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IMI/Publicaţii/CSJM/Ediţii/CSJM v.15, n.3 (45), 2007/

Constructing a uniform plane-filling path in the ternary heptagrid of the hyperbolic plane

Authors: Maurice Margenstern
Keywords: Hyperbolic plane, tilings, tiling problem, plane-filling property, Peano curve.

Abstract

In this paper, we distinguish two levels for the plane-filling property. We consider a simple and a strong one. In this paper, we give the construction which proves that the simple plane-filling property also holds for the hyperbolic plane. The plane-filling property was established for the Euclidean plane by J. Kari, see [2], in the strong version. We also give an application of the construction to devise a Peano curve in the hyperbolic plane.

Maurice Margenstern,
Laboratoire d'Informatique Théorique et Appliquée, EA 3097,
Université de Metz, I.U.T. de Metz,
Département d'Informatique,
Île du Saulcy,
57045 Metz Cedex, France,
E--mail:

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