Iterated Function Systems with OCaml

Fractals are images of infinite complexity, characterized by being "similar" to themselves in some sense at all scales of magnification.

Iterated function systems are a method of generating fractals using self-similarity. An IFS image is defined as being the sum of geometric transforms of itself. It turns out that simply specifying the transforms along with a weight for each transform is enough to determine the image.

How to use this code

In your shell

$ sudo apt install ocaml opam
$ opam init
$ opam install graphics
$ opam install ocamlfind
$ eval $(opam env)
$ ocaml
        OCaml version 4.11.1

# 

In your OCaml interpreter

# #use "ifs_fractals.ml";;
# draw barnsley 200000;;

Result

Resources

This work was carried out during a functional programming course.

Some information about Iterated Function Systems (with the Barnsley Fern):

• https://web.archive.org/web/20160913030719/http://nahee.com/spanky/www/fractint/ifs_type.html
• https://web.archive.org/web/20160509162647/http://paulbourke.net/fractals/ifs_fern_a/
• https://web.archive.org/web/20160401092248/http://mathcurve.com/fractals/fougere/fougere.shtml
• https://web.archive.org/web/20160401180724/http://charles.vassallo.pagesperso-orange.fr/fr/art/ifs.html

Alternatives

• IFS in Common Lisp: https://github.com/jl2/ifs-qt
• J: https://news.ycombinator.com/item?id=12803076
• Barnsley Fern in G'MIC: https://rosettacode.org/wiki/Barnsley_fern#G.27MIC