Fibonacci word

A Fibonacci word is a specific sequence of binary digits (or symbols from any two-letter alphabet). The Fibonacci word is formed by repeated concatenation in the same way that the Fibonacci numbers are formed by repeated addition.

It is a paradigmatic example of a Sturmian word.

The name “Fibonacci word” has also been used to refer to the members of a formal language L consisting of strings of zeros and ones with no two repeated ones. Any prefix of the specific Fibonacci word belongs to L, but so do many other strings. L has a Fibonacci number of members of each possible length.

Let ${\displaystyle S_{0}}$ be "0" and ${\displaystyle S_{1}}$ be "01". Now ${\displaystyle S_{n}=S_{n-1}S_{n-2}}$ (the concatenation of the previous sequence and the one before that).

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