not quite pure, but it is green enough to justify its name. The calculation time of 3-1/2 minutes on the P2000 machine would be extended to around 15 minutes on the P200 machine. It will be cut to seconds however by visiting the FOTD web site at: The weather here at Fractal Central on Wednesday was absolutely perfect. The deep blue sky, puffy white clouds, low humidity, light winds and high temperature of 70F 21C could hardly be improved upon. The cats made no effort to improve upon the weather. They were too busy watching a pair of doves. With a 9-rated FOTD to boast about, and the commercial work well under control, my day was well above average. Now if only tomorrow could be a repeat . . . Regardless, the next FOTD will appear in 24 hours. Until then, take care, and grasp at the great mysteries. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Emerald_Iterations { ; time=0:03:42.21-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident inside=0
params=-2/1.5/2/2.5/0/0/0/0 logmap=432 maxiter=4000
center-mag=+0.29719583945369130/+0.215567134695368\
40/6.652338e+009/1/55/-0.000245700507399387869
float=y periodicity=10
colors=000oxwmxvjxugxrdwoavlZujWtgUtdStaQtZOsWNsTM\
sQLsNBfcFiYJlSNoMOQSPYPPdMQkJpw_guTZsNbtiYs_UrQ`E0\
Ce`JlRpQLCvUGuQJtNNsKD9gIPZMcQl3X`TP3fiBj_JnQXtRSf\
fCK6mORacMGlk61CAF8ES4Id1_uISqGLmFUcEaUDjLDrBCz2Ca\
8XDEp3b4BX7ISAQNDXIGdDJk8MdFBYL1aQ7dUCgYIjaNneSqiY\
RlBTlBVkBWjAYiA_hA`hAVe9Qc9La8G_8BY76W79UACTCESEHR\
GJQIMPKOOMRNOTMQWLSYKU`JWbIYcM_dPaeTcfWeg_ghbiiekk\
bhl`emYcoW`pUZqRWsPUtMRuKPwIMuFKsHHoKFkNEgQDeTCcWB\
aYA__9Y`8Wa7Ub6Sc5Qd4Oc3Ma2K_1IY0GW0CT06Q00N00K00H\
00E00B0080550A20F8AKEFPFKUHPZIWcKXgLXjNXlOXnQXpRXj\
W`d_d_cgUhkPlnJprEtu8pn2mgGdWUWLmmmzzzmmmSB_RFbRId\
RMfQPhQTjQWlP_nPbpPfrPitRfqScnU`lVYiXVgYSd_Pa`M_bJ\
XcHVfMWhRXjWYl`Zne_pi`RseUtfWtfZtg`ugcuheuhhvijvim\
vjovjdwWUwHWwHXwHYwH_wH`wHawHcwHdwHhwHmwHrwHvwHzwH\
zwHwwKzwUzwczwSzw8zwBzwEzwUzw`zwRzwgzw_zwVzwQzwLzw\
uzwgzwUzwnzwYzwtzwjzw`zwR }
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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times.
