Pickover Mandelbrot/Julia Types

(type=manfn+zsqrd/julfn+zsqrd, manzpowr/julzpowr, manzzpwr/julzzpwr, manfn+exp/julfn+exp - formerly included man/julsinzsqrd and man/julsinexp which have now been generalized)

These types have been explored by Clifford A. Pickover, of the IBM Thomas J. Watson Research center. As implemented in Fractint, they are regular Mandelbrot/Julia set pairs that may be plotted with or without the "biomorph" option Pickover used to create organic-looking beasties (see below). These types are produced with formulas built from the functions z^z, z^n, sin(z), and e^z for complex z. Types with "power" or "pwr" in their name have an exponent value as a third parameter. For example, type=manzpower params=0/0/2 is our old friend the classical Mandelbrot, and type=manzpower params=0/0/4 is the Quartic Mandelbrot. Other values of the exponent give still other fractals. Since these WERE the original "biomorph" types, we should give an example. Try:

FRACTINT type=manfn+zsqrd biomorph=0 corners=-8/8/-6/6 function=sin

to see a big biomorph digesting little biomorphs!

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