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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The formula for today's image adds a very small bit of Z^(-20) to Z2 to produce a Mandelbrot set with disks of Z^(-20) stuff at the centers of all the bays and buds. The image is located on the X-axis, in the detail at the east edge of a disk almost filling the large period-2 bud of the M-set. More than anything else it resembles a surrealist's spider-web. I named the image "Stars of Iteration", which sounds a little poetic and in a way describes not only today's fractal, but all fractals. And then I rated it at an 8. I considered adding a half point for my coloring, but decided that I did not do quite enough color tweaking to merit the extra half-point. The calculation time of only 42 seconds is fast enough to cause no impatience. The finished image, which is posted on the FOTD web site at: With a temperature of 88F 31C here at Fractal Central on Monday, it was just a bit too warm to be perfect, but all else was the picture of perfection. The dynamic fractal cats, who never stop reiterating, agreed. Just after lunch they spotted an unfamiliar manx cat in the yard next door, and with a volley of hisses and growls, sent it on its way. I did not tell them that the cat was ready to move on anyway, and their empty threats had nothing to do with its departure. Otherwise the day was uneventful. The next FOTD will be posted in 24 hours. Until then, take care, and to become famous, solve the measurement problem. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Stars_of_Iteration { ; time=0:00:42.84-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident passes=1
center-mag=-0.9160783767764306/0/8.62e+008
params=1/2/1e-018/-20/0/0/0/0 float=y maxiter=1450
inside=0 logmap=153 symmetry=xaxis periodicity=10
colors=0000EC0FF0GI0HL0IO0JQ0LT0NW0PZ0Ra0Td0Vg1XiD\
_aPbV`cOldHwdAwgBwjCwmDwpEwsFwvGwyGvvFutFuqFtoFslF\
sjFrhFqeFqcFp`FoZFoWFnUFnSFoTEpTDqTCrTBsTAtT9uT8vT\
7wT6xT5yT4yT4pO9hJEsFTSAcJ5cB1cC2cC2ZD2UC2PB2KA2FA\
2AA3AA3AA3AA3AA3AC3AF3AI3AN5AS7FW9L`BReCWiEanGgsPz\
wUzvUzuUzuUztUztPysKwrHurHsqHsqHsmJmjLhgNcdPZaRUYT\
OVVJSXEPZ9M_4K`5Ja6Ha6Gb7Fb8Dc8Cc9Ad99dA8eB6eB5fC4\
fCm6Am9DmCGmFJmIMmKOmNRmQUcTXUW_OYaSdSWkJ_zAbzKYzU\
TzcOzmJztFzzGzzHzzHzzIzzIzzJzzKzzKkVLlYLm`MncMnfOl\
dQjcShbUg`We_YcZZbY``WbZVdXUfWShURjSQkRPceQXsQUrQQ\
qRNpRzoSznSzmTzlTzkTziQHhNLgLPfITeFXdD`cAdb7ha5cX5\
_T5VP5RL5PPAOSENWIMZMLbQKeVJiZIlbHpzGszIzzFrzCjz9c\
z6Wv4Pr3Mm3Kh2Ic2GZ1E_1Ce0Ak08q06v6CoCIhIOaOUVU_U_\
eZdkcamh_omYqrVsvzuzzwzzxzzyzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzezzNzz4zz6zz7zz8zz9zzAzzCzzDzzEzzFzzGzzIz\
zJzzezzfzzgzzhzzhzzezzbzz }
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.
