Iterated function: Difference between revisions

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[[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_centerSimilarity 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_Image (mathematics)#Image_of_an_elementImage of an element|image]] under {{math|''F''}}.  If  [[Transformation (function)|transformation]]  {{math|''F''}} <br
/>is  '''iterated'''  indefinitely,   then  ''A ''  and  ''K'' are  are<br
/>the  starting  points  of  two infinite 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.