Iterated function system

Iterated Functions Systems are a kind of fractal that was conceived in its present form by John Hutchinson in 1981 and popularized by Michael Barnsley's book "Fractals Everywhere".

IFS fractals as they are normally called can be of any number of dimensions, but are commonly computed and drawn in 2D. An IFS fractal is a solution to a recursive set equation. The fractal is made up of the union of several copies of itself, each copy being transformed by a function (hence "function system"). The canonical example is Sierpinski's Gasket. The functions are normally "contractive" which means they bring points closer together and makes shapes smaller. Hence the shape of an IFS fractal is made up of several possibly overlapping smaller copies of itself, each of which is also made up of itself, ad infinitum.

The most common algorithm to compute IFS fractals is called [[The Chaos Game]]. It consists of iteratively applying one of the functions chosen at random from the function system and drawing the point.

Fractal Flames are a generalization and refinement of IFS fractals.

Barnsley tried to use IFS to encode images and received a patent for his efforts. But his claims were exagerated and the company failed, and the whole effort is now regarded as a fraud.