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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's fractal has no quadratic midgets. I've been producing almost nothing but such midgets lately, and it might be time for a midget break. Oh, there are several midgets in today's picture -- one prominent one in the lower left quadrant, and others scattered throughout the scene, but they are not the usual quadratic midgets. Instead of midgets, today's image features trees -- three trees in fact, which is the name I gave to the picture. I rated the picture a 5, mostly because I was distracted by watching the election returns, and gave too little effort to nursing my fractal. Yesterday's image featured the number known as the Greek letter pi. Today's fractal features the number known as the golden ratio, which has a value of 1.618033989..., and which by a strange coincidence happens to be the square root of 5, plus 1, divided by 2. To make the fractal doubly golden, I also entered -1.618033989 into the MandelbrotBC formula as the second parameter. The parent fractal is a curious thing, an obvious Mandeloid standing on its head, with much chaos and many filaments around its main bay and rudimentary buds. The trees of today's image are located on the WSW shore of the bay, just below the second discontinuity. This parent fractal is filled with interesting nooks and crannies, all of which deserve a more thorough examination. Perhaps I'll return to it for tomorrow's C-FOTD. A benefit of an image with a magnitude as low as today's is that it is fast. The parameter file renders in only 26 seconds on a Pentium-200. On one of those 800mhz machines, it will finish in 10 seconds or so. But if running the parameter file is too much of a hassle, the GIF image file has been posted to the Usenet binary newsgroup: The fractal weather today was surprisingly mild. The temperature of 64F (18C) and partly sunny skies lured the cats outdoors, where they spent the afternoon lounging on the porch, watching the insects hovering around the still-blooming marigolds. For all those waiting with bated breath for my next round of fractal philosophy, there is nothing but disappointment. I'm sorry, but too much work combined with too much distraction left nothing to act as inspiration. So the philosophy will once again be delayed, but eventually it will appear -- it always has in the past. For now however, I'm settling down to watch the election returns to see how my guy makes out. Until tomorrow, when depending on the outcome, I'll be either pleased or disgruntled, take care, and may your wisest wishes come true. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Three_Trees { ; time=0:00:26.42 -- SF5 on a P200
reset=2001 type=formula formulafile=branchct.frm
formulaname=MandelbrotBC passes=t
center-mag=0.163588/-1.36873/6.622925/1/-142.5
params=1.618034/0/-1.618034/0 float=y maxiter=6000
inside=0 logmap=4 periodicity=10
colors=000F9gFIgFAjF3mO0pX7mcIllSisagzjfxVVuFLr0A70A\
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IzAJupP0cf0Ta0LYCATP1PalfF`aMPYTrJzuJz
}
frm:MandelbrotBC = { ; Z = Z^E + C
e=p1
p=real(p2)+PI
q=2*PI*trunc(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| < 100
}
END 20.0 PAR-FORMULA FILE==================================
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times.
