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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: When I create fractals that feature midgets, I always rotate the midget to the normal position, with the large period-2 bud and negative stem, (a classier term than negative tail), pointing to the left. I do this for the same reason that I usually set the inside fill to 0 and the outside to equal iteration bands -- to establish a standard by which different fractals and their midgets can be reliably compared. In today's fractal the midget at the center is askew. More accurately it is rotated about 20 degrees counter-clockwise. I could easily have remedied the situation by rotating the entire frame, but for some reason I was pleased with the downward drooping nose of the midget, and left it as it was. As a result, I have named the picture "All Askew", which might be a bit too strong to accurately describe today's picture. When all the calculation was finished, I studied the image a few minutes before rating it a 6. The mathematical expression that was iterated to create the image is Z^1.05+Z^(-1.1)+(1/C), another of my endless whimsical inventions that make fractaling such an enjoyment. The parent fractal is a wildly distorted Mandelbrot set, with an immense main bay that has barely visible buds around its perimeter. Today's midget lies on the shore of the M-set, about 9/10ths of the way from the tiny period-2 bud around to East Valley. It is located in what normally would be an elephant trunk, though with such distortion, little signs of the East Valley elephants remain. The parameter file runs in 20-1/2 minutes on a Pentium 200mhz. This is slow enough to make impatient fractaliers run to the Usenet binary group: The fractal weather, (is there any other kind?), today was hazy sun but chilly enough (47F [8C]) to keep the intrepid cats indoors. Rain is due tonight, but no sign of it has yet appeared. And I'm about ready to disappear for the next 24 hours. The philosophical muse is still dead, but a resurrection is possible at any time. Until tomorrow, when I'll return with another wonderful (IMO) fractal, take care, Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
All_Askew { ; time=0:20:32.14 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-2.33322282243550300/+0.22474639188344230\
/1.510841e+008/1/85 params=1/1.05/1/-1.1/0/0 float=y
maxiter=5000 inside=0 logmap=372 periodicity=10
colors=000SIceDhs8lz4pz3ly3hu2cr2am2Yi1Ue1Pb1MZ0IV0F\
Q0BO08K04G01C00A008207505B04F03I03O02S01W00a00e00i00\
f00c11a51ZC1WI2UO2QV3O_<3>4Dz4BzBCzHCwODuVDpaFm<2>vG\
bzHZzHW<3>zMizOlzPp<2>zUzzVzyZpscfjhWcjLeiOefPeeQfbU\
faVfZWfYYhV_hUahQbhPciLejHelFelBem8eo4fp2fp0fr0fs0fs\
0fu0hv0iv0jw0jw0ly0mz0mz0oz0pz0pvBrrMsmZsijuewvazvUy\
uMmsFwz8Ur2Kr7Pu<2>LayQezWjzaozeszjwzpzzuzzrzzozzlwz\
ivyfsvcpsaopZlmWijUhhQeeObbL__IZYGWVDUSBSP8PM5MK3LH1\
IF0GC0FBAOCMWD_cFmlGzuGypF<2>phBmeAjbA<3>aS4ZP3WM3UK\
2QH1<3>H70F40C20A00700500A00D25H4CK8IOCQSFYWIcZLjWMi\
UOiQPiPPhMQhKShHUhGUfDVfBWfAWf7Yc<2>2aW1bU0cQ<3>0iG0\
jD0lB0mA0oH1pO5rVCsaHuhfvAewCcyDczGbzHbzKazLazO_zP<2\
>ZzWYzYYzZbzQfzIlzBpz3uz0oz0iz0<3>Pz0Kz1Fz1Az24z20z3\
0z38z3Lz3Zz3YzAWzFWzLVzQUzYUzbSzifzK<2>Vz_
}
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.
