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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: While the mini-debate about the promptness of the FOTD rages, the FOTD goes on. Today's image has pinwheel-like characteristics. I could have named it "Pinwheel", but being one to do things differently, I have named it "Whinpeel", which is the same word with a few letters transposed. The expression 0.03(Z^50)+1.5(Z)+(1/C) was iterated by the MandelbrotMix4 formula to create the parent fractal, which is a Mandeloid with a bulb at the tip of the negative tail. Beyond the bulb lies an area of tiny dots, each of which expands into an entire fractal world when enlarged. Today's scene lies deep within one of those dots, on an axis of N-S symmetry that is removed from the actual X-axis. The coloring of this fractal was a bit problematical, with broad gradients giving a basically featureless image, and narrow ones not much better. I finally settled on one of the random palettes sometimes created by striking the The parameter file, which is attached below, takes 3 minutes to run on a 200mhz Pentium machine after the minute or so required to set it up and start it. The file of the GIF image takes only about 30 seconds to download from the Usenet binary group: The fractal weather today was once again perfect, though the temperature of 68F (20C) was a bit chilly for the ears of the fractal cats, who chose to rest in the sun on the porch rather than prowl the wilderness of the yard. The philosophy is coming along nicely, and in a couple days will burst forth in all its glory, but for the moment, the FOTD has come to an end. I'll have another fractal in 24 hours. Until then, take care, and you don't need to go searching for your fractal -- fractals are everywhere. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Whinpeel { ; time=0:03:09.22 -- SF5 on a p200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-2.37821892513348800/+0.15212393450154800\
/4.678664e+010 params=1/50/50/1/-0.97/0 float=y
maxiter=1400 inside=0 logmap=58 periodicity=10
colors=000<3>000000000<3>000zYwbdz000uPc0000006eEmzF\
000000q26<3>AtOZFTFmTKfYP_be54zzUcrBK_4PWO3uNHfYT5J<\
2>UNaYtU<2>V_dxvshgmV20UGMwQphSkIBWMH_QNc5qIEhRM`_6V\
_BojIgiO_hDKQJ00PQaMT0<2>STX75AFDMNLXt3p<2>_Ni8KjnVy\
wUzcUpZTkfqIj94E5Nrd6eZPjQf7qNvlPB0GLFUwLEhPT6vVIgan\
EygJs`OmTP6URPSXoH`wOFCPiw<2>TXkt_FfWUcnp<2>WYi45yDD\
sMLmVQd<2>UTgDB0JHFPNUSkj<2>UXg3gvyjVqeZiaaaXdWcKVcW\
7c`FccNce6cIEcRMc_fc1wcp6c_EcbMceUcd<2>Ucgsczjcsacmc\
cc_meXmfimupmz<2>ZmkDmAJmMPmXTm1<2>UmY8mtEmpJnmPpj2p\
UGp`VpF<2>Up`0tVFta4tb7tK<2>PtacwfZwgSwVTwapws4whDwg\
MwgZwdXzeWzfVzgKzO7z9<2>Pz_jzewzn<2>`zhXzHWzQVzZtzJk\
zq<2>YziGzH<2>Rza8zvIzc<2>RzfMz_QzcVzTUz`EzaKzcPzeRz\
bSzdTzfGzWLz_QzcAzt<2>Pzjtzu<2>_zjOzq<2>TziZziXzhVzg\
5zCEzNMzYDzdFzVIzK
}
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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