Iterated function: Difference between revisions

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{{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>]]

[[File:An iterated direct similarity yields spirals.svg|thumb|upright=1.8|[[Function composition|Composed]] with itself '''repeatedly''', [[Similarity (geometry)|similarity]] {{math|''F''}} of [[Similarity (geometry)#Similarity with a center|center]] ''S ''enlarges the smallest [[Regular polygon|'''regular''']] [[pentagon]] into successive [[Concentric objects|concentric]] pentagons,  in manner that the outline of each one passes through all vertices of the previous pentagon, of which it is the [[Image (mathematics)#Image of an element|image]] under {{math|''F''}}. If [[Transformation (function)|transformation]] {{math|''F''}} is '''iterated''' indefinitely, then ''A ''and ''K'' are the starting points of two infinite [[spiral]]s.]]

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.