The chaos game is my favourite method for producing Iterated Function Systems (IFS) fractals, because it's easy to learn and the images reach from nature to fantasy. I've developed a program called Dotfrak, which is still available for windows systems. The main concept is to see the IFS's transformations by its important parameters like angle and compression-factor and not by its matrix, so that people are able to create images, although not being academically trained in mathematics.
Move the red points and watch the result.
Each frame shows the result of one transformation (4 in the IFS) applied on the empty image rectangle.
I added a simple version of Dotfrak to my book titled Fraktale aus Natur und Fantasie. Now you can examine the abilities of IFS construction with my Sierpinski Family Machine (IFS II) and other machines in the IFS sections. Kurs Chaosspiel is an interactive module to learn the basics about IFS fractal constructions.
Michael F. Barnsley (b. 1946) is a mathematician who works on fractal image compression. He was the first who used Iterated Function Systems to generate pictures of ferns.