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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal is a picture of a ring around a midget, so that's what I named it. The iterated formula started as a whimsical -11Z^(-1.1)-Z^(-11), but I soon found that setting real(p3) to -1.99, which multiplied the original expression by -0.99, made the fractal far more interesting and resulted in a final image that rates a 7. The parent fractal is too large to fit on the default screen, and must be given one outzoom before it is all visible. When this is done, a curiously distorted Mandeloid comes into view, with a negative tail that leads in a graceful curving arc into a dazzling basin quite unlike any I've seen until now. Naturally, upon finding something I've never before seen in a fractal, my immediate impulse is to dive into it in search of midgets. On my dive today I came up with a midget and a fractal picture that rates a 7. At 10-1/2 minutes, the parameter file is annoyingly slow to render. But don't despair, for relief is but a few mouse clicks away, waiting at the Usenet site: Though today's fractal rates an above average 7, the fractal weather rated a below average 3. The temperature of 78F (25.5C) was comfortable enough, but it was cloudy, and the forecast or rain all week added to the depression. The fractal cats, who seldom get depressed, spent over an hour in the yard before retiring to their favorite chairs for the evening. The philosophy is moving along in high gear, and will soon appear on the Philofractal list. But it's not quite ready yet, so a bit more patience will be required. Until next time, take care, and don't do anything naughty, or you might turn into a fractal. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
RingAround_aMidget { ; time=0:10:36.14 -- SF5 on a P200
; Version 2000 Patchlevel 9
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-5.34265200320681500/+7.73134099829820100\
/6.046723e+011/0.9999 params=-11/-1.1/-1/-11/-1.99/0
float=y maxiter=1200 inside=0
logmap=234 periodicity=10
colors=0002742723873AB4BG4EK5HO<3>7Ke7Ki8Ln8Mr8Mv<9>\
cdygfyjhy<3>voz<3>kMkiEgf7cd0`<3>hIkiMnjQpf1VZQLRnC<\
3>T_NUWPUSSUPU<3>iOblOdbIUTDJJ89<6>aWNdZPgaR<3>qnZ<3\
>cTb`NcYIbRD`NE_PFZSGaTHeXIhXJkYKp<2>ZNwZOyZOzYNy<3>\
XNpWNnWMk<3>UMfUMeUMd<3>NDULBSJ9PI7N<3>CCNBEN9FN8GN7\
HN<8>UFLWFLZFL<3>gFL<3>s_ivdopbej`We_M<7>gbFgbEgbD<2\
>gcAgcAeaB<8>ROGQMHOLH<3>IFJ<3>gA9m96s84y72<3>`F5UG5\
OI6<2>6N7<5>WQC_QDcRE<3>tSH<2>L0F<3>okTvvWpwV<3>VyVP\
zVKzV<7>8tD7tB5s9<2>1q30q11jD<3>5Jw<3>LDmPCkTBi<11>r\
3q
}
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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