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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: On the wall opposite my desk hangs a framed print of a painting by the surrealist artist Magritte. It's one of his day-night pictures, titled "The Kingdom of Light". I admire the picture for its unexpected juxtaposition, but about 3 weeks ago I noticed that the frame was hanging slightly crooked. A quick examination revealed that a mud-daubing wasp had started a nest behind the upper corner of the frame, and the weight of the mud was causing the picture to hang crooked. As I studied the nest, the wasp suddenly arrived, carrying a fresh load of mud, which it neatly daubed onto the growing nest. When it had finished, the wasp went straight to the window, which has a small hole about 2cm wide in the corner of one of the panes. It found the hole with no difficulty and went outside to gather more mud. About 10 minutes later it returned with its mud, always knowing exactly where to find the tiny hole in the window. The wasp kept this up every day for about two weeks, then, its nest completed, it disappeared, never to return. I have been keeping careful watch over the nest ever since, hoping to see the new wasps hatch. I wonder if they will instinctively know where the hole is. What a waste it would be if after so much work of the parent, the offspring could not find their way to the inconspicuous hole in the window pane and died without ever reaching the outside world. I'll report on the fate of the baby wasps as the situation progresses. This little bit of diversion has absolutely nothing to do with today's fractal, which I have named "Fractal Coral Reef". The formula is the same one that produced yesterday's image, with the exception that the bailout radius has been raised to 900. The image almost has too much in it, with too many features competing for attention. The coral-like texture in some of the features inspired the coral name. The parameter file is a slow one, requiring over 20 minutes on an average Pentium. The GIF file, which has been posted to: The fractal weather today was quite pleasant, with a spectacular sky like those seen in the Caribbean. A few showers were in the area, though none fell at Fractal Central. The temperature of 80F (26.5C) was about as perfect as it ever gets in this area in mid-August. The fractal cats showed their approval by sleeping on the porch all afternoon. As a side event, the near-record coolness and copious rains this summer have effectively squelched the local environmental fanatics, who have been crying wolf about global warming and drought the past several years. The rain and coolness also have the beach resort owners crying no-profit. And right now I'm crying that it's Saturday night and "Doctor Who" is coming on the local TV station in less than an hour. I think it's the episode about the ship race in space. Regardless, it's time to shut things down and settle into my overstuffed chair for an evening of doing absolutely nothing. If I doze off, so much the better. Until next time, take care, and stay awake when searching for those elusive fractals. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Fractal_Coral_Reef { ; time=0:20:06.62 -- SF5 on a p200
; Version 2000 Patchlevel 13
reset=2000 type=formula formulafile=critical.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+1.706024857266035/-2.508261897988575/2.3\
2331e+008/1/2.5 params=-1/-11/-11/-1.1/0/800 float=y
maxiter=2800 inside=0 logmap=392 periodicity=10
colors=0004er2eu0cw0cy0cz0cz0ay0Zv0Wr0Vo0Sl0Ph0Me0La\
0IZ1GW2DS2CP3AL47I44G53C71A705803A01A00B00B00A008007\
405A24F33K52P81WB<3>0rK0wM0zP0zQ0zS0zS2zS5zU8zU<3>Ls\
VPrWSpWWoWZmWblY<3>peZscZwb_za_z__zZ_zYYzWVzWUzVQzUP\
zUMzSLzSIzQHyPFyPDwOBwMAvM7vL5uL3uK2sI0sI0rH0sI0rH0z\
G0oG0uF0lF0lD0<2>hB2fB2fA3eA4c84b85a77a77a77p3Oz5Qz7\
Ip8GjBFeCC<3>KI3FK1AL0FQ5KVCPZI<2>ejajocpscvwczzcrQ1\
yYDzhMvb4ja7la8lWAm_BoMCoZDhGFpZGrYHsYIsWKuWL<3>wVQO\
04M05<2>L05L05K07K07K07I07<3>H08G08G0820FG08D02D00<3\
>D00D00D00D00D00A005002000000000000F00U00V20V30W41W7\
<2>2cC3fD2jC<2>5ZK7QM8QOAQQBQUCQWDQYFPV<2>FLOGKMGLKG\
MIGOGHPF<2>HU8IV5IW4IY2IZ1K_0Ka0Kb0<2>Mf0Mh1Oi3<3>Qo\
DQpGSrIMsOSuLWvI_wGeyDizBmz8sz5ozKlzL<2>bzS_zVYzWVzZ\
SzaPzbLzeIzfGziDzlBzm8zp
}
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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