David Smith
Discovery
British shape enthusiast who discovered the hat, the first known single tile that forces an aperiodic covering of the plane.
Hat Tile
A 13-sided polykite, the hat, that tiles the plane but never periodically. The first aperiodic monotile; Spectre later dropped the reflections.
About this pattern
Smith, Myers, Kaplan & Goodman-Strauss, 2023
David Smith found the 13-sided hat in 2023; Myers, Kaplan, and Goodman-Strauss proved it is an aperiodic monotile: one shape, no periodic tiling, reflections allowed. The Spectre, later that year, tiles without mirrors.
Behind the mathematics
Joseph Samuel Myers
Proof and construction
Mathematician and tiling researcher who helped prove that the hat monotile admits tilings but can never tile periodically.
Craig S. Kaplan
Proof and visualisation
Canadian computer scientist whose research joins geometry, computation and ornamental design, including the proof and visualisation of the hat monotile.
Chaim Goodman-Strauss
Proof of aperiodicity
American mathematician and geometer whose work on substitution tilings helped establish the hat’s forced aperiodicity.