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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal is a slice of pie, or perhaps I should say pi. The expression that was iterated to draw the image is Z^(pi)+C. To add a bit of interest, I calculated the expression with the MandelbrotBC formula, which draws the remote parts of the infinite spiral of fractals with fractional exponents of Z. To keep with the 3.14159 theme, I also set the second parameter to pi. The parent fractal looks a lot like the Z^3+C Mandeloid fractal, though it is crooked, and its west valley is split. To see this parent fractal, reset the logmap to 1 and back out of today's image, which is located in the area where the west valley broadens and splits. Perhaps the most unusual feature of the image is the tattered appearance of the features surrounding the midget, and the near total lack of symmetry. The midget itself, which closely resembles the cubic Mandeloid, is surrounded by many other midgets, none of them explored. The attached parameter file takes 9-1/2 minutes to render on a 200mhz Pentium machine. The download of the image from usenet is far faster, that is if the image file makes it to your news server. The newsgroup in question is: The fractal weather today was perfect, with blue skies un-marred by the slightest trace of cloudiness, and a temperature of 56F (13C), which so thrilled the fractal cats that they spent most of the afternoon sleeping in the sun in their chairs on the porch. The philosophy went nowhere today, but it's time to shut down Fractal Central and go somewhere myself. Until next time, take care, and be kind to your fractals. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Pi_Fantasy { ; time=0:09:34.68 -- SF5 on a P200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC passes=1 center-mag=-0.3953\
8899237559290/-0.08378373837276828/2244856
params=3.14159265358979/0/3.14159265358979/0 float=y
maxiter=3000 inside=0 logmap=169 periodicity=10
colors=000IAIIAI<3>IGIJHIKII<3>PIIQIIRIITIIRII<3>QII\
PIIPIIQIIQIIPHINCIK7CI03H07<3>H9HHCJGEN<3>GOWGQZETa<\
3>EakEcmGalGakG`jG`h<3>GZeGYdGYdGWcGWa<3>GUZHTYHTWHR\
W<2>HQTHPTHPR<2>HNOHNOHLNHLLHKKGJJ<8>JLKKLKKLKKNKLNK\
LNKLNKNNK<8>QPKQPKQPK<2>RQKRQKTQK<5>VRKVRKVRKWRKWTKW\
TKYTK<7>_UK`UK`VK<2>aVKaVK`WGaVIaVKcVLcUO<2>dTTeTVeT\
YfRZfR`gRagQdgQehQghPjjPkjPmkOokOqjPr<2>lNvlNwmLxmLy\
yKzoKz<5>rHzrHzrHzsGzsGzuEz<2>vDzvDzuGzuHzsJzsKzrLzr\
OzqPzqQzpTzpUzoWzoYymZv<3>kegkfdjhejjghkjhmlgoogpphq\
mhqljrkjrjjshksgkuf<3>mvamw`mw_oxZ<3>pzUqzTqzR<3>szN\
szLszKuzJuzIwzIuzHszHqzHpzHozHlzHkzHhzH<3>czGazG_zGZ\
zGazf<4>_zd
}
frm:MandelbrotBC = { ; Z = Z^E + C
e=p1
p=real(p2)+PI
q=2*PI*trunc(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < 100
}
END 20.0 PAR-FORMULA FILE==================================
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