Kenyon's non FLC
A simple substitution, yielding a tiling which is not of finite local complexity (flc). The substitution maps the single prototile, a unit square, to three columns of three squares each, where the third column is shifted by an irrational amount t. In higher iterates of the substitution, there are neighboured squares shifted against each other by t, 3t+t, 9t+3t+t,… mod 1. Since t is irrational, these sequence contains infinitely many values (mod 1), thus there are infinitely many pairwise incongruent pairs of tiles.

Polytopal Tiles
Parallelogram Tiles
Rhomb Tiles