# Iterated function system

An iterated function system (IFS) is a collection $F$ of functions from a space to itself. Under certain conditions (for example, the functions are contracting), there is an invariant set $S = \bigcup_{f\in{F}} f(S)$, which is often a fractal.

Classic fractals that can be formulated as affine IFS include:

The fractal flame algorithm is based on non-linear IFS.

Original Page by Claude