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{{Short description|Result of repeatedly applying a mathematical function}}
{{Use dmy dates|date=May 2019|cs1-dates=y}}
[[File:An iterated direct similarity yields spirals.svg|thumb|upright=1.8|[[Function composition|Composed]] with itself '''repeatedly''', [[Similarity (geometry)|similarity]] {{math|''F''}}<br
/>of [[Similarity (geometry)#Similarity_with_a_center|center]] ''S '' enlarges the smallest regular pentagon into successive [[Concentric objects|concentric]] pentagons, in manner that the outline of each one<br
/>passes through all vertices of the previous pentagon,<br
/>of which it is the [[Image_(mathematics)#Image_of_an_element|image]] under {{math|''F''}}. If [[Transformation (function)|transformation]] {{math|''F''}}<br
/>is '''iterated''' indefinitely, then ''A '' and ''K''<br
/>are the starting points of two infinite [[spiral]]s.]]
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.
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