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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal is a true lawbreaker, which is what I named it. Everyone knows that the number of elements in the patterns around quadratic minibrots increases in the series 2,4,8... as the midget is approached. So how do we explain the midget at the center of today's image, which is obviously quadratic, but is surrounded by a 3,6,12... series of elements? I will not even try to explain it. I'll leave the explanation to the geniuses of fractal mathematics. To me it's just one of the unexpected things that make fractal exploration so fascinating. The parent fractal is another thin ring of radius 1 centered on the origin. This time to get the ring I combined 0.0003 parts of Z^(1001) with 0.0003 parts of Z^(-999) and added straight C. Today's scene is located in the critical detail where the ring intersects the positive X-axis. The rating of an 8 might seem a bit generous, but I think the mathematical curiosity makes the image worth the rating. The calculation time of 1-3/4 minutes is no problem. Viewing the completed image on the FOTD web site is even less of a problem. The web site may be accessed at: Despite a chill in the air, Sunday was near perfect here at Fractal Central. Blue skies and a temperature of 64F 18C are hard to beat. The fractal cats spent a good part of their day on mouse duty, checking every suspicious little hole where a mouse might get in. I did little but take it easy all day. Why do more? The next FOTD will appear in 24 hours. Until then, take care, and don't be a fractalist who has lost his faith. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Lawbreaker { ; time=0:01:49.08-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident passes=1
params=0.0003/1001/0.0003/-999/0/0/0/0 maxiter=1800
center-mag=+0.99754831985625280/+0.000073916471693\
98/1.967133e+007/1/165/3.64419725437659103e-006
float=y inside=0 logmap=143 periodicity=10
colors=000DALFBMFCNFDOFEPFFQGGRHHSIIUOKWUPZcUcmZht\
cmzhrzmvzqzzqzzqzzqzzszzuzzwzzzzzzzzzzzvzzrzvmzriz\
mgzhhzchzaiz_iz_jz_jzZkzZkzZlzZlzYmvYmrYnmXnhXocXo\
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NVzRRvVPrZUmbYhfXcjVZnUUrTPvSNzUOzVOzWOzXPzYPzZPz_\
Qz`QzbQzcRzdRveRrfSmgShhSfiTekTdlTcmUbnUaoU`pV_qVZ\
rV`oUamUbkTchTdfSedSfaRg_RhYQiVQjTPkRPlOOmMOnKNoIN\
iMOdQPZTPUXQO`RJcRDgS8jS9hQAfPBdNCbMDaLE_JFYIGWGHU\
FITEJRCKPBLN9ML8NK7OI5PG4QE2RC1SB0QE1OG1MJ1LL2JO2H\
Q2GT2EV3CY3A_39b47d45g44i44g64f74e94dA4cC4bD4aF4`G\
4_I4ZJ4XL4WM4VO4UP4TR4SS4RU4QV4PX4OY6P`8Qc9RdASdBT\
dBUeCVeDWeEXeEYfFZfG_fH`fHagIbgJcgKdgKehLfhMghMhhP\
ieSjbUk_XlXZmUanRcnOfnLinIknFnnCpn9sn6um4on8ioCcpF\
YqJSrMMsQHtTKuSUvRcwPmxOvyNzzLzzKzzJzzIzzGzzFzzEzz\
CzzBzzAzz9zz7zzSzzTzzUzzW }
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.
