Iterated function: Difference between revisions

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In [[mathematics]], an '''iterated function''' is a function {{math|''X → X''}} (that is, a function from some [[Set (mathematics)|set]] {{mvar|X}} to itself) which is obtained by [[function composition|composing]] another function {{math|''f'' : ''X'' → ''X''}} with itself a certain number of 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 in the function as input, and this process is repeated. For example on the image on the right:

:{{nobr|1=''L'' = <math>\mathit{F}\,</math>( ''K ''),   ''M '' = <math>\mathit{F}\,\circ \mathit{F}\,</math>( ''K '') = <math>\mathit{F}\;^{2}\,</math>( ''K ''), }}<br />with the circle‑shaped symbol of function composition, and so on.}}

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