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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Early in my research with the MandelbrotMix series of formulas I found that the expression (Z2)+(2*Z)+C is simply a more complex way to produce the Mandelbrot set. Not wanting just another Mandelbrot set, I changed the (2*Z) in the expression to (2*(Z0.999)), which resulted in a parent fractal that is almost but not quite a duplicate of the Mandelbrot set. This parent fractal closely resembles the Z^(2.003)+C figure, though the chaos along the negative X-axis has no symmetry and is less orderly. Today's image is located in a tiny valley on the east side of what once was the large minibrot on the negative spike, in an area that is filled with features that resemble tracks in a railyard. I named the image "Deep in the Corner" because the elements in the upper-right (and lower-left) corners have a far greater iteration value than even the area around the minibrot at the center. I rated the image at an 8 because I think it is worth it. Unfortunately, the calculation time of almost 15 minutes is rather lengthy. But relief for fractal indigestion is available on the FOTD web site at: Perfect weather prevailed once again here at Fractal Central on Saturday, and the fractal cats made the most of it. They spent the better part of the afternoon lounging in the sunlight streaming in the side window. At one time they had some kind of a quarrel going on, but whatever it was about, it ended before I found the cause. My day was peaceful enough. The next FOTD will appear in 24 hours. Until then, take care, and the theory of relativity tells us that time and space are not absolute, but change with the individual observer's relative motion. If they appear different to different observers, how then can they be considered objectively real? Perhaps the old song was right, and nothing is real -- not even fractals! (But if so, it's still a lot of fun pretending they are real.) Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Deep_in_the_Corner { ; time=0:14:45.35-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=ident passes=1
center-mag=-1.74584369496664200/+0.005937502955490\
11/8.95604e+009/1/102.5/0 logmap=747 periodicity=10
params=1/2/2/0.999/0/0/0/0 inside=0 maxiter=60000
float=y
colors=000OB`QEdSHhUKjWHlYMn_Rp`UraYsbauccwcexcgyc\
iyckxcmwcoxcqydszfuzhwzmyzrzzvzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzjYei_\
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5kK5U06UA6qK6sK6tK6oO8kHAfFCb8EZ1FX4IV6LT8ORBQPDTN\
FWLIZJK`HMcFPfDRiBTk9Wn7Yq5_sDatLbtTct`euUUUUbwhhk\
aiaVjSOrIHs9Jr8LK8NK8PK8RK8TX8VU8XS8cMHiGQoBYpEWqH\
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CHICFGBDEBBWBAaCFNDJSENXER`FVeG_jGcoHgbIkkIofXhZSd\
YSiLIZETV7L`04P8AVFGoMMdTaX_Yofctmhyjfxhexedwccwaa\
vZ`vX_uVZuSKcQKcNKcLFcJKcGFcEKcCFrIKsN_sS`sYatbbtg\
ctZdcQeOUfPXgQ_hRbiSejTdkXbl_`mcZnfXojWpmXqlYrlZsl\
_tl`ulavlbwlcxldykezkfzkgzkhzkizkjzkjzkkzjlzjmzjzz\
jzzjzzzzzczzzzzzzrzzzzzzz }
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.
