
Pickover Mandelbrot/Julia Types

formulas: manfn+zsqrd, julfn+zsqrd, manzpowr, julzpowr,
          manzzpwr, julzzpwr, manfn+exp, julfn+exp


These types have been explored by Clifford A. Pickover, of the IBM Thomas
J. Watson Research center. As implemented in xmfract, they are regular
Mandelbrot/Julia set pairs that may be plotted with or without the
{=@Biomorphs "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:

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

to see a big biomorph digesting little biomorphs!

