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Concept
Iterated function
Summary
In mathematics, an iterated function is a function X → X (that is, a function from some set X to itself) which is obtained by composing another function 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:
:with the circle‑shaped symbol of function composition.
Iterated functions are objects of study in computer science, fractals, dynamical systems, mathematics and renormalization group physics.
Definition
The formal definition of an iterated function on a set X follows.
Let ''X'' be a set and f: X → X be a function.
Defining f n as the n-th iterate of ''f'' (a notation introduced by Hans Heinrich Bürmann
Official source
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