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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image takes us into the parent fractal created when Z^(-1.1) is mixed with Z^(-2.2) and (1/C) is added. This somewhat oversized parent fractal consists of 3 large, nearly circular bays, with a large area of apparent chaos on the west side. There are also 2 fragmentary mandibles like those of a fire ant. It's not a very promising start, but I never give up on a fractal unless it is totally hopeless. The first thing I noticed was that the large area of chaos is filled with objects pretending to be minibrots, and that some of these are rather interesting. I decided to check just west of the largest 'minibrot', in an area consisting mostly of fractal sand, with occasional larger stones thrown in. I expected to find little of interest, but when I applied a very broad color palette I found that there is a subtle pattern hidden in the chaos. Once I emphasized this pattern, I found a previously invisible, symmetrical arrangement of elements that indicates the presence of either a dry valley or a real minibrot. Luckily, it turned out to be a minibrot, and that minibrot lies at the center of today's image. The minibrot is surrounded by a pattern equally as subtle as the pattern of the overall area. And it also needs to be emphasized by fine tuning the colors. Unfortunately, I seem to have gone a bit too far with the colors, resulting in a texture too rough and muddy to make a great image. But the rating of a 6 that I gave the image is fair enough. I named the image "Forever Fractured" because of the excessively rough texture of the image. The calculation time of 2-1/2 minutes will not be too much of a burden, but an even faster way to see the image is to view it on the FOTD web site at: Tuesday was a bit chilly around the edges, but a fine autumn day nevertheless here at Fractal Central, with a temperature of 50F 10C. The fractal cats, (designated so by me), were on their best behavior most all day. The only slip was when Cassie took her sharpened claws to the arm of my favorite chair. Other than this, my day went as good as could be expected. Only the day's fractal fell a bit short. But the next FOTD will be posted here in 24 hours, and who knows, it may be the best of all time. Until then, take care, and if the outer world is as real as the Mandelbrot set, then what's going on? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Forever_Fractured { ; time=0:02:30.61-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=recip inside=0
params=1/-1.1/1/-2.2/0/0/0/0 float=y periodicity=10
center-mag=-2.453051913790731/+0.0431330890981556/\
8.35236e+009/1/145/0 maxiter=3200 logmap=256
colors=0000000000000000000000000000000000000000000\
00000000z0zz0zz0zx0zs0zp0zk0vh0rd0ma0hX0cV0cQ0cO0c\
K0cH0cE0wB0w70w50w00w00c30Z50U90TB0OG0KH0GM0BQ07T0\
3X00_00d00e00k00p00zw0zw0zw0zw0zw0zw0zw0zw0zz0zz0z\
zzzzzzzzzzzzz0zz0zz0zs0zh0za0zV0zO0zH0zB0z50z00z00\
z00n00n00a00a00a00d00d00d00d00p00p00z00z00z00z00z0\
0z00z90zG0zO0zO0zV0za0ze0xh0sn0ns0hx0dz0_z0_z0az0a\
v0ds0dn0dk0ee0ed2h_3hX5hT7kQ7kM9kKBnGEnEGp9Hp7Kp3M\
s2Ms0Ov0Qv0Tv0Vx0Xx0_x0_s0ap0an0dk0de0dd0ea0e_3hV5\
hT7hQBkOEkKGnHHnGMnEOp9Qp7Tp5Xs3_s0av0ev0hv0kx0nx0\
sz0vz0xz0zz0zz0zz9zzKzzVzzezzszzszzszzszzszzszzszz\
szzszz0zz0zz0zv0zn0ze0ze0zd0za0z_0z_0zX9zVKzTVzTez\
QszOzzMzzMzzKzzHzxGzxGzxEzvBzvBzs9zv7zx5zz5zz3zz2z\
z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz2zz5zz7zz9\
zzBzzEzzGzzKzzMzzOzzQzzTzzVzz_zzazzdzzezzhzznzzkzz\
hzzezzdzzazz_zz_zzXzzzzzz }
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.
