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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: For today's fractal we once again break out the MandelbrotBC1 formula. This time we draw the Z^1.6+C Mandeloid fractal as it appears 131 levels up the logarithmic spiral. At this lofty height the fractal appears as a large open area broken by several spectacular discontinuities. Many small protobuds line the southern shore, which is marked by an area of chaos that extends far inland, constantly trying to organize itself into well-defined filaments as it dies out, but never quite succeeding. Many tiny midgets lie in this chaotic area. Today's scene, with its even tinier midget, lies in the suburbs of one of these tiny midgets. When I first saw today's image, I didn't know quite what to make of it. Eventually, the impression of billowing clouds of smoke came to mind, and I named it "Mandelbrot Billows". I'm not quite satisfied with the colors. Dark blue would give a better impression of billowing smoke clouds than the present dark green. Yet the image has a kind of uniqueness that made me decide to leave it untouched. As a result, I can rate the image at no more than a 5, a rating that is average. But don't be disappointed -- even an average fractal is well worth a look. To have that look at today's fractal, one may run the attached parameter file and wait 25 minutes, or give Paul and Scott a chance to render and post the image and download it from one of their web sites. The URL of Paul's site is: The fractal weather Saturday featured sunny skies, light winds, and a balmy temperature of 73F 23C. It was absolutely perfect for the fractal cats, who were in and out all day. But since we normally see ice at this time of year, some local cold weather lovers are beginning to ask where winter is. And of course, those who enjoy having something to worry about are once again fearful that it is the beginning of the global warming that will eventually end life on earth. As for myself -- I see nothing more apocalyptic than an unusually warm and pleasant Autumn in the local area. Regardless of the import of the mildness, it's another perfect day, it's not yet 10am, and the cats are already worrying me to let them out. When the fractal cats want to be outdoors, they had better be let out, or else they become most annoying. So I'm off to open the door. Until next time, take care, and what ever happened to the 'nuclear winter' crisis? Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Mandelbrot_Billows { ; time=0:25:21.65--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=+0.29929135794286550/-1.244993106283451\
00/1039074/1/-142.5/2.06540170383240351e-009
params=1.6/0/131/0 float=y
maxiter=10000 inside=0 logmap=-655
colors=000725825A47B58D7AE8BDADBBEADG8EH7GI5HK4HK2\
HK1IK0IK0II0II0KI0KI0KI0KH0LH0LH0LH0LH0LH0NI0OK0OK\
0QL0RL0RN1TN4VO7VO8WQBYREYRHZTI`TL`VOaVQcWTcWWdYYd\
YdcVjaTraRx`QzZOzZNzorzlpzioxgmudlrcjo`imZgjWegVdd\
RcaQaZN`YLZVIYRHWOEVLDTIARH8QGBOGENEHNEKLENKDQKDTI\
DWHBZHBaGBcGAeEAiD8lD8oB8rA7uA7x87z75z75z55z5Gz4Qz\
2Zz1iz0rz0pz0oz0oz0mz0lz0lz0jz0iz0iz0gz0ez0ez0dz0c\
z0cz0az0`z0`z0Zz0Zz0`z0`z2`z7`zB`zGazKazOazTazYaza\
czeczjczocztczwczwczwaztazpazm`zj`zg`zdZzaZzZZzWYz\
TYzQYzNYzKHzl1zzDzzNzzYzugzorzjtzguzduzawzZwzWxzTx\
zQzzNzzKzzHzzGzzDzzAzz7zz4zz1zz0zz0zz0zz0zz0zz0zz0\
zz0xz0uz0rz0pz0mz0jz0iz0ez0cz1`z2Zz2Wz4Tz5Rz5Oz7Lz\
8Kz8HzAEzBDzBNzGWzIdzNmzQlzRjzTjzTizVgzWgzWezYezZd\
zZcz`czaazaazc`zdZzdZzeYzgYzgazdezajzZmzWrzTwzQzzN\
zzLzzOzzRzzVzzYzzZzzazzdzzgzzizzlzzozzrzztzzwzzzzz\
zzzzzzzzzwzzrzzo2zt4zo5zl
}
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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times.
