**Fractal of the Dayby Jim Muth**

FOTD -- May 28, 1997

Fractal visionaries:

No other fractal is quite like the Mandelbrot set. No other fractal gives so great a variety from so simple a formula. But the Mandelbrot set is but one in an endless series of similar fractals. There is no reason one must stop at Z

However the higher order mandeloids soon degenerate into a monotonous circle with n-1 identical bays. Indeed, when n is greater than 12, the sets are barely distinguishable from one another, and the midgets, which grow in size and number until they nearly obliterate all else, soon become uninteresting off-center circles. The only really interesting higher order mandeloids are the Z

Today's fractal,

The little two-headed midget sits surrounded by its pattern, glowing like a vision of the holy grail, with its arms radiating around it in ascending powers of three, rather than in powers of two. Thus instead of 4, 8, 16, we have 9, 27, 81. BTW, this same increasing-powers-of-the-exponent sequence continues into the higher orders, though the features soon become too tiny to be distinguished. The sequence also prevails in the fractional order mandeloids, which is why those figures must be filled with such annoying discontinuities.

A finished 640x480x256 image of

Jim Muth

jamth@mindspring.com

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Go to Paul's Fractal Links webpage,

to the renowned Fractal Census,

or to the revised Spanky Fractal Database.

Plus, to Paul's hostings of:

O's Fractal Art Gallery,

to his own older Fractal Pages, or

to his latest web pages for Fractals.

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