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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal has a verdant appearance to it. After a modicum of consideration, I noticed the greenery and named the image "Chaplet of Flowers". The foliage effect was created by iterating the formula 0.8(Z^(-1.667)-0.8(Z^(1.667)+(1/C) a maximum of 2500 times, and coloring the outside with the <fmod> option. The parent fractal is a curious diamond shaped network, typical of fractals that combine positive and negative powers of Z. One of the more remote nodes of the network contains the scene of today's image. The color scheme appeared serendipitously as I rotated various palettes at random. One minute the image looked like a total loser, then today's palette flashed by and vanished as fast as it came. A few steps backward restored the lucky palette however, and the result appears as the FOTD for September 25, 2001. Undecided as to how to rate the effort of the day, I settled on a rating of an average 5. Running the parameter file is one way of viewing the image. Waiting an hour or so, then visiting Paul's or Scott's web site and downloading the GIF image from there, is another. Paul's web site is located at: The fractal weather today was quite exciting, with a tornado in the vicinity, which tore up the campus at the U of MD. But we had only a heavy thunder-storm here at Fractal Central as the twister passed by. The temperature of 81F 27C was just about normal, and kept the fractal cats behaving in a normal manner until the thunder began, when the dynamic duo took refuge in a coat closet. I lack the time for much philosophy this morning, but I will post a few thoughts. When I checked my philofractal e-mail, I found two letters about precognition, one from a skeptical scientist, the other from a mystical metaphysician. The scientist considers paranormal things such as precognition to be delusion, and would like to educate the world so that it does not believe in such fantasies, which admittedly sometimes do more harm than good. The metaphysician knows through personal inner experience that the ability to see into the future, as well as other things considered paranormal, do in fact exist. But the scientist does not consider the inner experience of the mystic to be a valid means of proof, so the mystic cannot convince the scientist of the truth of his discoveries. It is apparent that before we can make any progress in understanding these elusive paranormal phenomena, which will not go away regardless of how often or vigorously they are denied, someone must change their standpoint. One bit of encouragement is to see both scientists and mystics agreeing that fractals are great fun. The clock on the wall over the fractal desk now tells me that it's time to move on to other things. So I'll be shutting down the fractal department until next time, which will arrive in the right time. Until then, take care, and when the going gets tough, the tough get a fractal going. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Chaplet_of_Flowers { ; time=0:09:43.85--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-6.376602614525529/+3.854529883857569/2\
.701395e+008/1/180 params=0.8/-1.667/-0.8/1.667/0/0
float=y maxiter=2500 inside=0
proximity=0.95 outside=fmod
colors=000qsz6l`6hY5dV5`R4XO2VM4UL5TK7SK8RJAQIBPIC\
OHEOHFNGHMFILFKKELJEMIDOHCPHCRGBSFATEAVD9WC9YB8ZA7\
`A7a96b86d75e64g54h43i43g74eA5cC6aF6_H7YK8WM9UP9SR\
AQUBPWBNZCLaDJcEHfEFhFDkGBmH9pH7rI5uJ1yH3xI4wJ5vK6\
uK7tL8tM9sNArNBqOCpPDoQEoQFnRGmSHlTIkTJkUKjVLiWMhW\
NgXOfYPfZQeZRd_Sc`TbaUbaVabW`cX_dYZdZYe_Yf`XgaWgbV\
hcUijQsgSndUiaVeZX`WZXU_SRaOOcJLdFIfAGg6SLWTKVUKUU\
KUVKTVKTWKSWKSXKRYKQYKQZKPZKP_KO_KO`KNaKMaKMbKLbKL\
cJKcJKdJJdJJeJIfJHfJHgJGgJGhJFhJFiJEjJDjJDkJCkJClJ\
BlJBmJAuBBqFAmJAiM9eQ9bU8ZX8V`8Rd7Ng7Kk6Go6Cr58v55\
y55x65x75x75w85w95w95vA5vA5vB5vC5uC5uD5uE5tE5tF5tF\
5tG5sH5sH5sI5rJ5rJ5rK5rK5qL5qM5qM5pN5pO5pO5pP5oP5o\
Q5oR5nR5nS5nT5nT5mU5mU5mV5lW5lW5lX5lXCiYIgYOeZVcZ`\
a_f__kXYlYZlY_lZ`lZ`l_al_bl`cl`cladlaelbflbflcglch\
ldildilejmekmflmfmmgnmgomhpmhqmirmismjtmjumkvmkwml\
xmlymmzmmzmmznnzoozppzqqz
}
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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times.
