Category: Iterated Function Systems

This procedure called IFS (Iterated Function Systems) plots a curved fern. The program was found in the book Bausteine des Chaos - Fraktale written by Heinz-Otto Peitgen, Hartmut Juergens and Dietmar Saupe and slightly modified for Maple.

> restart:

> ifsmaple:=proc(imax)
> # Iterated Functions Systems
> # Originalprogramm 'Chaos-Spiel fuer ein Farnblatt' geschrieben
> # in BASIC, ver"ffentlicht in: 'Bausteine des Chaos - Fraktale',
> # Springer Verlag/Klett-Cotta, S. 415 von denselben Autoren
>    local e1, e2, e3, e4, f1, f2, f3, f4, x, y, xn, yn, z, pts;
>    pts:=NULL;
>    e1:=0.5; e2:=0.57; e3:=0.408; e4:=0.1075;
>    f1:=0; f2:=-0.036; f3:=0.0893; f4:=0.27;
>    x:=e1;
>    y:=0;
>    to imax do
>       z:=rand()/1e12;
>       if z<=0.02 then 
>          xn:=e1;
>          yn:=0.27*y+f1
>       elif z<=0.17 then 
>          xn:=-0.139*x+0.263*y+e2;
>          yn:=0.246*x+0.224*y+f2
>       elif z<=0.3 then 
>          xn:=0.17*x-0.215*y+e3;
>          yn:=0.222*x+0.176*y+f3
>       else
>          xn:=0.781*x+0.034*y+e4;
>          yn:=-0.032*x+0.739*y+f4
>       fi;
>       pts:=pts, [xn, yn];
>       x:=xn;
>       y:=yn;
>    od;
>    [pts]
> end:

> plot(ifsmaple(12500), axes=NONE, style=point, symbol=POINT, scaling=constrained);

Another version of 'IFS' uses the undocumentated goto command within the procedure: IFS2.MS or IFS2.TXT.

MAPLE V FRACTALS FERN #1.01 current as of July 27, 1997
Author: Alexander F. Walz, alexander.f.walz@t-online.de
Original file location: http://www.math.utsa.edu/mirrors/maple/mfrifs.htm