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A hierarchical strongly aperiodic set of tiles in the hyperbolic plane. (English) Zbl 1182.03072
Summary: We give a new construction of strongly aperiodic set of tiles in $$\mathbb H^2$$, exhibiting a kind of hierarchical structure, simplifying the central framework of M. Margenstern’s proof [Theor. Comput. Sci. 407, No. 1–3, 29–84 (2008; Zbl 1152.03036)] that the Domino Problem is undecidable in the hyperbolic plane.

##### MSC:
 03D35 Undecidability and degrees of sets of sentences 05B45 Combinatorial aspects of tessellation and tiling problems 52C20 Tilings in $$2$$ dimensions (aspects of discrete geometry) 68Q80 Cellular automata (computational aspects)
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