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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: We end the month of July with one of those mysterious parent fractals I so often mention but so rarely show. But this parent is so unique that I just could not let it fade into the shadows of lost fractals. It is so unique in fact that I intend to use it as the source of the next few days' images. And yes, it is the parent of yesterday's 'Endless Loop' image. Even more surprising, I reused the color palette of yesterday's image. The formula that created this parent combines 2.5 parts of Z^(-1.05) with 0.35 part of Z^(-5.05) and adds (1/C). Since it is an image which came about with no exploring, I could not fairly give it a rating. The name I gave the image -- "The Parent Fractal" -- is a simple description. The calculation time of 40 seconds is brief enough to make the most impatient fractalist happy. But the most convenient way to see the image is still to visit the FOTD web site at: One final note -- today's image is not the last we will see of this parent fractal. Hazy, hot and humid (86F 30C) was the weather story here at Fractal Central on Monday. Thunder-showers were in the general area most of the day, but none ever came close enough to cool things down. The fractal cats kept cool by ignoring the heat. I kept cool by being too busy to notice it. And the air conditioning helped keep me cool also. The next FOTD will appear in 24 hours. At least it is supposed to. Only time will tell if it actually appears. Until next time, take care, and how many 3-D spheres could fit in a 4-D hypersphere of the same diameter? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
The_Parent_Fractal { ; time=0:00:40.82-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=recip passes=t
center-mag=131.174/240.484/0.003475104/1/-47.5/\
3.88578059e-016 params=2.5/-1.05/0.35/-5.05/0/0/0/0
float=y maxiter=3600 inside=0 periodicity=10
colors=000CUdEUcGUaIV`KVZLVYNWXPWVRXUTXSVXRXYPYYO_\
YNaZLcZKeZIg_Hi_Fk`En`Dn`Bq_Ara8uY7vb5wX4yb3uW5u_6\
sV8qX9oUBmVClTDjSFhQGfQIcNJbNLYLM_LNUJXWIQRH`SFTQE\
bODWNCfPEYQFfRH_TIgUKaVLlXNmYOrZQz`PzaTzbTzdWzeWzf\
ZzhZziazjazldzmdzngzpgzqjzrjztmzumzvpzxnzyszwpzxqs\
vnotkjsifqfbocYnaUlZPjWLiUHjWIjXIjYJjZJj_Kj`KjbLjc\
LjdMjeMjfNjgNjhOkjOkkPklPkmQknQkoRkpRkrSksSktTkuTk\
vUkwUkxUEdaFb`Ga`G``H__HZ_IY_IXZJWZKVZKUYLTYLSYMRX\
MQXNPXOOWONWPMWPLVQKVQJVRIUSHUSGUTFTTETUDTUCTVDSVD\
RVEQVEPVEOVFNVFMWGLWGKWGJWHIWHHWIGWIFWIE_JHbJKfJMi\
JPlJRmJSmITnIUoHVoHWpGXqGYqGYpIXpJXpLXpMWoNWoPWoQW\
o`VobVncVneVnfUngUmiUzjUzkTzmTznTzpTzqSlrSltSkkSkl\
Rkzmkzmkzmezm`jOWgMRdLMaJHZICWHBXIBXIBXJBXJAXKAXKA\
XLAXLAYM9ZM9_N9`N9aO9bO8cP8dP8eQAfQFgRKhRPiSUjSZkT\
clThmUmnUroVvpVzqWzrWzsXztXzuYzvYzwZzxZzy_zz_zz`zz\
`zzazzGzzHzzHzzWzzizzgzzf }
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.
