This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
 Functional Iteration Long used in its simplest form in mathematics, functional iteration is an elegant way to represent repeated operations. Mathematica's symbolic architecture makes powerful general forms of functional iteration immediately accessible. NestList — successively nest a function: {x, f[x], f[f[x]], f[f[f[x]]], ...} Nest — give the result of nesting a function: f[f[f[x]]] etc.      FoldList — successively fold in a list of values: {x, f[x, 1], f[f[x, 1], 2], f[f[f[x, 1], 2], 3], ...} Fold — give the result of folding in a list of values: f[f[f[x, 1], 2], 3] etc.      FixedPoint, FixedPointList — nest until a fixed point is reached NestWhile, NestWhileList — nest while a condition is satisfied      TakeWhile — take from a list while a condition is satisfied LengthWhile — the length while a condition is satisfied TUTORIALS Applying Functions Repeatedly MORE ABOUT Functional Programming Looping Constructs