The Hat and the Spectre: Mathematicians Find a Shape That Tiles Without Repeating
The Hat and the Spectre – Recent Groundbreaking Discoveries in Mathematics
The National Museum of Mathematics highlights two groundbreaking discoveries in tiling theory: the Hat, the first aperiodic monotile, and its chiral relative, the Spectre. Unlike the Hat, which requires reflected copies, the Spectre tiles the plane using only rotations and translations, with no repeating pattern. The page includes press coverage, videos of author discussions, and details on the Einstein Mad Hat Competitions.
In tiling the plane, the Hat mixed unreflected and reflected tiles, leaving open the question of whether a single shape could tile aperiodically using translations and rotations alone.