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Built-in
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Applying Functions Repeatedly
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FixedPointList
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FixedPoint
FixedPoint
[
f
,
expr
]
starts with
expr
, then applies
f
repeatedly until the result no longer changes.
MORE INFORMATION
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]
provides a way to use a general comparison function.
EXAMPLES
CLOSE ALL
Basic Examples
(3)
Find a value
such that
:
In[1]:=
Out[1]=
In[2]:=
Out[2]=
Fixed point of an integer-valued function:
In[1]:=
Out[1]=
In[2]:=
Out[2]=
Repeated application of a rule until the result no longer changes:
In[1]:=
Out[1]=
In[2]:=
Out[2]=
Scope
(2)
Generalizations & Extensions
(1)
Options
(2)
Applications
(8)
Properties & Relations
(3)
Possible Issues
(1)
SEE ALSO
FixedPointList
NestWhile
Nest
ReplaceRepeated
TUTORIALS
Applying Functions Repeatedly
MORE ABOUT
Functional Iteration
Functional Programming
Looping Constructs
RELATED LINKS
NKS|Online
(
A New Kind of Science
)
New in 1 | Last modified in 3
© 2008 Wolfram Research, Inc.
EXAMPLES
Basic Examples 
Scope 