Geometric realizations of two dimensional substitutive tilings

Nicolas Bedaride; Arnaud Hilion

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arXiv · 1101.3905

Geometric realizations of two dimensional substitutive tilings

Nicolas Bedaride·Arnaud Hilion

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Abstract

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 $\mathbb{H}^2$. However, we give an example of substitutive tiling of $\Hyp^2$ which is non-primitive.

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Nicolas Bedaride, Arnaud Hilion. 2011-01-20. Geometric realizations of two dimensional substitutive tilings. https://arxiv.org/abs/1101.3905

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