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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.---
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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.
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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.
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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
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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). --
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Yes, I am guilty of reproducing that information without checking it, because OEIS is generally so trustworthy. Thanks for fixing it.
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I have added the definition of standard word, which gives a connection with continued fractions. I think that
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contains all of 00, 01, 10, and 11, which violates the
Sturmian condition. I added a comment on their entry.
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Thank you for sending a comment to OEIS. Now it does not report the erroneous information anymore.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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The Thue-Morse sequence is not a
Sturmian word, so I deleted such false sentence.
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