Trihex
A simple rule to generate nonperiodic tilings with one prototile, a triangle with angles 30°, 60°, 90°. It looks pretty much periodic: the hexagonal patches cover 75% of the plane, and this part is clearly periodic. The triangles in between the hexagons destroy the periodicity. But, by the selfsimilarity of the tilings, one finds larger periodic subsets in the tiling, covering 93,75%, 98,44%… of the plane. Thus, the tiling is limitperiodic.