We consider Sturmian trees as a natural generalization of Sturmian words. A Sturmian tree is a tree having n+1 distinct subtrees of height n for each n. As for the case of words, Sturmian trees are irrational trees of minimal complexity. We give various examples of Sturmian trees, and we characterize one family of Sturmian trees by means of a structural property of their automata.
['Jean Berstel', 'Luc Boasson', 'Olivier Carton', 'Isabelle Fagnot']
A first investigation of Sturmian trees