Geodesic
Combinatorial aspects of Escher tilings
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010).

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In the late 30's, Maurits Cornelis Escher astonished the artistic world by producing some puzzling drawings. In particular, the tesselations of the plane obtained by using a single tile appear to be a major concern in his work, drawing attention from the mathematical community. Since a tile in the continuous world can be approximated by a path on a sufficiently small square grid - a widely used method in applications using computer displays - the natural combinatorial object that models the tiles is the polyomino. As polyominoes are encoded by paths on a four letter alphabet coding their contours, the use of combinatorics on words for the study of tiling properties becomes relevant. In this paper we present several results, ranging from recognition of these tiles to their generation, leading also to some surprising links with the well-known sequences of Fibonacci and Pell. 
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     author = {Mass\'e, Alexandre Blondin and Brlek, Srecko and Labb\'e, S\'ebastien},
     title = {Combinatorial aspects of {Escher} tilings},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2868/}
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Massé, Alexandre Blondin; Brlek, Srecko; Labbé, Sébastien. Combinatorial aspects of Escher tilings. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) (2010). doi : 10.46298/dmtcs.2868. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2868/

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