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Paul Harrison @paulfharrison
Wang (1961, section 4.1, A Generalized Game Of Dominos)
Given a set of squares with colored edges, can we tile the plane with copies of these squares so all the edge colors match?
(Rotations and reflections are not allowed.)
Wang's conjecture:
If we can tile the plane, we can do so with a repeating pattern.
Wang's student Berger (1966) showed this is wrong.
There are aperiodic tile-sets.