Discovered by


A substitution tiling with inflation factor sqrt(3), using a single prototile, namely a 60ยบ rhomb. The substitution sends one rhomb to seven rhombs (instead of three, as one would expect from the inflation factor), thus the tiles in higher iterations do overlap. But the substitution is chosen in a way such that tiles do either overlap completely, or not at all. So overlapping tiles can be identified, and the substitution yields a proper tiling.

The prototile occurs in three different orientations in the tiling, as indicated by the colours. After one iteration of the substitution, the tiles occur in three different orientations. After two iterations the tiles occur again in the original three orientations.

Substitution Rule

Rule Lord


Patch Lord