A construction of the Hat tilings by a Markov partition

The Hat tile, an aperiodic monotile discovered by Smith, Myers, Kaplan & Goodman-Strauss A construction of the Hat tilings by a Markov partition • Labbé & Selinger • arXiv:2604.20964 HatsPositive (+) orientations Anti-HatsNegative (−) orientations Undo Redo Clear canvas Shift grid Continuous tiling (C) ⚙ Options ? Help 0 tiles placed + − Options ✕ Display Show grid Show Markov partition Opacity: Show kite outlines on tiles How to use ✕ Place a tile: drag from sidebar, or click