You Can Hold In Your Hand

Paul Harrison @paulfharrison

And Makes A Wrong Conjecture

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.