Displaying similar documents to “Locally catenative sequences and Turtle graphics”

Locally catenative sequences and Turtle graphics

Juhani Karhumäki, Svetlana Puzynina (2011)

RAIRO - Theoretical Informatics and Applications

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Motivated by striking properties of the well known Fibonacci word we consider pictures which are defined by this word and its variants so-called turtle graphics. Such a picture can be bounded or unbounded. We characterize when the picture defined by not only the Fibonacci recurrence, but also by a general recurrence formula, is bounded, the characterization being computable.

Return words in Sturmian and episturmian words

Jacques Justin, Laurent Vuillon (2010)

RAIRO - Theoretical Informatics and Applications

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Considering each occurrence of a word in a recurrent infinite word, we define the set of return words of to be the set of all distinct words beginning with an occurrence of and ending exactly just before the next occurrence of in the infinite word. We give a simpler proof of the recent result (of the second author) that an infinite word is Sturmian if and only if each of its factors has exactly two return words in it. Then, considering episturmian infinite words, which are a natural generalization...