In the tiling of wallpaper and bathroom floors, collective repeated patterns often emerge. Mathematicians have long tried to find a tiling shape that never repeats in this way. In 2023, they lauded an unexpected amateur victor. That discovery of the elusive aperiodic monotile propelled the field into new dimensions. The study of tessellation is much more than a fun thought exercise: Peculiar, rare tiling formations can sometimes seem to tell us something about the natural world, from the structure of minerals to the organization of the cosmos. In this episode, co-host Janna Levin speaks with mathematician Natalie Priebe Frank on the subject of these complex geometric combinations, and where they may pop up unexpectedly. Specifically, they explore her research into quasicrystals — crystals that, like aperiodic tiles, enigmatically resist structural uniformity.