An Aperiodic Monotile

From the paper:

> A single hat is asymmetric, and so in any patch we can distinguish between “unreflected” and “reflected” orientations of tiles.

Interesting, thanks for sharing! Also it's the first time I ever find graphical advertising in a paper, at the very end though.

The images aren’t necessarily generated with LaTeX! That being said, TikZ [https://pgf-tikz.github.io/pgf/pgfmanual.pdf] is really nice for making pictures — just look at the front page of their manual!

Less effort than MS Word, I assure you.

Almost all math papers are written in LaTeX. There is nothing unusual about this.

Probably not that much. The figures are almost certainly just included vector images.

It's hard to make aperiodicity matter in a board game: as players place tiles, they either extend an aperiodic layout to a bigger one (unexciting) or they are unable to place a tile because someone, possibly much earlier, deviated from the "correct" construction.

Moreover, with a single einstein there is no tile unpredictability or choice whatsoever, eliminating two of the main strategic dimensions of tile-laying games.

Could make for more interesting "terrain" of tiles used to form hex-based playfields.

This shape seems exceptionally suitable for matching continuous decoration patterns (e.g. knotwork) across tile edges and half edges.