Aperiodic Monotile - Mad as a Hat

An aperiodic monotile (also known as an einstein) is a tile that can cover the plane, but never repeats. After decades of searching, mathematicians have finally found one. Sections 0:00 Intro 0:44 Tilings 1:33 Aperiodic tilings 3:45 Aperiodic sets of tiles 5:00 The hat 5:21 (Proof 1) Metatiles 7:12 (Proof 1) Meta-metatiles 8:54 (Proof 2) Family 10:59 (Proof 2) Common period 13:02 Open questions References The paper itself: https://arxiv.org/pdf/2303.10798.pdf Interactive metatiles: https://cs.uwaterloo.ca/~csk/hat/app.... Animated families: https://cs.uwaterloo.ca/~csk/hat/anim... Additional resources from the authors: https://cs.uwaterloo.ca/~csk/hat/ Wang tiling:    • Bathroom Tile Programming   Penroes tiling:    • Why Penrose Tiles Never Repeat