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Article Dans Une Revue Quarterly Journal of Mathematics Année : 2013

GEOMETRIC REALIZATIONS OF TWO-DIMENSIONAL SUBSTITUTIVE TILINGS

Arnaud Hilion

Résumé

We define 2-dimensional topological substitutions. A tiling of the Euclidean plane, or of the hyperbolic plane, is substitutive if the underlying 2-complex can be obtained by iteration of a 2-dimensional topological substitution. We prove that there is no primitive substitutive tiling of the hyperbolic plane H 2. However, we give an example of a substitutive tiling of H 2 which is non-primitive.
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hal-01219087 , version 1 (22-10-2015)

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Nicolas Bedaride, Arnaud Hilion. GEOMETRIC REALIZATIONS OF TWO-DIMENSIONAL SUBSTITUTIVE TILINGS. Quarterly Journal of Mathematics, 2013, ⟨10.1093/qmath/has025⟩. ⟨hal-01219087⟩
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