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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The parent fractal of today's image, which was created by combining Z with Z^(-0.5) and adding C, resembles a fractal bullet. Today's scene is located on the north shore of the bullet, where some very tiny mandel-buds are located. I named the image "Nevermore Land" because after finding what lies there, it is unlikely that I'll ever go there again. I could rate the image itself at only a 5. My semi-expert coloring efforts added the extra half-point. Today's fractal image shows an abstract land of fractals -- a land created by numbers and populated by the horde of similar figures that fill the frame. Not surprisingly, as we dive deeper into the image, these figures are repeated at ever smaller sizes without end, all the way to infinitesimal infinity. That's the way fractals are. An overwhelmingly prominent, blazing white minibrot sits at the center of today's scene, looking strangely out of place, almost as though it were dropped there by some higher power. It has little symmetry to betray its existence, and almost no basin of attraction around it. Other smaller minibrots are scattered throughout the scene, all of them similar to the one in today's image. The parameter file at the end of this discussion takes just over 5 minutes to complete on the fireball P4-2000mhz machine. On the droopy old P-200mhz snowball unit it takes about 1/2 hour. On the FOTD web site the image has already been calculated and posted for maximum enjoyment. The web site may be accessed at: Heavy clouds and occasional rain spoiled the day Tuesday here at Fractal Central. The temperature of 72F 22C, however, was quite pleasant. The fractal cats, who dislike rain, spent the day watching the humans do their work. My work was finished earlier than expected, which gave me a chance to find today's parent fractal. The next fractal will be posted in 24 hours. Until then, take care, and numbers describe the universe so well because we created them intentionally to do just that. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Nevermore_Land { ; time=0:05:11.42-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident passes=1
center-mag=-1.0890400699647/+0.07599607053382/7288\
.355/1/-35/1.85112133954667968e-011 periodicity=10
params=1/1/1/-0.05/0/0/0/0 inside=255 maxiter=6000
float=y logmap=128
colors=000aAp_8nY8nW8lU7lS7jQ5jO5hM5hK3fI3fG1dE1dC\
0bA0b80_70_50Y30Y10W00X10X10X10V30V30U30U30T50T50T\
50U70T70U70T70TC0QG3OK7OOAMTEMXIK_MKdQIiXIn_GrdGvg\
EzlEzpCztCzxAzz8zzMzzXzzezzpzzzvzzrzzmzpmzemzXmzMm\
zCmzAmzAizAezCazCYzCUzCQzCMzCIzCEzCAzC6zC3zC0zC0zC\
0zC0zA0zC0vC0rC0nE0iI0eM0aQ0YV1VX5Q_8MbCIeGEiIAlK7\
nM3pO0nO0lM0jK0iI0jG0kE0lE0mE0nE0mE0lE0kE0kE0kE0kG\
0kG0kG0kG0kG0kG0kG0kG0kG0kG0kG0kG0kG0kG0kI0lI0mK0n\
K0oM0pM0pO0pO0pQ0pQ0pQ0pT0pT0pT0pV0pV0pV0pV0pV0pV0\
pV0qV0rV0sV0tX0uX5vYAwYFxZKy_Kz`LzaNzdKzdMzaMzaNza\
KzaJzaIzaJz_Iz_Jz_Jz_Lz_Lz_NzYNzYPzYPzYRzYRzYQzXSz\
XRzXRzXSzXSzXRzVUzVTzVTzVVzVVzVVzTXzTXzTXzTYzTYzTY\
zQ_zQ_zO_zMazKazIazGdzEdzCdzAez8ez7ez5ez3ez1ez0ez0\
ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0ez0gz0iz\
0lz0nz0pz0rz0tz0vz0xz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\
z0zz0zz0zz0zz0zz0zz0zzzzz }
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.
