Interlocking Aperiodic Octopuses

These interlocking “Octopus” and “Water” tiles connect together to make infinite patterns that never repeat.

See here for video: https://youtu.be/_7TBXOL_Egw

See here for stable download: https://than.gs/m/847335

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.

See here for similar designs:
Interlocking Einstein Monotile: https://than.gs/m/824816
Einstein Monotile Lego: https://than.gs/m/822932

This tile set is an artistic interpretation of the real Einstein Aperiodic Monotile. 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.

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/

Octopus design is derived from the Lulzbot “Rock2pus” found here: https://lulzbot.com/content/rock2pus