This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# FixedPointList

 FixedPointListgenerates a list giving the results of applying f repeatedly, starting with expr, until the results no longer change.
• FixedPointList 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 applies SameQ to successive pairs of results to determine whether a fixed point has been reached.
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:
 Out[1]=
 Out[2]=

Repeated application of a rule until the result no longer changes:
 Out[1]=
 Out[2]=
Stop after at most 5 steps:
 Options   (1)
Stop as soon as successive iterations differ by less than :
 Applications   (6)
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 []:
New in 2