gives a list of the results of applying f to expr 0 through n times.


  • NestList[f,expr,n] gives a list of length n+1.


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Basic Examples  (2)

The function to nest can be a pure function:

Scope  (3)

Nesting a function can build a formula:

Nesting can return a single number:

The nested function can operate on a list:

Generalizations & Extensions  (1)

To nest a function of more than one argument, the arguments can be put into a list:

Applications  (15)

Powers of 2:

Successive integers:

Successive squaring:

Growth of annually compounded capital:

Successive derivatives:

Newton iterations for :

Continued fraction:

Iterated map:

Iterates in the problem:

Linear congruential pseudorandom generator:

Random walk:

Iterated string replacements:

Successively append to a list:

Successively rotate a list:

Operations on a pair of values:

Properties & Relations  (5)

Nest gives the last element of NestList:

Nesting zero times simply returns to the original argument:

FixedPointList goes on until the result no longer changes:

NestWhileList goes on while a condition is true:

FoldList automatically inserts second arguments from a list:

Neat Examples  (4)

Text effects:

Power towers:

Argument doubling:

Sierpiński text:

Introduced in 1988