Conferencia “Matching Rules for Rep-tiles (Tiling 2)” Chaim Goodman-Strauss en la UNAM

Resumen:

Four copies of this L-shape can be fitted together to form a larger L-shape; four of those can be fitted into a larger L still, and so on ad infinitum, in the end producing a non-periodic, hierarchical tiling of the plane. But this L-shape can form lots of other kinds of patterns too — how can we enforce this hierarchical structure? Today there are a few dozen specific examples (most famously the Penrose tiles and the Hat monotile) and a series of general constructions (Mozes '89, GS '98, Fernique-Ollinger '10), but these are not widely understood. We aim to demystify these methods with a simple to state and easy to prove lemma that applies to each of these constructions (pushing the hard work into showing the hypotheses of the lemma hold in whatever setting we are considering).

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