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Fractal of the Day
by Jim Muth
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FOTD -- December 18, 2008 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows a Mandelbrot set. The name "The Mandelbrot Set" is a little confusing. To begin, there is not one Mandelbrot set, but an infinity of them. The Mandelbrot shape is kind of a universal shape, much like the parabolic shapes that appear so often when the graphs of functions are plotted. Actually, the scene shows a tiny minibrot just east of the large Minibrot on the main negative spike of the Mandeloid that results when the familiar M-set just starts changing into the Z^(-2) Mandeloid. At this early stage of the changeover, only a few extra rings around the original M-set are obvious. Most of the effect of the image is a result of rendering it with the outside set to 'summ'. The apparent X-axis symmetry is an illusion. A close look will reveal that no symmetry exists. If I had more time to work on the colors, the image might have rated a 7. As it is, the predominant theme of orange and green is rather unattractive, holding the rating to a 6. The calculation time of a fireball 50 seconds makes up for the less-than-great colors. And the finished image is posted for instant viewing on the FOTD web site at: Two centimeters of snow overnight Tuesday changed to rain at daybreak Wednesday here at Fractal Central. By midday, the temperature had reached 37F 3C, and the snow was gone, making the fractal cats happier. But the cats' main interest was watching the squirrels, which were unusually active gathering nuts all day. Maybe the squirrels know something about the coming weather that the weather people don't. We'll keep our eye on things for the next several days. My day was very busy, making for another hasty FOTD. The next in the apparently endless series of FOTD fractals will be posted in 24 hours. Until then, take care, and check for reason. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
The_Mandelbrot_Set { ; time=0:00:50.66-SF5 on P4-2000
reset=2004 type=formula formulafile=basic.frm
formulaname=DivideBrot6 passes=1 inside=0 logmap=yes
center-mag=-1.7459134924/0/13838 float=y maxiter=750
params=-2/6/0.001/100 outside=summ
colors=000zZ0zZ0zZ0zZ0zZ0zZ0zZ0zZ0zZ0zZ0zZ0zZ0zY0z\
X0zW0zV0zU0zS0zQ0zO0zM0zK0tF0gA0W50L20BD06N02W09P0\
GL0NDBU9Rz2zz0zz0zz0zz0zbgzYgzzgzzgzzgzGgzBgz6IR2J\
N0KI0MD0O90Q40S00U00U00V00W00X00Y00Z00_20aD0cR0db0\
cm0cm0cm4bjD``NWRWRIeP9eRDeWIg`NgeRgjYglbjqgjvljzq\
jzvjzzlzvozqozoqxjqvettbtqYvoUxlRxjNzjIzgGzeBzb6z`\
4zY0zW0zU0zR0zP0zP0zR0zR0zR0zR0zU0zU0zU2zU4zW6xWBx\
WDvWGtYItYLqYPqYRo`Uo`Wl`Yl`bjbejbggbjgblWe`LeR9eG\
0e60e00e00b00b00b00b00b04`09`0G`0L`0P`0U`0YY0bY0gY\
0oY0tY0xW0zW0zW0zW0zW0zW0zl0zz0zz0zz00000B00b00Y00\
W00U02R0BP0LN0UL0bI0lG0vD0zB0z90zG0zL0zP0xU0vY0tb0\
og2ll4jq9exzbzz`zzWzzUzzRzzNzzLzzIzzLzzLzzLzzLzzLz\
zLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzLzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:DivideBrot6 { ; Jim Muth
z=(0,0), c=pixel, a=real(p1), b=imag(p1)-2,
d=real(p2)+0.00000000000000000001, f=imag(p2)+16:
z=z^(a)/(z^(-b)+d)+c
|z| < f }
END PARAMETER FILE=========================================
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times.
