View source for Recurrent word

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An infinite word over an alphabet $A$ (finite or infinite) in which every factor occurs infinitely often.  It is sufficient for a one-sided infinite word (an element of $A^{\mathbf{N}}$) to be recurrent that every prefix occurs at least once again.

A word is uniformly recurrent if for every factor $f$ there is an $N = N(f)$ such that $f$ occurs in every factor of length $N$.

The [[Thue–Morse sequence]] is uniformly recurrent.

====References====
* Lothaire, M. "Algebraic Combinatorics on Words", Encyclopedia of Mathematics and its Applications '''90''', Cambridge University Press (2002) {{ISBN|0-521-81220-8}}  {{ZBL|1001.68093}}
* Sapir, Mark V. "Combinatorial algebra: syntax and semantics" with contributions by Victor S. Guba and Mikhail V. Volkov. Springer Monographs in Mathematics. Springer  (2014) {{ISBN|978-3-319-08030-7}} {{ZBL|1319.05001}}