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

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