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We define two-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 two-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.

GEOMETRIC REALIZATIONS OF TWO-DIMENSIONAL SUBSTITUTIVE TILINGS