[abetusk]

Just a note about applications, there is a pretty direct application of aperiodic tiles with quasicrystals [0]. Diffraction patterns of quasicrystals can have symmetry that can't occur with periodic tiling which explained some weird diffraction patterns people were observing.

One can imagine a scenario, occurring for metal or mineral creation or even in a biological setting, where only one shape is allowed because of some external constraint, including not allowing it's mirror.

[0] https://en.wikipedia.org/wiki/Quasicrystal