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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: After a long fractal drought, we finally have a fractal that rates an 8, a rating that equals much above average on my conservative 0-to-10 scale of fractal worth. Actually, the fractal itself is quite humdrum in the mathematical sense. Most of the high rating is based on the coloring, which in a moment of excessive fractal zeal, I devoted an entire half-hour to. The parent fractal of today's scene consists of a Mandelbrot figure with several large irregular open holes at the end of some of its filaments, and strings of smaller holes at the ends of others. There is also a string of holes extending outward from the center of East Valley. Today's image lies in an isolated, cut-off feature near this string of holes. The string-of-holes nature of the area in which today's image lies is reflected in the four strings of holes radiating from the brilliant red flower around the central midget. Since there are four of these 'arms', I named the image "Quadrapus Minibrot". (I have no idea what a real 'quadrapus' might be, though the fractal cats might fit the description.) The formula of the image uses the golden ratio, 1.618..., which often appears in the designs of nature. The ratio also appears at places in the Julibrot, where least expected, but that's another story for another day. The render time of 3 minutes from the parameter file is close to the time required to go online and download the completed GIF image from Paul's web site at: The fractal weather Thursday here at Fractal Central featured a pleasant break from the oppressive heat and humidity that usually plagues this part of the world at this time of year. Lots of clouds and a cool breeze off the ocean held the temperature to 79F 26C. The grass, still wet from an early morning shower, was a bit too uncomfortable for the dynamic duo, who prefer their paws dry, but they did spend a few relaxing hours on the dry porch, watching the local birds. And I'm also going to relax -- but not until I finish the work that needs to be done. Until next time, on Monday the 28th, take care, and keep the ratio golden. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Quadrapus_Minibrot { ; time=0:03:39.53--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-2.85097707624026200/-3.007861364773440\
00/5821280/1/-115/1.56494616987412627e-008
params=1.5/1.618/1.5/16.18/0/0 float=y maxiter=400
inside=0 logmap=71 periodicity=10
colors=00020K10K00K40MBAQI9WPMcXcadt_lzZtzXlzUdvRX\
qOPlLKgIPcFU_C_W9eR7lM4sI1yE0z90zd0zZ0yS0sB0nB2gC5\
cE7XF9TFCMHEIIHCKK8KL7PH5WCBTEHRFLOFRMHXLHaIIgHIlE\
KsCKyBLz8Lz7Mz5Mz8Pz9RzCTwEUtFWoIXlKZgMadOc_PdXTeT\
UgPXiLZjI_lIZlIWlBTg4Pc0PZ0PU0tU0PW0PW0PW0PWIIa09W\
0BW0BX0BX0CX0CX1EX1EZ1EZ1FZ2FZ2FZ2HZ2H_4I_4I_4I_5K\
_5Ka5La5La7La7Ma7Ma7Mc8Oc8Oc8Pc8Pc9Pd9Rd9Rd9RdBTdB\
TdBUeBUeCUeCWeCWeCWgEXgEXgEZgEZgFZgF_iF_iF_iHaiHai\
HdjHggIjdLnaOqZRtWUtTUtPUtITtBTt4Tt1Rt2Rt5Rt7Pt9Pt\
BPtEOtFOqIOnKMjMMgOMdRLaTLZWLWXKW_KXaK_dPacXcadd_l\
dZtdXzcWzcUycTwcTtcUscWqcWncXlcZicZgd_dd_cda_dcZdc\
XddUdeTdePddXaXdZPlWItTBwR4vT0vU0tW0tX0sZ0s_0qa0qc\
0od0ne0ng0li0lj1jl1jn2io4iq5gs7gt8et9dt9dtBctCctEa\
tFatH_tI_tKZtKXtLXtMWtOWtPUtRUtTTtTTtURtWRtXPt_Otc\
OteMtiMtlLtoLtsLtvKtyItzKtzItzItzItzItzItzItzItzIt\
zItzItzItzItzItzItz5tq4to }
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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