Fractal of the Day
by Jim Muth
FOTD -- December 22, 1998
Fractal visionaries:
A dull, cloudy day with a temperature of 54F 12C proved to be perfect for fractal hunting. For the hunt, I once again turned to the MandelbrotMix7 formula, and came up with several unusual scenes.
On an unrelated and absolutely cynical note, it was also a perfect day for our city school system. The results of the latest third-grade literacy tests came in, and two city schools posted perfect scores. In those two schools, zero percent of the third-graders passed the test. What worries me is that on several school buses are written the words, "drive carefully, this bus holds the future of our nation." Maybe if those students had fractals to study . . .
Luckily for me, the fractal search went better than the third-graders' test. That MandelbrotMix7 formula holds no end of surprises. My recent "Teardrop", (or shark as some see it), fractal investigates the area between Z^0 and Z^(-1). Today's fractal focuses on the area between Z^0 and Z^1.
There are lots of interesting images in this area when the small differences between close powers of Z are multiplied by increasing factors, until fractal detail appears. Today's picture shows a scene in the fractal that appears when the difference between Z^0.5 and Z^0.5001 is multiplied by a factor of 1150.
I named the image "Kali Yuga", a term I borrowed from the Hindi religion. The words indicate a period of hardship on earth. There is no real reason in the picture for such a name; I simply liked the sound of the words as I studied the image.
The GIF file has been posted to:alt.binaries.pictures.fractalsand to:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Tomorrow, I'll have another image created with today's formula. Until then, take care, and do you know why people hate cynics?
Jim Muth
jamth@mindspring.com
START FORMULA================================================
MandelbrotMix7 {; 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=pixel:
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| <= l
}
END FORMULA==================================================
START PARAMETER FILE=========================================
Kali_Yuga { ; 1-1/4hrs on 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 center-mag=+4.801729873393\
365/+6.01937457146125800/2563.056/1/-24.999
params=10/0.5/-10/0.5001/1150/0 float=y maxiter=3600
bailout=25 inside=0 logmap=194 symmetry=xaxis
periodicity=10 colors=000lFR`JenRsaPtq6H<2>WJjCKUHLbLM\
k`D9<2>SLhfNqdOOZNZUNioQqfPrYOsX43<2>RJgkLHLH`6Vt3Pt\
<2>5Tw<6>RaXUbU_Z`<2>qQtduX<7>fho<4>2Gv<4>Ko9HsNEv_Cy\
l<7>AtbZOG<6>nqOpuPqiOqZO<4>T7B<3>6J9<3>UR`<5>LHPNKddm\
sCH8pcMbVcqv9gjPYZdnXtxbZfVi1u0DcTQh7P`OPUdiPleUw<2>TO\
t9GJFJWKLhkDFJAoMHrmRcJu6McWFI0JKJMMaVPtmyD`eZ2cgiQ4ZO\
VDtGJc`5vNJ4i<2>OJrM57NBOOHd91P<2>LIlojl<2>VTrHA2LHUX5\
lTEpf6w`CvVIuowwGSWf1Q<2>TImkkXcbdWVlRV9<2>PPhYp0VTJSQ\
aHY8<2>NPhzYz_NnO8D<2>PKiJND<2>ONi_oXWedSWlLOi<2>ONrfl\
V`ccVdlSeTYfbVggThkRipNjZOkfPlmXmeTnmVoiTpmRqqlri`solt\
`<2>Vwo4xdUyPSz_QzjHzLKzXNzhOzdPzjPzoIzUAzV2zV<3>czf\
<3>DzjZzsJzoXzZbzbWzkyzB
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Kali_Yuga { ; 1-1/4hrs on 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 center-mag=+4.801729873393\
365/+6.01937457146125800/2563.056/1/-24.999
params=10/0.5/-10/0.5001/1150/0 float=y maxiter=3600
bailout=25 inside=0 logmap=194 symmetry=xaxis
periodicity=10 colors=000lFR`JenRsaPtq6H<2>WJjCKUHLbLM\
k`D9<2>SLhfNqdOOZNZUNioQqfPrYOsX43<2>RJgkLHLH`6Vt3Pt\
<2>5Tw<6>RaXUbU_Z`<2>qQtduX<7>fho<4>2Gv<4>Ko9HsNEv_Cy\
l<7>AtbZOG<6>nqOpuPqiOqZO<4>T7B<3>6J9<3>UR`<5>LHPNKddm\
sCH8pcMbVcqv9gjPYZdnXtxbZfVi1u0DcTQh7P`OPUdiPleUw<2>TO\
t9GJFJWKLhkDFJAoMHrmRcJu6McWFI0JKJMMaVPtmyD`eZ2cgiQ4ZO\
VDtGJc`5vNJ4i<2>OJrM57NBOOHd91P<2>LIlojl<2>VTrHA2LHUX5\
lTEpf6w`CvVIuowwGSWf1Q<2>TImkkXcbdWVlRV9<2>PPhYp0VTJSQ\
aHY8<2>NPhzYz_NnO8D<2>PKiJND<2>ONi_oXWedSWlLOi<2>ONrfl\
V`ccVdlSeTYfbVggThkRipNjZOkfPlmXmeTnmVoiTpmRqqlri`solt\
`<2>Vwo4xdUyPSz_QzjHzLKzXNzhOzdPzjPzoIzUAzV2zV<3>czf\
<3>DzjZzsJzoXzZbzbWzkyzB
}
frm:MandelbrotMix7 {; 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=pixel:
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| <= l
}
END 19.6 PARAMETER-FORMULA FILE==============================
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