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  "body": "\n## Summary\n\nA continuous map is topologically mixing when every nonempty open set, after some time, meets every other nonempty open set at all later times.\nIt strengthens [[topological transitivity|FR49Y9GQHR]], which only asks for one such time.\nIt is the topological counterpart of strong [[mixing|S3RJQ9CX2P]] in ergodic theory.\nExpanding maps such as the doubling map of the circle are mixing, while rotations are never mixing.\n\n## Explanations\n\n### L1 human\n\nPut a drop of ink in a glass of water and stir with a fixed rule.\nMixing means that after enough stirring the ink reaches every small region of the glass, and stays present there at every later moment.\nThe doubling map $x \\mapsto 2x \\bmod 1$ of the circle is mixing: it stretches every small arc until it covers the whole circle.\nAn irrational rotation is transitive but not mixing: a small arc just moves around rigidly and keeps missing a given region at many times.\n",
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