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In mathematics, an iterated function is a function (that is, a function from some set to itself) which is obtained by composing another function 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 number, the result of applying a given function is fed again in the function as input, and this process is repeated. 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 be a set and be a function. Define as the ''n''-th iterate of , where ''n'' is a non-negative integer, by: :: and :: where is the identity function on and denotes function composition. That is, ::, always associative. Because the notation may refer to both iteration (composition) of the function or exponentiation of the function (the latter is used in trigonometry), some mathematicians choose to write for the ''n''-th iterate of the function . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Iterated function」の詳細全文を読む スポンサード リンク
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