Interlocking Einstein Monotile

These interlocking tiles are derived from the recently discovered "Einstein Aperiodic Monotile." An aperiodic tile covers two-dimensional space in such a way as to create infinite patterns that never repeat. Until recently, the existence of an aperiodic monotile was purely theoretical. But here it is!

Tiles are provided with or without an embossed Einstein face. Use the plain files to make your own remixes!

See here for video: https://youtu.be/LX8urkEtsWk

See here for stable download: https://than.gs/m/824816

This tile set is an artistic interpretation of the real Einstein Monotile. There are a few caveats for the math purists in the room.

Firstly, the real Einstein Monotile tiling system ("The Hat") is composed of mirrored versions of the same shape. In this design, the process of making the pieces interlocking results in the two versions looking quite different. Even though they look different, they are derived from the same reference geometry and so follow the same rules for tiling.

Secondly, the "Einstein the Monotile" has nothing to do with "Einstein the Physicist." The word "einstein" is German for "one stone," referring to the challenge of finding a single tile that would tile space aperiodically. In this design, the geometry needed to make the pieces interlocking just looked like Einstein's messy hair, so I embraced the wordplay and went for it.

This shape was discovered in March 2023 by mathematicians David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. They refer to the shape as "The Hat." You can learn more here: https://cs.uwaterloo.ca/~csk/hat/