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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: As I related a couple weeks ago, a wasp has made her mud nest on the corner of the Magritte picture hanging on the wall opposite my work desk. When the wasp was building her nest and laying her eggs, I wondered if, when the new wasps hatched, they would be able to find the small hole in the window their mother had used to gain access to the room. Early this afternoon, while I watched, the first cell in the nest hatched out a fully-developed wasp, which flew immediately and directly to the proper window. Alas, the young wasp buzzed all across the inside of the window pane, but could not find the coin-sized hole which its mother had been using. After watching for a few minutes, I opened the window and let the newborn wasp fly free. The nest has 11 cells, so I might have to repeat my life-saving action 10 more times. But before that happens, it's back to fractals. Once again I used the M-Mix4 formula and the parent fractal as sources for the FOTD. (And yes, I'm working on a M-Mix3 formula, but I can't quite decide what I want it to do.) Today's picture shows a midget that lives in the parent fractal, in an area that on the surface appears most unlikely to hold midgets. But fractals can be deceiving, and sometimes they just don't do what they're supposed to. Today's midget, being from an area that is not supposed to have midgets, is one of the most fantastic I have yet found. In fact, it's a bit too fantastic, with too many disorganized and unrelated structures and no central theme. As a result, it rates only a 5. I named the picture "Fractal in a Playpen". The name was inspired by the two prominent dark areas in the lower-left and upper-right corners, which appear to confine the gaudy colored midget to the center of the screen. The parameter file runs in 11 minutes, a large improvement from yesterday's 2-hour leviathan. But it is still slow enough to make a download of the GIF image file the wiser choice. The GIF file may be found on Usenet, posted to the binary newsgroup: The fractal weather today was still comfortable, but the brilliantly clear atmosphere of the past few days has been replaced by the haze that is so typical of the east coast in summer. The temperature of 81F (27C) was ideal for the fractal cats, who prowled in the yard a good part of the afternoon. My thoughts grazed some deep philosophical byways as I watched the cats in the yard, but nothing crystallized enough for me to write about. As always, I'll have another go at it tomorrow. Until then, take care, and don't get stung while watching a wasp hatch. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Fractal_in_Playpen { ; time=0:11:16.68 -- SF5 on a p200
; Version 2000 Patchlevel 14
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+4.008671473993992/+1.645216203990216/230\
54.52/1/114.999 params=-1/-11/-11/-1.1/0/800 float=y
maxiter=1500 inside=0 logmap=129 periodicity=10
colors=000F7KF7KFAKFFKFGKFLIJOGOSESXCX_A`c9dg7ij6mm4\
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zTlz<2>LuzIxzFyzCzz<3>0xz0xz0rz0vz<13>0vz
}
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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