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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 must be seen to believed. One outzoom is needed before the entire thing will fit on the screen, but once this is done, a fractal with more convolutions than a junkyard dog has fleas appears. This parent is one of the most enigmatic figures I have yet stumbled upon. It has narrow valleys, broad valleys, mandel-buds, near-mandel buds, plus an unlimited number of holes and indents of various and assorted sizes and shapes. The broad features are those of a high-order Mandeloid or Julia set, but these features do not make up the entire fractal. Rather, they form a kind of pattern theme around the smaller, more irregular features. Today's scene lies in one of the broader valleys. I named it "Mathematical Scythes" when the reddish crescent-shaped features impressed me as blades of scythes. Actually, with its strong reds and greens, the scene has a rather Christmasy look about it, but since we are about as far from Christmas as it is possible to be, I decided against the Christmas theme. I rated the image a 6, since it is a bit above my long-term average. The simple formula (1/Z)-Z^(300)+(1/C) created the parent fractal. Taken by itself (1/Z)+C does little, and Z^300+C does little more. But when combined, and when 1/C instead of C is added, these two expressions work wonders. One of the wonders, which is today's FOTD, can be seen by running the Fractint parameter file attached to the bottom of this letter. The parameter file renders in only 5-1/2 minutes on my tired old Pentium 200mhz machine, but notably faster on one of the current screaming fireballs. The alternate way of viewing the scene is to go to one of the internet web sites where the GIF file of the image will soon be posted. Paul's site can be found at: The fractal weather today was the image of a lazy summer day, with sunny but hazy skies, unhealthy air, and a temperature of 90F (32C) that kept Thomas happy. Tippy however was not happy, since it was the day for his annual visit to the doctor. He cried all the way there and back. After being pronounced healthy, he cried all the way back, and then sulked for several hours before becoming his normal self. Thomas was glad it was not his time to go to the doctor, but his time is not far off. And my time to do some useful work has arrived. In fact, it arrived an hour ago, and I've yet to get started. So until next time, take care, and regardless of how many fractals we find, the number of fractals yet to be found will never be reduced. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Mathematic_Scythes { ; time=0:05:28.34--SF5 on a p200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-19.25482682013031000/-0.26917358759950\
070/6407.871/1/52.5 params=1/-1/-1/300/0/0 float=y
maxiter=4000 inside=0 logmap=91 periodicity=10
colors=0007ma7mb6nc6nd6oe5pf5pg5qh5qi6oh7mg7kf8ie9\
he9fdAdcBbbB`aC_aDY`DW_EUZFSYFRYGQUGQRHQOHQKIPHIPE\
JPAJP7JP4NR5QT6TU7WW8_X9bZAe`BhaClcDodErfFugFqeImc\
LiaOe_RaYUYWXUU_QSbVQYZPUbNQfMMjLHnJDrI9vH5uG5tG5s\
G5rG5qF5qF5pF5oF5nE5mE5mE5lE5kD5jD5iD5iD5dG9_IDVKH\
QMLLOPHQTLSVOUWSWYVYZZ_`aaaecchedVWkINr5EyBAlG7`L4\
PQ1DR3GS5JT7LT9OUBQVDTWFVWGYXI_YKbZMdZOg_Qi`Sl`Tn9\
1wB2pD2jF2cH3YJ3RL3LM3FJBMGJTDQZAYe8dkC`gGXcKT_OPW\
SLSWHOZELXJHVODTTARY6Qa3QXBQSIQNQQIXQEcVGbZHabIagK\
`kL_oM_mTSkZKieChk4_m7SnAJoCBpF3qH7rNArTDrZGrcKsiN\
soQsuTszWrwYru_qsaqqcqoeplgpjiohkofmodonaqn_smYumW\
wmUulTtlSskRrkQpkPojOnjNmiMkiLjiKihJhiIgjHdkGalFZm\
EWnDToCQpBNqAKr9Hs8Et7Cu7EvDGwJIxOKyUMz_OzdQzjBzcC\
zdDzeEzeFzfFzfGzgHzgIzh_zqezpkznqzlwzkmzBsz_yzwZzu\
9zsQziez`uzSmzXez`ZzdRziJzmCzqDzoEznFzlGzkHzjIzjIz\
iCzECz9Cz4BzCAzK9zS8zZ7z`
}
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.
