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          { ; 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\
  F0oJ0qM0sP0vP0vP0yP0yQ0zQ0zR0zR0zR0zQ0zR0zS0zT0zU0\
  zV0zW0zX0zY0zZ0z`0za0zb0zc0zd0ze0zf0zg0zh0zi0zj0zk\
  0zk0zk0zl0zl0zm0zm0zn0zn0zo0zo0zp0zp0zq0zq0zr0zr0z\
  s0zs0zs0zt0zt0zu0zu0zv0zv0zw0zw0zx0zx0zy0zy0zz0zz0\
  zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\
  0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\
  z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\
  zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\
  0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\
  z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\
  zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\
  0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\
  z0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\
  zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz\
  0zz0zz0zz0zz0zz0zz0zz0zzz }

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=================================