Talk:Sturmian word

The Thue-Morse sequence is not a Sturmian word, so I deleted such false sentence. Fudo Wow, I too was surprised to learn (just now, from this page) of the Thue-Morse goof. I just came here to say that somone should add the lovely connection with simple continued fractions, Farey-Stern-Brocot tree, and give a figure with the first few digraphs in their proper place in the tree. Eventually someone should link this to Penrose tilings and their generalizations, due to N. G. de Bruijn; see example at right, showing construction by oblique tiling method of a one dimensional Sturmian tiling space associated with the golden ratio. These are sometimes called the Fibonacci tilings.---CH (talk) 18:41, 18 August 2005 (UTC)
 * The reputable OEIS explicitly says it is, but it would seem that you're right: Thue-Morse contains all of 00, 01, 10, and 11, which violates the Sturmian condition. I added a comment on their entry. Brighterorange 14:18, 12 July 2005 (UTC)
 * I'm surprised that an important database such as Sloane's OEIS was wrong. I am an Italian PhD student, and Sturmian words are my field of research, so I am sure of that. Anyway, I see that you already understood it by yourself. I erased the same sentence also on Thue-Morse sequence. --fudo 12:54, 13 July 2005 (UTC)
 * Yes, I am guilty of reproducing that information without checking it, because OEIS is generally so trustworthy. Thanks for fixing it. Brighterorange 17:49, 13 July 2005 (UTC)
 * Thank you for sending a comment to OEIS. Now it does not report the erroneous information anymore. fudo 11:30, 31 July 2005 (UTC)
 * [[Image:FibonacciTiling.gif|frame|right|Construction of Fibonacci Tiling]]
 * I have added the definition of standard word, which gives a connection with continued fractions. I think that now the page is not a stub anymore. Anyway, I'm not an expert about tilings, so I'll leave that to someone else (or at least, I need more time to study it). --fudo 18:07, 2 May 2006 (UTC)

Where are they used?
Could we add one or two sentences in the introduction before Section 1 listing (with wikilinks) the main fields where Sturmian words appear and are "used"? Otherwise they'll just look like some mathematical curiosity. PhS (talk) 07:49, 20 June 2020 (UTC)