# FindTransientRepeat

FindTransientRepeat[list,n]

returns a pair of lists {transient,repeat} where the elements of repeat occur successively at least n times after the elements of the transient part of list.

FindTransientRepeat[string,n]

returns a pair of strings {transient,repeat}.

# Details and Options

• In FindTransientRepeat[list,n], n must be a positive integer.
• FindTransientRepeat[list,1] returns {{},repeat}, where repeat is the shortest repeated part found in list, or list itself if no repetition is found.
• FindTransientRepeat[list,n,SameTest->test] applies test to each pair of elements in list to determine whether they should be considered the same.

# Examples

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## Basic Examples(2)

Find the transient and repeated parts of a list:

Find the transient and repeated parts of a string:

## Scope(4)

Find the transient and repeated parts of a list of any kind of elements:

Change the constraint on the minimal number of occurrences of the repeated sublist:

The elements of the first argument of FindTransientRepeat can have different heads:

FindTransientRepeat accepts SparseArray and structured array objects:

## Generalizations & Extensions(1)

FindTransientRepeat can detect an incomplete copy of the repeated sublist in the last position:

The minimum number of repetitions refers to complete repetitions:

## Options(3)

### SameTest(3)

Use equivalence classes based on absolute value:

Use equivalence classes based on Floor:

Use Total of list elements:

## Applications(7)

Recover the generator of a StringRepeat expression:

Select all sublists containing a repeated part of given properties:

Compare with Repeated:

Find the period of a function on a given interval:

Compare with FunctionPeriod:

Quadratic irrational numbers have continued fractions that are ultimately periodic:

Compare the representations for a rational number with an infinite decimal part:

Find the repeated part of a cellular automaton:

Find periods of the rule 90 cellular automaton with different sizes:

## Properties & Relations(4)

When no repeated part exists, FindTransientRepeat returns its first argument and an empty list:

When no repeated part satisfies the condition on the number of occurrences, FindTransientRepeat returns its first argument and an empty list:

FindTransientRepeat returns the pair of sublists {transient,repeat} for which transient has a minimum length:

FindTransientRepeat finds the transient part and the repeated part of an expression:

FindRepeat expects a periodic expression:

When an expression has no transient part, FindRepeat[expr,n] is identical to Last[FindTransientRepeat[expr,n]]:

Wolfram Research (2016), FindTransientRepeat, Wolfram Language function, https://reference.wolfram.com/language/ref/FindTransientRepeat.html.

#### Text

Wolfram Research (2016), FindTransientRepeat, Wolfram Language function, https://reference.wolfram.com/language/ref/FindTransientRepeat.html.

#### CMS

Wolfram Language. 2016. "FindTransientRepeat." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FindTransientRepeat.html.

#### APA

Wolfram Language. (2016). FindTransientRepeat. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindTransientRepeat.html

#### BibTeX

@misc{reference.wolfram_2022_findtransientrepeat, author="Wolfram Research", title="{FindTransientRepeat}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/FindTransientRepeat.html}", note=[Accessed: 29-May-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_findtransientrepeat, organization={Wolfram Research}, title={FindTransientRepeat}, year={2016}, url={https://reference.wolfram.com/language/ref/FindTransientRepeat.html}, note=[Accessed: 29-May-2023 ]}