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, email@example.com
Original file location: http://www.math.utsa.edu/mirrors/maple/mfrmark.htm