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Article Dans Une Revue Theoretical Computer Science Année : 2013

A study of Jacobi-Perron boundary words for the generation of discrete planes

Annie Lacasse
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Geneviève Paquin
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Xavier Provençal
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Résumé

The construction of a Sturmian word, and thus of a discrete line, from a continued fraction development generalizes to higher dimension. Given any vector v in R3 a list of 6-connected points approximating the, line defined by v may be obtained via a generalized continued fraction algorithm. By duality, a discrete plane with normal vector v can also be generated using a related technique. We focus on such discrete planes, more precisely on the finite patterns generated at each step of the process. We show that the choice of Jacobi-Perron algorithm as a higher dimension generalization of Euclid's algorithm together with the specific substitutions deduced from it allows us to guaranty the simple connectedness of those patterns.
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Dates et versions

hal-00943823 , version 1 (09-02-2014)

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  • HAL Id : hal-00943823 , version 1

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Valerie Berthe, Annie Lacasse, Geneviève Paquin, Xavier Provençal. A study of Jacobi-Perron boundary words for the generation of discrete planes. Theoretical Computer Science, 2013, 502, pp.118-142. ⟨hal-00943823⟩
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