iterated map

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A function f : XX from which is defined the iteration x, f(x), f(f(x), f(f(f(x))), … for any element x in set X. Thus a new function F : X × NX is created by F(x,t) = ft(x) where N is the set of natural numbers. The construct that makes F from f is, under certain circumstances, equivalent with the construct of primitive recursion. Iterated maps are used to model the dynamical behavior of computers (for example, by iterating a next state function) and physical systems (for example, a neurone firing), and to generate fractals.

f : XX

x, f(x), f(f(x), f(f(f(x))), …

F : X × NX

F(x,t) = ft(x)

Subjects: Computing.

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