Category: Escape-time Fractal

A function originally designed by me for FRACTINT. As shown by the iteration command 'z:=cos(z)*z^2+c' it is a variant of the Mandelbrot set.

> # BIOMORPH2
> # Based on a Maple V algorithm taken from the book 
> # 'Maple V - Programming Guide' by M.B. Monagan, 
> # K.O. Geddes, G. Labahn and S. Vorkoetter, 
> # Springer Verlag, modified by John Oprea
> #
> # modification of initialization and iteration by Alexander F. Walz
> # May 22, 1996
> #
> biomorph2:=proc(x, y)
>    local z, m, c;
>    z:=evalf(x+y*I);
>    c:=z;
>    m:=0;
>    to 100 while abs(z) < 4 do
>       z:=cos(z)*z^2+c;
>       m:=m+1;
>    od;
>    m;
> end:

> plot3d(0, -2 .. 2, -1.5 .. 1.5, orientation=[-90,0], grid=[250, 250],
> style=patchnogrid, scaling=constrained, color=biomorph2);

MAPLE V FRACTALS BIOM2 #1.00 current as of July 27, 1996
Author: Alexander F. Walz, alexander.f.walz@t-online.de
Original file location: http://www.math.utsa.edu/mirrors/maple/mfrbio.htm