Category: Escape-time Fractal

This is a variation of the Mandelbrot set. The original formula 'z:=z^2*c^(p-1)+c' was developed by Mark Peterson and contributed to FRACTINT. Hence the fractal is named 'Complex Mark's Mandelbrot'. The procedure does not return 'm' but 'ln(n)' instead resulting in a different color of the fractal. You can also try other functions.

> restart: with(plots):

> cmplxmarkmand:=proc(x, y)
> # 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 25, 1996
> #
>    local c, m, z;
>    c:=evalf(x+y*I);
>    z:=evalf(x+y*I);
>    m:=0;
>    to 30 while abs(z) < 2 do
>       z:=z^2*c^0.1+c;
>       m:=m+1;
>    od;
>    ln(m);
> end:

> plot3d(0, -2 .. 0.7, -1.2 .. 1.2, orientation=[-90,0], 
grid=[250, 250], style=patchnogrid, scaling=constrained, 
color=cmplxmarkmand);

MAPLE V FRACTALS CMPLMARK #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/mfrmark.htm