An iterated map is a map that is applied repeatedly to an object. The Mathematica function NestList[f, expr, n] gives a list of the results of iterating the function times on the initial expression expr. Similarly, Nest[f, expr, n] gives the last element of this list, i.e., the result after iterations.

Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, pp. 149-155, 2002.

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Weisstein, Eric W. "Iterated Map." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/IteratedMap.html