A classical example of a substitution with inflation factor 2. It arises from the well-known related rep-tile. It is not easy to see that this one is limitperiodic. This was shown in [LM01] , thus this one is a cut and project tiling, and therefore pure point diffractive. The prototile is not mirror symmetric. It occurrs in two versions in the tiling. The colours indicate if a tile is left- or right-handed.
Lee, J-Y and Moody, R V
Lattice substitution systems and model sets.
Discrete Comput. Geom. 2001, 25, 2, pp. 173--201, MR1811757