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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal rates a most exceptional 9. This is not due to its artistic merit, which is mediocre at best, but to its mathematical merits, which are unlike anything I have yet come upon. The name I gave to the image tells it all -- it is a picture of a midget on "The Brink of Oblivion". Oblivion in this case means an existence only as a vague outline in the random dots that fill the lower left half of the image. The imag(p3) parameter tells the entire story. The slightest change makes the greatest difference. If the value is reduced to 26.6, the midget is all there; if it is increased to 29.7, the midget totally evaporates. A midget that had no reality to start becomes even less real. The actual value of 29.647, which equals a bailout of 129.647, catches the midget half there and half gone. However, the midget never totally vanishes, for even when the screen becomes a total blank, the midget's ghost remains in position, and can be revealed by rendering the scene with an inside setting of something like bof60. Since so much of the scene consists of inside area, and the single-pass algorithm must be used to pick up all the bits and pieces, the image is a slow one, requiring 25 minutes on a slow old Pentium 200mhz. But relief is at hand on the internet at the web sites of Paul and Scott, where the image will soon be posted. Paul's site can be found at: The fractal weather was near perfect today, with brilliant blue skies and a temperature of 88F (31C). The fractal cats made up for the time they lost yesterday by spending most of the afternoon in the yard, watching for the cat that lives across the street. But luckily for someone, the other cat never showed up. That's it for now fractal fiends. Until next fractal, take care, and always be all there. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
TheBrinkOfOblivion { ; time=0:24:11.35--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-1.789309750688749/-0.9580640953043432/\
8290.843/1/39.999 params=1/-1.2/-1.2/1/-1.8/29.647
float=y maxiter=1000 inside=0
logmap=306 periodicity=10
colors=000wDkwCmvAov8qv7sv5uv4vpBtjIsdPrZWpTboNhnK\
QfI7_K9YMBXODVQFUSHSUIRWKQYMO_ONaQLcSKeTJgVHiXGkZE\
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PfeOedNedLecKecJebIebKgcMhdNiePjfQkgSlhTmiVnjWokYq\
kZrl`smatncuodvpfwqgxriys
}
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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