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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Fractals are total abstractions. There is no 'real' Mandelbrot set or Julia sets lurking in as-yet-undiscovered hiding places. It is all about numbers and the things numbers do. But we are a part of reality and cannot escape it. Our minds are wired to see 'real' objects even where none exist. Perhaps the strongest evidence of this wiring is the way we so often invent, then actually see, faces in random patterns such as clouds. I could find no face in today's image, though I did find a bagel. In fact, the whole scene is of one big bagel, which is why I named the image "Fractal Bagel". The midget lies in a chaotic filament on the northwest border of the fractal that results when the expression Z^1.44225+C is iterated by the MandelbrotBC1 formula, using the <recip> function. I chose the value 1.44225 as the exponent of Z because it is the cube root of 3, and whole-number roots of whole numbers seem to make more interesting images. The rating of 5 is average, and says nothing about the image. The proper function to use with the MandelbrotBC1 formula is <floor>, but most other functions also produce interesting fractals. In today's case I used the <recip> function to see what it would do. On my machine, the parameter file takes over 1/2 hour to run. But my machine is old and tired, and most machines will render the image in less than 15 minutes. Those who would rather do no rendering at all can find the GIF image posted to the W.W.Web at: The fractal weather today (Sunday) suffered a setback, with only a few brief periods of sun and too much wind for the sensitive fractal cats. The temperature of 75F 24C was pleasant enough, but the wind limited the cats to a couple brief outings. A heavy shower fell after dark, bringing a less-than-perfect end to the inauspicious day, but by this time, the cats had long since given up and settled into the world of sleep. The Philofractal list is still down, so the philosophy is still in cold storage. And I'm hot to get the day's work started. Until next fractal, take care, and fractals are real because we see them, but are they really real. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Fractal_Bagel { ; time=0:34:17.78--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=recip passes=1
center-mag=-1.08717603028377500/+1.205061829294592\
00/1.889778e+011/1/42.4995365922868444/-0.00193853\
530842458266 params=1.44225/0/0/0 float=y
maxiter=45000 inside=0
colors=000ebHfcFgcEhdDieCjfBkfAlg9mh8ni7oi6nj7nj8n\
j9njAnjBmjCmjDmjEmjFmjGmjHlkIlkJlkKlkLlkMlkNkkOkkP\
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Q4YP3XO2XN2XMa_Lb`Kc`JdaI
}
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
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