# iterated map

**iterated map** A function *f* : *X* → *X*

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* × *N* → *X*

is created by *F*(*x*,*t*) = *f ^{t}*(

*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.

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