Fractal of the Day
by Jim Muth
FOTD -- December 30, 1998
Fractal visionaries:
It's been a slow day here at F.C. as well as on the fractal lists -- a cold, raw day with a temperature of 41F 5C, which was just right for fractal hunting. When conditions are perfect for hunting, I hunt.
As has been the case on most days recently, I went to the MandelbrotMix7 formula for the fractal, although this one would have been slightly faster if I had entered the same parameters into the MandelbrotMix6 formula.
The formula subtracts the Z^(-2) figure from a tiny part of the Z^10 figure. I named the picture "Mandelbrot Necklace" because of the ring of red beads that circles the central midget like a necklace.
When positive and negative exponents are combined, the results are often unpredictable and usually quite interesting, as in the GIF file of today's fractal, which has been posted to Usenet at:alt.binaries.pictures.fractalsand to the WWW at:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Tomorrow will arrive with another fractal and a few more words. Until then, take care, and try for the best.
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======================================
MandelbrotNecklace { ; 39min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1 center-mag=-0.600\
82430338989270/-0.42436405476238610/1.973555e+009/1/145
params=0.005/10/-1/-2/0/0 float=y maxiter=6000
bailout=25 inside=0 logmap=98 symmetry=none
periodicity=10 colors=00064IMNX75M86O<5>k4o<2>Vrt<4>i\
n2<5>AHU76H5BOCJQJORQRSWXT<3>vlY<4>hlSkmcmnn<6>GoxFis\
Ednx6F981XOHsbXbQfMDojRT<3>HVe<4>rAv<6>Qu5<6>2rm<3>Ud\
E<2>oqH<5>vxt<4>Xfp<2>QLT<5>uNr<5>LFU<31>`RTWbT<2>M`l\
B_S1Z7<4>d8pf3tZKiLUD48F<2>D3kG2vH5u<5>LKpmAlc9VV8D9X\
P<7>kvPlwemxdnyc<4>szcWzcZzc<7>Vzc<2>Fzc<10>EzcYzcqzc\
<2>xzc<2>bzc<5>Mzc<5>RzcezctzcAzc<2>OzcSzcWzc_zcczc\
<2>ozc<4>RzcWzcUzc
}
END PARAMETER FILE========================================
START 19.6 PARAMETER-FORMULA FILE=========================
MandelbrotNecklace { ; 39min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1 center-mag=-0.600\
82430338989270/-0.42436405476238610/1.973555e+009/1/145
params=0.005/10/-1/-2/0/0 float=y maxiter=6000
bailout=25 inside=0 logmap=98 symmetry=none
periodicity=10 colors=00064IMNX75M86O<5>k4o<2>Vrt<4>i\
n2<5>AHU76H5BOCJQJORQRSWXT<3>vlY<4>hlSkmcmnn<6>GoxFis\
Ednx6F981XOHsbXbQfMDojRT<3>HVe<4>rAv<6>Qu5<6>2rm<3>Ud\
E<2>oqH<5>vxt<4>Xfp<2>QLT<5>uNr<5>LFU<31>`RTWbT<2>M`l\
B_S1Z7<4>d8pf3tZKiLUD48F<2>D3kG2vH5u<5>LKpmAlc9VV8D9X\
P<7>kvPlwemxdnyc<4>szcWzcZzc<7>Vzc<2>Fzc<10>EzcYzcqzc\
<2>xzc<2>bzc<5>Mzc<5>RzcezctzcAzc<2>OzcSzcWzc_zcczc\
<2>ozc<4>RzcWzcUzc
}
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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