Iterated function

In mathematics, iterated functions are the objects of study in fractals and dynamical systems. The formal definition of an iterated function on a set X follows:

Let X be a set and

$f:X\rightarrow X$

be a mapping. Define the n'--th iterate

$f^{n}$

of the map by

$f^{0}={\textrm {id}}_{X}$

where ${\textrm {id}}_{X}$ is the identity function on X, and

$f^{n+1}=f\circ f^{n}$.

Examples

Famous iterated functions include the Mandelbrot set and Iterated function systems.