This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

Nest

Nest
gives an expression with f applied n times to expr.
The function to nest can be a pure function:
In[1]:=
Click for copyable input
Out[1]=
 
The function to nest can be a pure function:
In[1]:=
Click for copyable input
Out[1]=
Nesting a function can build a formula:
Nesting can return a single number:
The nested function can operate on a list:
Use Throw to exit a Nest:
To nest a function of more than one argument, the arguments can be put into a list:
Continued fraction:
Power tower:
Growth of annually compounded capital in 10 years:
Newton iterations for :
Iterated string replacements:
Consecutive pairs of Fibonacci numbers:
Functional composition for higher-order Newton iteration (for ):
Generate a bifurcation diagram for an iterated logistic map:
Nest gives the last element of NestList:
Nest is effectively Composition using the same function multiple times:
Use RSolve to symbolically compute Nest operations:
Different length compositions or nests give the same result:
FixedPoint automatically goes on until the result no longer changes:
NestWhile goes on while a condition is true:
Fold automatically inserts second arguments from a list:
Binary tree:
Gray codes of length 4:
New in 1 | Last modified in 3