Fractal of the Day
by Jim Muth
FOTD -- December 25, 1998
Fractal visionaries:
Today (Dec 24) was perfect! Yes, there's the last minute rush to contend with, but for the first time in almost three decades here at fractal central, the ground and trees are covered with snow -- 3 inches of the fluffy white stuff. The temperature of 24F -4C with cloudy skies insures that the snow will still be around for Christmas.
There is something about this darkest time of year that demands a celebration of some kind. Nearly every culture on Earth celebrates the winter solstice -- each with its own special festival, but all ultimately celebrating the coming of the light. (How strange it must seem in the southern hemisphere, where the seasons are reversed.)
I celebrate the return of the light by the frantic rushing that the Christmas festival has turned into. But behind the rushing lurks a haunting feeling -- a feeling of some wonderful but forgotten thing that I once had but have now lost. And to me, this time of year, with its gifts and traditional music and family reunions, and most of all its nostalgia, is a striving to return to whatever it is that I long for.
So to all my fractal friends, too numerous to mention individually, (except for Dr. J, who is in a universe by himself), I wish a joyous festival time, and may all people ultimately find what they long for.
Today's fractal is a decoration, an ornament to hang on the tree. I found the midget lurking in the difference area around Z^0.9. The elements around the midget resemble candy canes, so I named the picture "Holiday Mandelbrot".
The GIF file has been posted to Usenet at:alt.binaries.pictures.fractalsand to the W.W.W. at:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Tomorrow I'll arrive on schedule with another fractal. Until then, take care. (I wonder how many fractals Santa could fit into his bag.)
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=========================================
Holiday_Mandelbrot { ; 30min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1
center-mag=-0.47592524818786550/+0.0193688955148758\
3/2.670681e+007/1/-87.499 params=1/0.9/-1/0.901/1000/0
float=y maxiter=2100 bailout=25
inside=0 logmap=67 symmetry=xaxis periodicity=10
colors=000sQi<5>yVo<7>RgkMhjIhjEhjFffGdc<10>M44M11O33\
<25>nnboocnnb<24>TXO<8>eWtfWwhXv<6>tbp<5>oXmnWlnVlnUk\
<10>yUfzUezUezUd<4>zUbzUbzUazU`<7>zUXzTWzUV<4>zVSzVSz\
WRzXR<9>zgLzhN<8>rqbqrdpseotf<4>kyjjzkhzl<4>rzptzpvzo\
xznzzm<25>zzW<2>zz0<8>zzs<4>zzN<10>zzQ<3>zzE<4>zzW
}
END PARAMETER FILE===========================================
START 19.6 PARAMETER-FORMULA FILE============================
Holiday_Mandelbrot { ; 30min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=critical.frm
formulaname=MandelbrotMix7 passes=1
center-mag=-0.47592524818786550/+0.0193688955148758\
3/2.670681e+007/1/-87.499 params=1/0.9/-1/0.901/1000/0
float=y maxiter=2100 bailout=25
inside=0 logmap=67 symmetry=xaxis periodicity=10
colors=000sQi<5>yVo<7>RgkMhjIhjEhjFffGdc<10>M44M11O33\
<25>nnboocnnb<24>TXO<8>eWtfWwhXv<6>tbp<5>oXmnWlnVlnUk\
<10>yUfzUezUezUd<4>zUbzUbzUazU`<7>zUXzTWzUV<4>zVSzVSz\
WRzXR<9>zgLzhN<8>rqbqrdpseotf<4>kyjjzkhzl<4>rzptzpvzo\
xznzzm<25>zzW<2>zz0<8>zzs<4>zzN<10>zzQ<3>zzE<4>zzW
}
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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