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

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

FilledSmallSquareFixedPoint always returns the last result it gets.

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

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

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

FilledSmallSquare See The Mathematica Book: Section 2.2.2.

FilledSmallSquare See also: FixedPointList, NestWhile, Nest, ReplaceRepeated.

Further Examples