# Iterated function system

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