Fractal visionaries:

Today's fractal is a real quickie -- it draws in under 25 seconds -- but don't let its speed deceive you.  It's quite an unusual image.

For quite some time now I've been involved with the four-dimensional julibrot figure, (or object, or whatever it is), and the more I explore, the more bizarre become the objects I find.  The midget pictured in today's fractal is one of the most bizarre.

The julibrot figure is like a swiss cheese, with midgets sprinkled all through it.  Many of these midgets do not exist in the plane of the classic Mandelbrot set, and today's picture shows one of these obscure midgets that live in the remote outskirts of the julibrot.

I have examined this midget from other angles, and so far have been unable to find a slice that resembles the expected Mandelbrot midget shape.  This may mean that it doesn't have such a slice, or simply that I have not yet located it.

The attached image shows the midget sliced in the XW plane direction.  In this direction, the midget resembles neither a Mandelbrot nor a Julia plane object.  My first impression was of an arrow or chevron.  So I named it "Arrow".  Bits and pieces of Mandelbrot and Julia debris lie scattered around the midget, mixed together in a most unexpected fashion.

Almost all objects in these odd planes are stretched, sometimes by a factor of tens of thousands.  When exploring in these planes, one must become skilled at unstretching, (or stretching in the opposite direction).  Luckily, Fractint makes this simple.

Today's image has been posted to a.b.p.f. and a.f.p. for the convenience of those who can't spare the 25 seconds it takes to draw it.  Tomorrow, I'll post a series of six fractals, all of another way-out midget, this one sliced in the six perpendicular directions.

Before ending, I'd like to recommend Benno Schmid's Julibrot web site.  It's still at an early stage of development, but already quite interesting.  The URL is

    <http://www.shop.de/priv/hp/3133>

Jim Muth
jamth@mindspring.com


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