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.

Examples

Find a fixed point:

FixedPoint[Cos, 1.0]
(* 0.739085 *)

Newton's method for square root:

FixedPoint[(# + 2/#)/2 &, 1.0]
(* 1.41421 *)

Please visit the official Wolfram Language Reference for more details.