Einstein Tile - 26 Mar 2023

Einstein wearing a hat

Not Albert but ‘single stone’ in German - as in there was a recent proof that there is an aperiodic monotile due to Kaplan et al. In other words, it is a single tile that can only tile the plane in an aperiodic way. Compare this with Penrose or Ghiri tiles that require more than one tile in the set.

What does it look like, this hat?

It’s not hard to draw, but it does get tricky to get the tiling right:

Aperiodic monotile Aperiodic monotile tiling

As you can see from the ‘ugh’ on the tiled image, it’s not trivial to get that right. Maybe it takes practice?