An aperiodic monotile
David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss, 2023
In our paper we present a single shape called "the hat" that tiles the plane aperiodically. That shape turns out to be just one point in a broader continuum of related shapes. In this video we move smoothly through the space of all these shapes. The second half of the video is the reverse of the first; the whole thing is meant to be watched in a loop. The shapes shown at the start (and end), 1/4 position (and 3/4) and 1/2 position are degenerate cases that can also tile periodically. All other shapes are aperiodic.
Full details about the paper are available at https://cs.uwaterloo.ca/~csk/hat/.
