This excites me much more than the original result, which I considered to use two tiles[1]. The fact that it’s a such tiny modification of the original result is crazy. Even if you don’t intend to read the paper, look at the illustrations of the hierarchical substitution algorithm at the top of pages 6 and 7, those are just beautiful.

[1] The authors discuss various historic definitions of tilings and whether reflections should be allowed or not (they argue that most definitions allow them). For me, the answer is simple: nature is chiral, you can’t reflect things willy-nilly. Puzzle pieces, bathroom tiles, even polygons in 3D rendering all have distinguishable sides.