Category: Escape-time Fractal
This is the 'speed' version of the complex Mandelbrot algorithm. It makes use of Maple V's evalhf command, which conducts floating-point calculations by using the hardware coprocessor. As a result a calculation that takes around 25 minutes with complex arithmetics is finished after around two minutes on a Pentium 90 MHz PC.
> restart: with(plots): > mandelbrot_fast:=proc(x, y) > local xn, xnold, yn, m; > Digits:=10; # optional > xn:=x; > yn:=y; > for m from 0 to 25 while evalhf(sqrt(xn^2+yn^2)) < 2 do > xnold:=xn; > xn:=evalhf(xn^2-yn^2+x); > yn:=evalhf(2*xnold*yn+y) > od; > m; > end: > plot3d(0, -2 .. 0.7, -1.1 .. 1.1, orientation=[-90,0], grid=[250, 250], > style=patchnogrid, scaling=constrained, color=mandelbrot_fast);
See also Faster Generation of Fractals for tips on how to transform complex formulas to corresponding real ones in order use the evalhf command.
MAPLE V FRACTALS MandelbrotFast #1.00b current as of July 27, 1996
Author: Alexander F. Walz, firstname.lastname@example.org
Original file location: http://www.math.utsa.edu/mirrors/maple/mfrmandf.htm