Fibonacci Type Coding for the Regular Rectangular Tilings of the Hyperbolic Plane

Maurice Margenstern (Laboratoire d'Informatique Théorique et Appliquée, Université de Metz, France)

Gencho Skordev (CeVis, University Bremen, Germany)

Abstract: The study of cellular automata (CA) on tilings of hyperbolic plane was initiated in [6]. Appropriate tools were developed which allow us to produce linear algorithms to implement cellular automata on the tiling of the hyperbolic plane with the regular rectangular pentagons, [8, 10]. In this paper we modify and improve these tools, generalise the algorithms and develop them for tilings of the hyperbolic plane with regular rectangular s-gons for s 5. For this purpose a combinatorial structure of these tilings is studied.

Keywords: cellular automata, hyperbolic plane, tiltings

Categories: F.1.1, F.1.3