; June 4, 1997: Hyperactivity 
;
; hyper
;
; 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
; jamth@mindspring.com
;
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