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  "body": "\n## Summary\n\nA shift space, or subshift, is a closed set of infinite sequences over a finite alphabet that is invariant under the shift by one place.\nEquivalently, it is the set of all sequences that avoid a given list of forbidden finite words.\nShift spaces with the shift map are the objects of symbolic dynamics, and they serve as models for coding more general dynamical systems.\nThe full shift, the [[subshifts of finite type|624XDXX8FN]] and the sofic shifts are the main classes.\n\n## Explanations\n\n### L1 human\n\nTake an alphabet such as $\\set{0, 1}$ and consider infinite words in it.\nForbid some finite patterns, for example the pattern $11$.\nThe set of all infinite words that never contain a forbidden pattern is a shift space: here, the words in which no two $1$s are adjacent.\nShifting such a word by one place gives again such a word, so the set is mapped to itself by the shift.\nShift spaces are the simplest systems in which complicated dynamics can be described exactly.\n",
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