Combinatorial and Computational aspects of Tilings

Recently Margenstern has given a proof of the undecidability of the Domino Problem in H^2, adapting the ideas of the Berger-Robinson proof in the Euclidean plane; the original construction rests on a hierarchical non-periodic structure. Margenstern's insight is that there can be useful analogues in the hyperbolic plane, despite a lack of scale invariance. We give a greatly simplified version of Margenstern's method.