June 4, 1997: Hyperactivity | June 3 | June 5 | 1997 | FOTD Home |

Fractal
visionaries:

Today's fractal is a riot of playful shapes, and it's also a part of
the classic Mandelbrot set -- at least a part of a different part of
the Mandelbrot set -- one of the "perturbed" sets. The blue
part
of today's picture is what I call a ghost image -- the high iteration
remnants of the classic set. These ghost images do not become
visible until the maxiter is raised to an unusually high
value.
To see the blue part unobscured, keep the same borders, change the
starting point to 0,0 and lower the maxiter to 250.

The classic Mandelbrot set is the center slice of a four-dimen-sional
fractal sometimes called the Julibrot figure. The Julia sets
are
part of this same figure sliced from a different direction.
But
since the figure has four dimensions, there are four other
perpendicular directions in which the Julibrot may be sliced.

The Julibrot figure has four axes, X, Y, Z, and W, each axis
perpendicular to the other three. The Mandelbrot sets are
slices
of the Julibrot taken in the XY direction, while the Julia sets are
slices in the ZW direction. But what of the slices in the XZ,
XW,
YZ, and YW directions.

The XZ slice through the origin appears as an irregular, round sided
rectangle with drawn out traces of the top and bottom buds.
The
XW slice appears as an irregular rectangle with concave
sides.
The YZ slice is most baffling -- a shape smoothly curved on one side
and bounded by an area of chaos on the other, while the YW slice is
almost as strange -- the same shape as the YZ slice, but with the area
of chaos on the opposite side.

When oblique slices of this four-dimensional Julibrot figure are taken,
they are totally unpredictable, the features frequently drawn out in
the manner of the quaternion Mandelbrot sets.

As always, today's picture has been posted to a.b.p.f. and
a.f.p.
I'm getting reports that some people are unable to pick up the posted
images from these groups. Apparently some news servers do not
carry these groups, and some newsreaders miss some articles in groups
that are carried. My news reader is Free Agent, which is most
efficient. It always picks up the images within one minute
after
I post them.

For tomorrow's fractal, I think I'll return to my Tower series of
pictures.

Jim Muth

jamth@mindspring.com

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