Iterated function: Difference between revisions

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{{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''}} of [[Similarity (geometry)#Similarity_with_a_center|similaritycenter]] ''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''}}<br. If [[Transformation (function)|transformation]] {{math|''F''}} is '''iterated''' indefinitely, then ''A ''and ''K'' are the starting points of two infinite [[spiral]]s.]]

/>of [[Similarity (geometry)#Similarity with a center|center]] ''S '' enlarges the smallest [[Regular polygon|'''regular''']] [[pentagon]]<br

/>into successive [[Concentric objects|concentric]] pentagons,  in manner that the outline<br

/>of each one 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''   are<br

/>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.