June 16, 1997: Corrosion | June 15 | June 17 | 1997 | FOTD Home |

Fractal
visionaries:

Today's fractal is one of those that I just couldn't find a name
for. It looks like nothing I've seen on this world.
It
vaguely resembles a neural network, so at first I was going to name it
"neural". Then I imagined a scene on an alien planet and
decided
to call the fractal "alien". In the end I decided to name it
"Vicious" because it has a certain nastiness about it.

The fractal itself combines several tricks. First, it is
drawn in
the YW plane, which gives parts of it a tortured, stretched-out
appearance. Second, it is a combination of the Z^2 and Z^-2
mandeloids, which creates the many floating blobs and twisted
filaments. Third, I've colored it so that it appears to be
illuminated from behind by a lurid light.

Combining positive and negative powers of Z in the same formula is one
of my favorite tricks. Today's formula, for example, combines
Z^2
and Z^-2, which fills the Mandelbrot lake with interesting
details. But the positive and negative terms cannot simply be
added together as (Z^2)+(Z^-2). If they are, the terms tend
to
cancel out, and nothing more than a few bands appear.

To solve this problem and keep the formula under control, I combine
different portions of the positive and negative terms. In
today's
fractal, for example, I use the formula, (0.75*(Z^2))+(0.03*(Z^-2)).

Iterating only 0.75 of Z^2 makes the figure somewhat larger to give
more inside room, while the 0.03 portion of Z^-2 is just enough to add
inside detail without clogging the interior. Tomorrow, I'll
post
one of the many striking straight Mandelbrot images I've found with
this method.

For those who prefer their images pre-drawn, today's finished image is
posted to a.b.p.f. and a.f.p.

Jim Muth

jamth@mindspring.com

START COMBINED FILE FOR 19.6===============================

Corrosion
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time=0:00:10.49-SF5 on P4-2000

reset=1960 type=formula formulafile=basicer.frm

formulaname=ManN-2-pro-YW passes=1 periodicity=10

center-mag=0.819581/0.0188454/1.328656/1/90/0

params=-0.5/0.5/0.75/2/0.03/-2 float=y

maxiter=3600 bailout=100 inside=255 logmap=3

colors=000D00100F00H00J00I00J00L00O00Q00T00Y00b00j\

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frm:ManN-2-pro-YW { ; Jim Muth

z=real(p1)+flip(real(pixel)),

g=imag(p1)+flip(imag(pixel)),

a=real(p2), b=imag(p2), c=real(p3), d=imag(p3):

z=(a*(z^b))+(c*(z^d))+g,

|z| <= 16

}

END COMBINED FILE FOR 19.6=================================