FixedPoint

FixedPoint[f, expr] starts with expr, then applies f repeatedly until the result no longer changes.

FixedPoint[f, expr, n] stops after at most n steps.

FixedPoint always returns the last result it gets.

You can use Throw to exit from FixedPoint before it is finished.

FixedPoint[f, expr] applies SameQ to successive pairs of results to determine whether a fixed point has been reached.

NestWhile[f, expr, comp, 2] uses a general comparison function.

See The Mathematica Book: Section 2.2.2.

See also: FixedPointList, NestWhile, Nest, ReplaceRepeated.

Further Examples