The name “Fibonacci word” has also been used to refer to the members of a formal languageL 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 <math>S_0</math> be "0" and <math>S_1</math> be "01". Now <math>S_n = S_S_</math> (the concatenation of the previous sequence and the one before that).
The infinite Fibonacci word is the limit <math>S_</math>.
The Fibonacci words
The first few elements of the infinite Fibonacci word are: