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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