The hat is part of an infinite family of aperiodic tiles, as illustrated in the last image on this page: https://cs.uwaterloo.ca/~csk/hat/ https://cs.uwaterloo.

The hat is part of an infinite family of aperiodic tiles, as illustrated in the last image on this page: https://cs.uwaterloo.ca/~csk/hat/ https://cs.uwaterloo.ca/~csk/hat/ This adjustability was a surprise, we have not seen an aperiodic tiling like this before.