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Fractal of the Day
by Jim Muth
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Fractal enthusiasts and visionaries: Today's fractal has a rather playful frivolous feel about it, which inspired the name "Mandelbrot Playpen". The patches of flat color remind one of a child's first drawing -- all the more reason for the name. The formula that created all this fun is Z^(-11)+(1/Z)+C. The parent fractal is an irregular island floating in emptiness, with today's midget hiding in one of the more remote corners. The parameter file takes only a minute to render. The image file has been posted in GIF format for today only. This is because the JPEG version suffers too much degredation. That image may be found posted to Usenet at: The fractal weather was cloudy and cool today, with occasional sprinkles of rain. The temperature of 56F (13C) was good enough for a playful and not too serious fractal. As for the philosophy -- I just didn't have it today. But I'll try again tomorrow, when I shall reappear with another fractal. Until then, take care, and be free, but not too free. Jim Muth jamth@mindspring.com |
START FORMULA==============================================
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 FORMULA================================================
START PARAMETER FILE=======================================
Mandelbrot_Playpen { ; time=0:01:02.28 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=+0.17601866980631000/+0.5211272526815811\
0/525689.4/1/55 params=1/-11/1/-1/0/0 float=y
maxiter=1250 bailout=25 inside=0 logmap=19
symmetry=none periodicity=10 cyclerange=1/252
colors=000FAKIaNLPC5KUBHSHEEzUFJSvtE8n4M<2>UA6IhGKK\
CLH8ME4RD4<2>OC1HnlKVPyl_l_O_OCLdgMQMAW3HM2urd<2>VM\
BG0CJ48L84ln3_V2SvhQfUORFG1zcFQp5_a9I3f4AW3HM2ZZ2TN\
1MEc<2>NCAw8Q<2>WB7RrL<2>OM6eorWWSmJIdL_ZIOTFC`xh<2\
>QOCz_JfOAItoKeZMRIRBdw8JjADZB7NMlNHP4mTEVFccpFbwIU\
cLLKou88W9GM5IYhKSYLNNMHCQ88PA5OB3cXe3lM<2>IL61x97k\
7C_5IO3QDq<2>NCE1Pptn4ha3YP2x_CeO6CaTGTJKKA92EAfZFW\
NJMCW4wT7cQAKR`cPOKxcPWnGTaBQP6KQOYR80Sj8TVGUGkVkZW\
O9XJGYAUZiR_RP`EjaYdbCcc6Yd4Se2hfC`g8Uh48itGjTPk0Ol\
1fme_mSTmEdmFZmATm5LmqMm_NmIamCXmWSmGAmBRmzPmeOmL8m\
TGmF4mADmmHmXKmHumLcmBHmd<2>MmBCmc<2>LmAdmz<2>RmGjm\
F<2>Tm4emgWmM_m5Vm3Rm27me1mG9mRXmu<4>amzbmz<40>cmz
}
END PARAMETER FILE=========================================
START 19.6 PAR-FORMULA FILE================================
Mandelbrot_Playpen { ; time=0:01:02.28 on a p233, SF5
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=ident passes=1
center-mag=+0.17601866980631000/+0.5211272526815811\
0/525689.4/1/55 params=1/-11/1/-1/0/0 float=y
maxiter=1250 bailout=25 inside=0 logmap=19
symmetry=none periodicity=10 cyclerange=1/252
colors=000FAKIaNLPC5KUBHSHEEzUFJSvtE8n4M<2>UA6IhGKK\
CLH8ME4RD4<2>OC1HnlKVPyl_l_O_OCLdgMQMAW3HM2urd<2>VM\
BG0CJ48L84ln3_V2SvhQfUORFG1zcFQp5_a9I3f4AW3HM2ZZ2TN\
1MEc<2>NCAw8Q<2>WB7RrL<2>OM6eorWWSmJIdL_ZIOTFC`xh<2\
>QOCz_JfOAItoKeZMRIRBdw8JjADZB7NMlNHP4mTEVFccpFbwIU\
cLLKou88W9GM5IYhKSYLNNMHCQ88PA5OB3cXe3lM<2>IL61x97k\
7C_5IO3QDq<2>NCE1Pptn4ha3YP2x_CeO6CaTGTJKKA92EAfZFW\
NJMCW4wT7cQAKR`cPOKxcPWnGTaBQP6KQOYR80Sj8TVGUGkVkZW\
O9XJGYAUZiR_RP`EjaYdbCcc6Yd4Se2hfC`g8Uh48itGjTPk0Ol\
1fme_mSTmEdmFZmATm5LmqMm_NmIamCXmWSmGAmBRmzPmeOmL8m\
TGmF4mADmmHmXKmHumLcmBHmd<2>MmBCmc<2>LmAdmz<2>RmGjm\
F<2>Tm4emgWmM_m5Vm3Rm27me1mG9mRXmu<4>amzbmz<40>cmz
}
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 19.6 PAR-FORMULA FILE==================================
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times.
