Generalized Substitutions and Stepped SurfacesReport as inadecuate

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1 IML - Institut de mathématiques de Luminy 2 ARITH - Arithmétique informatique LIRMM - Laboratoire d-Informatique de Robotique et de Microélectronique de Montpellier 3 ADAGIO - Applying Discrete Algorithms to Genomics and Imagery LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications

Abstract : A substitution is a non-erasing morphism of the free monoid. The notion of multidimensional substitution of non-constant length acting on multidimensional words introduced in AI01,ABS04 is proved to be sell-defined on the set of two-dimensional words related to discrete approximations of irrational planes. Such a multidimensional substitution can be associated to any usual Pisot unimodular substitution. The aim of this paper is to try to extend the domain of definition of such multidimensional substitutions. In particular, we study an example of a multidimensional substitution which acts on a stepped surface in the sense of Jam04,JP04.

Author: Pierre Arnoux - Valerie Berthe - Damien Jamet -



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