2.19 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" (p. 95) 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!