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  "body": "\n## Summary\n\nA substitution tiling is a tiling of Euclidean space built from finitely many tile shapes.\nThe rule inflates each tile and cuts the result into tiles of the original shapes.\nRepeating the rule produces larger and larger patches, and the tilings whose patches all arise in this way are the substitution tilings.\nThey give the standard examples of aperiodic order, such as the Penrose tilings, and they model quasicrystals.\nThe tilings of one substitution form a compact space on which translations act, and this [[dynamical system|BBZP1R872N]] carries much of their structure.\n\n## Explanations\n\n### L1 human\n\nStart with a few shapes of tiles.\nBlow each tile up by a fixed factor, then cut the big tile into tiles of the original shapes.\nDo it again and again, and the patches grow to cover the whole plane.\nA unit square, blown up by $2$ and cut into four unit squares, gives the ordinary square grid.\nCleverer rules, like the one for the Penrose tilings, give tilings that never repeat periodically.\nSee the [[definition|T4403SAMB2]].\n",
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