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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is more a mathematical curiosity than a work of fractal art, which is why I gave it no rating. When I first saw it, I could hardly believe my eyes. I had never witnessed such a gathering of Mandelbrot midgets in all my days of fractal exploration. (I consider myself a fractal explorer rather than a fractal artist.) I was astounded, but then a closer look revealed that there is only one real midget in the image. (It is easy to spot.) The other 'midgets' are ringers -- just plain holes playing the role of actual midgets. I immediately named the image "Mandelbrot Ringers". Today's image is from the same parent fractal as yesterday's far-better image. In fact, it is located in the much larger seahorse-type valley just north of the tiny valley that held yesterday's image. The Mandelbrot 'ringers' that fill the scene are not total losses. They are centers of much chaos, some of which is quite interesting and might appear as a source of a future FOTD. The render time of 53 seconds on a P2000 is about all the image is worth. The best way to see the image is to go to the FOTD web site at: Warm sun and a temperature of 81F 27C made Thursday quite pleasant here at Fractal Central. The fractal cats spent the day idling about the place. The most excitement came when a wandering tomcat passed by, calling for any lady within hearing. When they heard him, the fractal cats rushed to the window and wondered what the tomcat was so worked up about. My day was totally average, and this includes the fractal. The next FOTD, hopefully better than average, will appear in 24 hours. Until next time, take care, then do as you will. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Mandelbrot_Ringers { ; time=0:00:53.15-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident inside=0
center-mag=+0.30973458659775410/+0.249770164311793\
80/1411.637/1/-107.5/2.67205008119830723e-012
params=-2/1.5/2/2.5/0/0/0/0 float=y periodicity=10
maxiter=1600
colors=000I`bI`aJa`Ka`Ka_LaZLaYMaYNaXNaWOaVOaVN`UN\
_UNZUNYUMXUMWTxQcwQawP_wOZvOXvNWvMUuMSuLRuKPuJOtJM\
tIKtHJsHHsGGsFErFCrEBrD9rD8qC9pBApBBoACnADn9Em8Fl8\
Gl7Hk7Ij6Jj5Ki5Lh4Mi1Nh4Nh7NgANgCNfFNfINfKNeNNeQNd\
TNdVNcYNc`NcbNbeNbhNakNamN`pN`sN`uNZsPYrQXpRWoTVmU\
UlVTjXSiYRgZQf`OdaNcbMadL`eKZfJYhIWiHVjGTlFSmDSqER\
nERkFQiFQfGPcGPaHOZHOXHOUINRINPJMMJMKKLHKLELKCLK9Q\
AALK7GU4Bb1Ca4D`6E_8FZAGYCHXEIWGJVJKULKTNLSPMRRNQT\
OPVPOYQN_RMaSLcSKeTJgUIiVHlWGnXFpYErZDt_Cv_Bx`Cv`C\
taCraCpbCnbCmcCkcCidCgdCegAfdCdbDb`F`YGZWIXUJVRKTP\
MRNNPLPNIQLGRJETHBUF9WD7XB5Y97XA8XBAXCBXDCXEEWFFWG\
HWHIWIJWJLVKMVLOVMPVNRWMQVOPUQPUSOTUOTWNSYMS_MRaLR\
cLQeKQgJPiJPkIOmIOnJNmKMmKLmLKlMKlMJlNIlOHkOGkPGkQ\
FkQEjRDjSDjSCjTBiUAiU9iV9iW8hW7hX6hZ4gX6hW8hV9hUBh\
TChSEhRFhQHhPIhOKhMLiLNiKOiJQiIRiHTiGUiFWiEXiDZiC_\
iD`hE`gE`fF`fF`eG`dH`cH`c }
frm:MandAutoCritInZ {; 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)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
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times.
