|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Today's fractal reminds me of a spider's web on a dewy morning. And the midget at the center could be the spider waiting for its prey. With little hesitation I named the image "A Spider and a Web". The dewdrops on the web must be supplied by the imagination, which limited the rating to an average 5. The outside of the fractal has been rendered with the <tdis> option, which calculates the total distance the points travel before escaping. I chose this option because the normal equal-iteration-band method produces a decidedly inferior rendering. I rendered the image with the <passes=b> option because with today's image it is the fastest, and also because it is the most fun to watch in operation. The parent fractal first appears as a rather normal Mandeloid with extra bays extending along the negative X-axis. An outzoom eliminates all resemblance to normalcy however, when a huge empty circle looms into view to the right of the Mandeloid. This circle is apparently the extension of the negative real part of the fractal, which has gone past infinity and returned from the opposite direction. The sharply defined borders of the circle would seem to indicate that no midgets are to be found there. But the small sharp spikes around the circle offer a bit of hope. Examining the northern spike, I found it filled with signs of midgets. When I zoomed in on one of these signs, I found today's scene. What today's image lacks in quality it makes up for in speed. The parameter file renders in less than one minute on most machines. And if the minor hassle of running a parameter file is too inconvenient, the finished image may be found posted on the WWW at: The fractal weather today (Saturday) featured a temperature of 56F 13C, heavy clouds, and occasional light rain. The rain amounted to only 1 mm or so, but it was enough to keep the grass wet and the fractal cats indoors. Fractal cats are unhappy when kept indoors, so the cats spent most of the day showing their unhappiness by doing things such as sitting in obvious places and sulking with their backs to me, thrashing their tails. As for myself, I'm neutral about the rain. But I'm not neutral about fractals, and I've got 24 hours to find the next one. The time to start the search is right after I enjoy a relatively slow day off. Until the next FOTD, take care, and be at peace with almost everything. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
A_Spider_and_a_Web { ; time=0:00:58.65--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=b
center-mag=+11.08677453289806/+10.44004619354802/3\
4698.16/1/-132.5/7.51154181910518304e-009
params=1.3/2/-0.26/3/0/0 float=y maxiter=3200
inside=255 outside=tdis periodicity=20
colors=000BT`4UZ8RbBPeENhHLlKJoNHrXKmfMhoOcpPepQgq\
RiqSkrTmrTolSqfSr`RsVRuPQvKQwLOxMNxNMxOKyPJyQIyRHy\
VNmZTbaYRecGhh5mlProhjhdbbaVXYNRVFLR7FO6GS6HW6I_6J\
c5Kg5Lk5Mo5MsALfFLVKKIPK6MA3K00N45Q8ATCEWGJZKO`OSd\
RagTkjVuo_btdKxh1x`2xU2xN2xF3x83x13o54g94ZD5RH5JK5\
GM5EN5JCTX9bj7laVWTqFRpCPoANn8Lm6Kl4Rf6Xa7cX9iRApM\
CvHDhJKVLRHNY3PdQeiOfWMgIKh4WlGfoRqrafigW`mLSrVRic\
QalQUeSY_UaUWeNYiH_mBaq5btCfiJjZPnPWrEav4wnUpgaiai\
bVqWPy`TxdXxi`xmdxnepofiogbphWpiPqjIqjBrf9rc8r_6rX\
5rT4rQ2rM1rJ0mL1iM2eN3`P4XQ5TR6PS6MQCJOIHMNEKTCJYA\
IW8IU6IS5IQ3IO1IM0IL7HJDHIJHHPHGVHF`HEnUsmVrkWrjXq\
iZph_pg`ofaoebndcncembflagl_hkZikYjjXkjWmiVnhUohTp\
gSqgRrfQsfOqeMpeKndImdGkdEjcChcAgb8eb6dbDgZJjVPmRV\
oO`rKfuGlxCrz9nyEjyJfxObxT_xXWwaSwfOvkKvpHvt4LCFsp\
EqlDohCmdBk`AiX9gU7dQ6bM5`I4ZE3XA2V6ul1sk2rk2qj2oj\
2ni2mi2kh2jh2ig2gg2QQf000
}
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==================================
|
times.
