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) = 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.
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) = 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.
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iterated map