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Cyclic[{x1,…,xn}]

represents a cyclic sequence of elements. The list of elements will be drawn from repeatedly to fill available positions.

Cyclic[{x1,…,xn}][k]

extracts the k^(th) element in the cyclic sequence defined by the xi.

Details
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Basic Examples  
Scope  
Applications  
Properties & Relations  
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Cyclic

Cyclic[{x1,…,xn}]

represents a cyclic sequence of elements. The list of elements will be drawn from repeatedly to fill available positions.

Cyclic[{x1,…,xn}][k]

extracts the k^(th) element in the cyclic sequence defined by the xi.

Details

  • A Cyclic specification may use none, some or all of the xi elements, depending upon the number of available positions. If the number of positions is not a multiple of n, then remaining positions toward the end will be filled with x1, x2, etc.
  • Cyclic[{x1,…,xn}][0] returns xn, Cyclic[{x1,…,xn}][-1] returns xn-1, and so forth. In general, Cyclic[{x1,…,xn}][k] returns xMod[k,n,1] for any integer k. »

Examples

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Basic Examples  (4)

Obtain the fifth element of a sequence that repeats every three elements:

Extract element in a sequence that repeats every three elements:

Use cyclically repeating colors for the columns of a grid:

Use cyclically repeating colors for the rows of a grid:

Scope  (4)

Alternate the rows between bold and italic font:

Combine this with cyclically repeating colors for the columns:

Specify the colors for the first few columns, then fill in the rest cyclically:

Extract an element with a very large index:

Compute elements , and in a sequence:

Applications  (1)

Create a list of a given length by repeating a list of elements:

Properties & Relations  (3)

Cyclic[list][1] gives First[list]:

Cyclic[list][0] gives Last[list]:

Cyclic[list][k] gives Part[list,Mod[k,Length[list],1]]:

Wolfram Research (2025), Cyclic, Wolfram Language function, https://reference.wolfram.com/language/ref/Cyclic.html.

Text

Wolfram Research (2025), Cyclic, Wolfram Language function, https://reference.wolfram.com/language/ref/Cyclic.html.

CMS

Wolfram Language. 2025. "Cyclic." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Cyclic.html.

APA

Wolfram Language. (2025). Cyclic. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Cyclic.html

BibTeX

@misc{reference.wolfram_2025_cyclic, author="Wolfram Research", title="{Cyclic}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/Cyclic.html}", note=[Accessed: 04-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_cyclic, organization={Wolfram Research}, title={Cyclic}, year={2025}, url={https://reference.wolfram.com/language/ref/Cyclic.html}, note=[Accessed: 04-August-2025]}