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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: As I write this, I have on the desk beside me the most recent issue of 'Skeptic' magazine, a publication that I often read, which features articles about many strange and wonderfully interesting paranormal things that do not happen. On the cover is a fractal created by a well-known fractal artist, and a well-known fractal generating program other than Fractint. As I study the image with its multiple layers and different coloring methods, I remember the Mandelbrot set as it was in 1985, with its one layer and flat equal-iteration bands. Fractals are (or were) graphs of the things iterated complex numbers do. When I see so-called fractals such as the one on the magazine cover, I ask myself, "is this what the numbers have done or what the artist has done?" If this type of image is to be considered a fractal, so be it. But then I must think of some new name to call the conservative images that I produce, which emphasize the behavior of the numbers rather than any possible artistic ability on my part. (The word 'protofractals' comes to mind.) I'll be pondering this minor dilemma over the next few days. I may invent a new name; I may not. But regardless, the images as well as the blather will keep coming. And speaking of images, with today's 6-rated image we begin a slow climb back to the lofty heights of fractal excellence. The rating of 6 is only slightly above average, but it is 2 points above yesterday's less-than-stellar effort. I named the image, which was created by the iterated expression -Z^(-1.3)-0.02Z^(-13)+(1/C), Fractal Shortfall. I gave it this name because the magnitude of the image falls short of revealing the midget at the center. In fact, the midget is so tiny that not a trace of it is visible. Instead of my normal inside=0 outside=iter coloring, I set the inside to bof61 and the outside to tdis. This is not too much of a sacrilege, since the basic forms are still clearly visible. Unfortunately, the parameter file takes well over 1/2 hour to render. Therefore, a download of the GIF image from: The fractal weather today was once again perfect, with blue skies, puffy white cumulus clouds, a temperature of 83F (28C), and happy cats. As for me, I've about had it for the day. It's already past midnight and there's not much left to do but settle into my favorite chair and grow sleepy watching an exciting old sci-fi movie. But I'll be back in 24 or 36 hours with the next fractal image. Until then, take care, and after 16 years of fascination with fractals, I don't even know what a fractal is. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Fractal_Shortfall { ; time=0:36:18.07--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-60.81552655003062/-416.9838484676321/8\
.371123e+007/1/94.999 params=-1/-1.3/-0.02/-13/0/0
float=y maxiter=6400 inside=atan
outside=tdis periodicity=10
colors=0001zW0od0_n0Lx0Ko0Ih0Hb0GX2ER4EL2HG2KB2N6L\
XBggEzsIokObbTRWYGOb6Hh0Bn06s0Kh6Y_GoRRzITnUUYdWKo\
RGhNDbK9XG7RC4L91H0v07q2KlDYgQoohzxzXQz40zC0zK0vT0\
q`0lk0hb1eW1bO2`H2YB2W54U04R04Q07L59IBCEHECOI9WL6b\
O4kR1lU7nWDoXKq_Rs`Ytbevdlq_kzXkgTkbQkYLkUIkQEkNCk\
0UrLlWG`QBRL7HH29D01900600200806E5GL9RTEb_KogQzo2g\
0C_6LTKXLYgEos8zqX`oxCqt7sq2zz0tl0tk0zX4zLIzBYzCbz\
DgvDlsEqqEvb8qR4nE0h50e00b00Y40U70RQObRK_RGXRCUR8R\
T5OT1LT0IT0H_0Qg5Yo9gxEqzIzzGttEnqCglB`h8Wd7Q`5KX4\
GU1BQ06N01I00G00C00900I70RN0_e0hz2dv4_s5Wq5Rn6Ol6L\
oWNqRNqOOqLOqHQqE0z12z5Dv80zz0zo4zdBxUItK00g02Y5HR\
EYI00v00q10n20k51g65d89`9DYCIWDNTGRQHXNK`KLgHOlEt0\
0h95YU84n8LsnNqkNqgNqdNq`OqYOqWOqTOqQQqNQqKQqHQqE5\
B57E68H69L7CO7DT8EW8HY9Ib9KeBNkBOnC78X9DUBHTDLQEQO\
GULIYKKbHNgGOlD02k07e2Bb5E_7KX9OUCTQEXNHbKKgHNlEWX\
2CO4DR5ET6GW6HX7H_7I`8Kd8
}
frm:MandelbrotMix4 {; 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,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END 20.0 PAR-FORMULA FILE==================================
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