Built-in Mathematica Symbol

FixedPointList

FixedPointList[f, expr]
generates a list giving the results of applying f repeatedly, starting with expr, until the results no longer change.

FixedPointList[f, expr] gives expr as the first element of the list it produces.

The last two elements in the list produced by FixedPointList are always the same.

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

FixedPointList[f, expr, ..., SameTest->s] applies s to successive pairs of results.

Find the sequence of values leading to a fixed point:

Repeated application of a rule until the result no longer changes:

Find the sequence of values leading to a fixed point:

Repeated application of a rule until the result no longer changes:

Stop after at most 5 steps:

Stop as soon as successive iterations differ by less than

:

Show convergence to

in Newton's method:

Number of steps needed to converge to a fixed point of Cos:

Matrix convergence:

Evaluate combinators:

Go up a directory tree to its root (the result will depend on computer system):

Repeated differentiation:

FixedPoint gives the last element of FixedPointList:

NestList goes for a fixed number of steps:

Apply rules repeatedly until the result no longer changes:

FixedPointList is equivalent to a particular choice of arguments of NestWhileList:

When finding a fixed point, numerical precision may increase:

The depth of intermediate expressions in a combinator evaluation [more info]: