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June 23, 1997: Offside Penalty June 21 June 24 1997 FOTD Home

offside

Fractal visionaries:

Fractals are almost magical in the way they can create so much beauty from so little information.  How is it possible that a formula as simple as Z^2+C can hold within itself the infinity of information contained in the Mandelbrot set?  Are mystical forces actually involved?

The answer, of course, is that the formula is not the carrier of the infinitely detailed Mandelbrot set, but merely a set of directions telling us which way to go to build the set and reveal for ourselves the potential riches that are always waiting there.

The Mandelbrot set never runs out of surprises.  It is part of a larger object, the four-dimensional Julibrot figure, which I am currently exploring.  Just as the Mandelbrot sets and the Julia sets each have their distinctive, easily recognizable characteristics, as well as their similarities, the XZ, XW, YZ, and YW sets each have their own distinctive characteristics as well as their similarities.

Today, and every day for the rest of this week, I will concentrate on the YZ direction by posting images sliced in that direction.  Then I'll devote a week to images from each of the other three slices.  This does not imply, however, that the quality of the images will be compromised.  The other slices are every bit as rich as the Julia and Mandelbrot slices.

Today's fractal is a picture of a midget -- not a Mandelbrot midget, nor a Julia midget, but a YZ midget.  The midgets in this plane have characteristics a bit closer to the Julia plane than the Mandelbrot plane, though not close enough to be mistaken for a Julia set.  The feeling of great forces at work stretching the shapes like cosmic rubber, so evident in today's fractal, is a feature that characterizes the entire YZ world.

The finished image has been hopefully posted to a.b.p.f. and a.f.p.  I say hopefully because I've had a couple images vanish recently.

Jim Muth
jamth@mindspring.com


START 19.6 COMBINED FILE===================================

Offside_Penalty    { ; time=0:01:13.60-SF5 on P4-2000
  reset=1960 type=formula formulafile=basicer.frm
  formulaname=Man2-YZ passes=1 center-mag=+0.2750977\
  599871218/+0.0027705419458246/102.6103/1.0402/\
  7.80896713033748036/-0.605979584844571262
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  logmap=yes periodicity=10
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  zbVz`VzZVzXVzWVzUUzSUzQUz }

frm:Man2-YZ {
z=real(pixel)+flip(real(p1)),
c=flip(imag(pixel))+imag(p1):
z=sqr(z)+c,
|z| <= 36 }

END COMBINED FILE==========================================