Editing Iterated function (section)

{{Short description|Result of repeatedly applying a mathematical function}}
{{Use dmy dates|date=May 2019|cs1-dates=y}}

[[File:Powers of rotation, shear, and their compositions.svg|thumb|400px|Iterated transformations of the object on the left<br>On top is a clockwise rotation by 90°. It has [[Order (group theory)|order]] 4, because that is the smallest positive exponent that produces the identity. Below is a [[shear mapping]] with infinite order.<br><small>Below that are their [[Function composition|compositions]], which both have order 3.</small>]]

In [[mathematics]], an '''iterated function''' is a function that is obtained by [[function composition|composing]] another function with itself two or several times. The process of repeatedly applying the same function is called [[iteration]]. In this process, starting from some initial object, the result of applying a given function is fed again into the function as input, and this process is repeated.

For example, on the image on the right:
:{{nobr|1=<math>L = F(K), \ M = F \circ F (K) = F^2(K).</math>}}

Iterated functions are studied in [[computer science]], [[fractals]], [[dynamical system]]s, mathematics and [[renormalization group]] physics.