June 13, 1997: Galactic Supercluster | June 11 | June 14 | 1997 | FOTD Home |
Fractal
visionaries:
Every once in a while when I am exploring in the world of fractals, I
make a major discovery that opens a whole new world of
adventure.
Today, while casually noodling around at lunchtime, I made one of those
discoveries.
Before putting my oblique plane formulas under wraps, I wanted to try a
few things with them. The first thing I did was to add a
third
variable to my Man-YZ-XZ formula, so that I could try different
exponents of Z.
The higher order mandeloids were uninteresting in the odd planes --
squares instead of circles, but still uninteresting. Then I
tried
Z^-2. The results knocked my socks off.
I discovered that the fractals drawn by the negative powers of Z, which
are of limited interest in the Mandelbrot and Julia planes, are hiding
their goodies in the other planes. Here are all the spirals
and
whorls and seahorse tails that one would expect in a Mandelbrot
fractal. I've not yet found a midget, but I'm not sure if I'd
recognize one even if I did find it.
While the positive exponent Mandeloids become less interesting in the
odd planes, the negative exponent mandeloids become more
interesting. Now I've got another whole new world to explore.
This is what keeps me going in the world of fractals -- even after
eight years. A serendipitous new approach, and the fractals I
had
virtually given up on have opened up and revealed . . . I don't know
what. But I'll be posting some Z^-2 images in the days to
come.
Today's fractal, Galactic Supercluster, is the first of the new -2
world. I've stretched it out in the vertical dimension to
counter
the tendency of the YZ plane to smear everything out
horizontally. The image has been posted to a.b.p.f. and
a.f.p.
for convenience. And now I've got to get back to that -2
Mandeloid . . .
Jim Muth
jamth@mindspring.com
START COMBINED FILE FOR 19.6===============================
Galactic_Superclus { ; time=0:00:16.80-SF5 on P4-2000
reset=1960 type=formula formulafile=basicer.frm
formulaname=ManN-YZ-XZ passes=1 center-mag=-2.8895\
1188/+0.73347537/433.6914/0.04891/-0.283/-20.784
params=0/0/-2/0/0/0 float=y maxiter=750 inside=253
logmap=yes periodicity=10
colors=0000000000000000000000000000000000000000000\
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j`Ej`Ei`Ei`Dh`Dh`Dg`Dg_Df_Df_Ce_Ce_Cd_Cd_Cc_Cb_CbZ\
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tdbtfhthnshnshnrgmqgmpgmpgmogmngmmflmfllflkflkflje\
kiekhekhekgekfekedjedjddj }
frm:ManN-YZ-XZ {; Jim Muth, Thanks to Benno
; p3 = 0 = Julibrot YZ plane
; p3 = 1 = Julibrot XZ plane
; p3 = >0 <1 = Oblique planes
z=real(pixel)+flip(real(p1)),
c=imag(pixel)+flip(imag(p1)),
a=p3, b=flip(cos(asin(p3))):
z=z^p2+((a+b)*c),
|z| <= 25 }
END COMBINED FILE FOR 19.6=================================