Fibonacci word

${\displaystyle S_{10}}$

${\displaystyle S_{17}}$

Fibonacci curves made from the 10th and 17th Fibonacci words^[1]

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 and specifically, a morphic 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.