Plane digitization and related combinatorial problems

Authors:
Valentin E. Brimkov;Reneta P. Barneva
Affiliations:
Fairmont State University, 1201 Locust Avenue, Fairmont, WV;State University of New York at Fredonia, Fredonia, NY
Venue:
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Year:
2005

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Abstract

In this paper we propose a simple scheme for obtaining plane digitizations. We study digital plane periodicity and consider various issues related to two-dimensional (2D) Sturmian words. Concepts and results, already known for one-dimensional words, are extended to 2D words. In particular, we address a conjecture by Maurice Nivat for the case of digital 2D rays. Our approach is based in part on extending periodicity studies in theory of words to 2D words based on (Proceedings of the Third ACM-SIAM Symposium on Discrete Algorithms, 1992, pp. 440-452; Proceedings of the 33rd IEEE Symposium on Foundations in Computer Science, 1992, pp. 247-250).