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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: We recently had a short series of Julia sets for all, so why not a similarly short series of Mandelbrot sets for all? Today's image is the first in the series, but it has a problem -- it looks nothing like a Mandelbrot set. It looks more like an apparition of a golden shield. A quick glance gives the impression that the image has L-R symmetry. But a second glance reveals that first appearances can be deceiving. The fractal has no symmetry. Today's image actually is the Mandelbrot set that results when portions of Z^(-0.7) and Z^(-1.7) are combined and (1/C) is added. Of course, to create the special effects I used a few tricks. Rendered in the usual manner, the Mandeloid is little more than a roughly circular empty hole, with a few bits of debris scattered about. The extra excitement was added by rotating the image minus 90 degrees and rendering it with the inside set to 'atan'. Several other inside fills also work satisfactorily, but I had to choose one, so I chose the 'atan' fill. The name of the image is "A Mandel Set for All-1". I might have done better if I had named it something like "Golden Shield" or "Sunburst", but a name is a name and today's name has been determined. The image renders in 4 minutes on my machine. It downloads in even less time from: Monday here at Fractal Central turned out to be another day with lots of sun and unusually warm temperatures. As a result, the cats behaved like angels. My day was about as close to average as it is possible to come. The next FOTD will appear right here in 24 hours. Until then, take care, and fractals might exist only in the mind, but from where did they enter the mind? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
AMandelSetForAll-1 { ; time=0:04:01.07--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=-19.0779/0/0.01902579/1/-90/-1.2337e-014
params=0.5/-0.7/0.25/-1.7/0/0 float=y maxiter=1500
inside=atan logmap=yes periodicity=10
colors=000cAUaAUYAUUAUTAUEAU7AU0AU4AU8AUAAUCAUCAUD\
ATDASDARDAQDAPDAPDAODANDAMDALD9LD9KD9ID9FD9CD99C96\
B93A90A80A70A60A50A40A30A20A10A00A00A00A00A009B0DB\
0AA0A90A80A70A60A50A40A32A24A16A08A0AA0CA0EA0GA0ID\
0KG3MJ6OM6QP5SS4UV6WY7Y`8_b9acBcdCeeDgfEihGkiHmjIo\
kJqlLsmMunNwoOxqQyrRzsSztTzuVzvWzwXzxZzu`zrazoczmd\
zjdzgezdezbez_fzXhzWizVjzVkzVlzVmzVozVqzUozUmzUkzU\
izUgzQezUczXaz__zc_zfZwiYtlYqiWngUkeTgcReaPb_O`YMY\
WLWUJTSHRQGOOEMMCJKBHI9EG8CICGKFKMJNOMRQQURTYTXaV_\
dXchZfk`joamr`kp`in`hl`fk`di`cg`ae`_d`Zb`X``VZ`UY`\
SW`QUZNV`PTaRRcTQdUOfWMgYLi_Jj`IlbGmdEofDpgBri9sk8\
vm6zn4zl5zk6zj7zi8zh8yg9xfAweBvdBvcCvbDvaErbEqaFp`\
Go_HnZHmYKmXMmWOm`QmcSmfUmiVlgWkfXjeYidZhc_hb`gaaf\
_beZcdYdcXecWfbVgaUh`Ti_RjZQkZPlYOmXNnWMoVLpVKqUMp\
TOpSQoRSoQUnPWnOYnN_mMamLclKelJgkIikHkkGmjFojEqiDs\
iCuhBwh9yjBxhDwgFvfHudJtc }
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 PARAMETER FILE=========================================
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