June 23, 1997: Offside Penalty | June 21 | June 24 | 1997 | FOTD Home |
Fractal
visionaries:
Fractals are almost magical in the way they can create so much beauty
from so little information. How is it possible that a formula
as
simple as Z^2+C can hold within itself the infinity of information
contained in the Mandelbrot set? Are mystical forces actually
involved?
The answer, of course, is that the formula is not the carrier of the
infinitely detailed Mandelbrot set, but merely a set of directions
telling us which way to go to build the set and reveal for ourselves
the potential riches that are always waiting there.
The Mandelbrot set never runs out of surprises. It is part of
a
larger object, the four-dimensional Julibrot figure, which I am
currently exploring. Just as the Mandelbrot sets and the
Julia
sets each have their distinctive, easily recognizable characteristics,
as well as their similarities, the XZ, XW, YZ, and YW sets each have
their own distinctive characteristics as well as their similarities.
Today, and every day for the rest of this week, I will concentrate on
the YZ direction by posting images sliced in that direction.
Then
I'll devote a week to images from each of the other three
slices.
This does not imply, however, that the quality of the images will be
compromised. The other slices are every bit as rich as the
Julia
and Mandelbrot slices.
Today's fractal is a picture of a midget -- not a Mandelbrot midget,
nor a Julia midget, but a YZ midget. The midgets in this
plane
have characteristics a bit closer to the Julia plane than the
Mandelbrot plane, though not close enough to be mistaken for a Julia
set. The feeling of great forces at work stretching the
shapes
like cosmic rubber, so evident in today's fractal, is a feature that
characterizes the entire YZ world.
The finished image has been hopefully posted to a.b.p.f. and
a.f.p. I say hopefully because I've had a couple images
vanish
recently.
Jim Muth
jamth@mindspring.com
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