June 25, 1997: Skimming the Thing | June 24 | June 26 | 1997 | FOTD Home |

Fractal
visionaries:

Sometimes it pays to step back and look at something from a new
angle. That is what I did with one of the least interesting
places of the entire Mandelbrot set. The place in question is
the
point where the stem of the north bud splits into two. I have
followed this Y-shaped feature to a magnitude of 1e030, and can report
that it looks the same regardless of how deep one goes.

But there is something strange about the splitting point of the north
stem. A number of years ago, I drew the Julia set of this
3-armed
object and to my surprise, noticed that the Julia set has six
arms. This led me to think: if the Julia set of this point
has
six arms and the Mandelbrot set has only three arms, what does the
point look like in the other four directions. When I finally
checked it a few days ago I was surprised indeed. The other
slices have an infinity of arms!

The point, which in the Mandelbrot set is a simple fork and in the
Julia set a six-pointed star, has riches beyond belief in some of the
other planes. Today's fractal, node, is a picture of the
simple
north bud fork sliced in the YW direction.

I might add that there is no actual single point where all the branches
of this amazing four-dimensional network of barbed wire filaments come
together. Rather, the entire area of the Julibrot figure is
filled with an infinitely intricate jumble of threads and crosses,
stretched and pulled in every possible direction. What at
first
appeared so dull turns out to be full of interest.

The finished image is posted to a.b.p.f. and a.f.p. I have
even
more Mandelbrot surprises in store for tomorrow.

Jim Muth

jamth@mindspring.com

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