Sturmian word
（重定向自Sturmian）
![The Fibonacci word is an example of a Sturmian word. The start of the cutting sequence shown here illustrates the start of the word 0100101001.](/Images/godic/202502/13/Fibonacci_word_cutting_sequence1813.png")
![Enlarge for animation showing the Sturmian sequence generated by an irrational rotation with θ≈0.2882 and x≈0.0789](/Images/godic/202502/13/Sturmian-sequence-from-irrational-rotation1813.gif")
In mathematics, a Sturmian word (Sturmian sequence or billiard sequence), named after Jacques Charles François Sturm, is a certain kind of infinitely long sequence of characters. Such a sequence can be generated by considering a game of English billiards on a square table. The struck ball will successively hit the vertical and horizontal edges labelled 0 and 1 generating a sequence of letters. This sequence is a Sturmian word.