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  "body": "\n## Summary\n\nAn aperiodic set of prototiles is a finite set of shapes that can [[tile|GKJK293DXS]] the plane, but only in ways that never repeat.\nNo tiling by these shapes is [[periodic|WFRGSBFZGV]].\nSuch sets show that local rules can force global order without periodicity, a phenomenon related to quasicrystals.\n\n## Explanations\n\n### L1 human\n\nMost shapes that tile the floor, such as squares, can be laid out in a repeating pattern.\nAn aperiodic set is a set of tiles that do cover the whole plane, but any covering by them is forced to be non-repeating.\nThe [[Penrose tiles|MBE83FTRBG]], two shapes with marked edges, are the best known example.\nIn 2023 a single tile with this property was found, which answered the [[einstein problem|F456KQGPFV]].\n",
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