Yet Another Proof of the Aperiodicity of Robinson Tiles

An aperiodic tile set is a finite set of tiles which can tile the plane (i.e. cover it without overlap), but not in a periodic way (i.e., no tiling is invariant by a translation). To prove the undecidability of the the Domino problem, Robert Berger constructed in 1966 the first aperiodic tile set [1]. His proof was simplified in 1971 by Rafael Robinson, who introduced a six-tile set and proved its aperiodicity. Fig. 1 depicts these celebrated six tiles and introduces some terminology.