The Socolar-Taylor aperiodic tiling

Yesterday on the arXiv appeared a preprint by Socolar and Taylor presenting an aperiodic tiling of the plane with one tile. I haven’t had time to check in any depth yet but that certainly looks interesting indeed, it had been a bit of a holy grail for a long time.

This subject of aperiodic tilings is fascinating: some tilings are aperiodic such that any finite patch will not be enough to say so. Even worse: others are aperiodic but it is impossible to actually prove it (undecidability of the domino problem).

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