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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: I passed an hour or so Wednesday afternoon pondering the much sought after theory of everything (except self-awareness, that is). I have lost track of the current leader of the pack of theories, but the last time I checked, M-theory, which is supposed to explain everything including the cause of the 'big bang', was coming on strong. I think this theory requires 11 dimensions, though I heard somewhere that a 12th dimension, which would be a second dimension of time, might be needed to get the numbers to add up. What would it be like to live in a universe with two temporal dimensions. We would no longer be trapped on a line moving ineluctably into the future. We would be able to move sideways in time, to circle around and experience the same event again and again, from different directions. Of course, it would be impossible to predict the future, if there even was a past and a future, because we would be able to choose any part of the future we preferred. And what would happen to fractals such as the Mandelbrot set in a 12-dimensional world? Speaking of fractals, today's image takes us to the southernmost fringes of the parent fractal for December, all the way to the terminal ring of the filament extending from the period-14 bud. The image is nominally interesting, and I have named it "As Far As It Goes". The name refers to the magnitude, which has just exceeded the limit of resolution. 5*(109) is not an unusually large magnitude, but the decimal point has been shifted several places in the calculation, making this magnitude as large as resolution will permit. Considering the lack of sharpness and the lack of oomph in the colors, I rated the image at a 6-1/2. My coloring is not included in this rating; the basic image earns the entire 6.5 points. The parameter file is quite a fast one, finishing as it does in a supersonic 1-3/4 minutes. And if even this is too slow, the completed image is or soon will be available on the FOTD web site at: Heavy clouds all morning, light flurries of snow all afternoon, and a temperature that hung around freezing all day made Wednesday of questionable worth here at Fractal Central. The fractal cats wondered why the dog that hung around the neighborhood for several hours did not go home and get warm. I had another notably average day. The next FOTD will be posted in 24 hours. Until then, take care, and when I posted the first FOTD to the Fractal-Art list almost 11 years ago, I expected to post one or two more before I grew tired of it. I guess I was wrong. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
As_Far_As_It_Goes { ; time=0:01:45.12-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandAutoCritInZ function=recip inside=255
center-mag=-56.69915584369026/-148.8951750514287/5\
.10025e+009/1/-2.5/2.26305686272451623e-005 float=y
params=-2.475/-1.05/-0.275/-5.5/0/0/0/0 maxiter=1200
logmap=162 periodicity=10 mathtolerance=0.05/1
colors=000BBNBBMDDRBBLDERBBJDGQB9IDGQBBLJEGBDB4E80\
N20a00Y00n1Bi8QtEbqJqzQstXzzazxdzzfxtgwwipqklqldln\
blpXgsRftNdwIaxD_z8Xz2Tz0Rz0Vx0Xq0Yk0ad0bY0dR0gL0i\
E0k80n10p00q00s00p04n0Dl0Ji2Rg8qfEgdJxaOw_TzYYzXbz\
NgTDl84pB9aEENIJ8GIEGIJEGQEGVEE_DEfDDkDDpLJqRQsYXs\
datkgtqnwxtwzzxzzxzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzznzfTObQOaOO_NOYJOVIOTGORDOQBON9OL6OJ4OD4N\
I1OJ1QN1TO1TR0VT0YX0_Y0aa0ab0bf0fg0fk0gl0ip0kq0lt0\
nw0px0qz0sz0tz0wz0xz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\
0zz0zz1zz4zz8zx9zwBzsDzpGznIzkJzgLzdOxaQx_RxXTwTXw\
QYwN_tLatIdtDfs9gs4iw8isBgpEglIfiLffOdbQdaTbYXbTYa\
QaaNd_Jf_IdXJdVJdTLbRLbQNbONbNNaLOaJOaIQaGQ_ET_DT_\
BT_9TY8TY6VY4VY1VX0YX0YX0_X0_V0aV0aV0aV0aT0aT0bT0b\
J0fO0fT0bY0ab0ag0_l0Yq0Vw0VzELzTBzi2zw0zz0zz0zz0zz\
0zz0zz0zz18GV9EVDBTE9TG6T }
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.
