In computer science, the complexity function of a string, a finite or infinite sequence u of letters from some alphabet, is the function of a positive integer n that counts the number of different substrings of n consecutive elements from the string u.

A Sturmian word

Sturmian word

In mathematics, a Sturmian word, named after Jacques Charles François Sturm, is a certain kind of infinite word.- Definition :A word is a infinite sequence of symbols drawn from a finite alphabet. Call any finite contiguous subsequence of a word a factor...

 is one of minimal complexity function n + 1. An example is the Fibonacci word

Fibonacci word

thumb|350px|Characterization by a [[cutting sequence]] with a line of slope 1/\varphi or \varphi-1, with \varphi the [[golden ratio]].A Fibonacci word is a specific sequence of binary digits...

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