ifs-fractals

Fractals defined by iterated function systems, drawn with the chaos game — in a graphics window, or into a PNG file with no display needed.

An iterated function system is a handful of affine maps, each contracting. Applied over and over to a point, in an order drawn at random, they trace out a single figure — the attractor of the system — no matter where one starts. A whole fern is four such maps:

  let barnsley =
    { po = {x= -2.25; y= -0.50};
      sz = {x=  5.00; y= 11.00};
      lt = [{pb= 0.84; kf= [| 0.85;  0.04; 0.00; -0.04; 0.85; 1.60|] };
            {pb= 0.91; kf= [|-0.15;  0.28; 0.00;  0.26; 0.24; 0.44|] };
            {pb= 0.98; kf= [| 0.20; -0.26; 0.00;  0.23; 0.22; 1.60|] };
            {pb= 1.00; kf= [| 0.00;  0.00; 0.00;  0.00; 0.16; 0.00|] }] }

The library

Everything is in a single module, Ifs_fractals.

  utop # open Ifs_fractals;;
  utop # show barnsley 200_000;;          (* draw it, wait for a key *)
  utop # save_png ~color:true lace 300_000 "lace.png";;

Sixteen systems are predefined, listed in Ifs_fractals.all, and more can be read from Fractint .ifs files with Ifs_fractals.load_fractint, including the three-dimensional ones, which are projected from a direction of your choosing.

The command

The same from a shell:

  $ ifs-fractals --list
  $ ifs-fractals barnsley
  $ ifs-fractals -o lace.png -s 800x800 -c lace
  $ ifs-fractals -f classics.ifs -v 30,20 3dfern

See also

• The source repository, whose README has pictures.
• Michael Barnsley, Fractals Everywhere, Academic Press, 1988 — where the fern and the theory behind it come from.