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  "body": "\n## Summary\n\nThe Julia set of a [[rational function|0XDK9CGYKJ]] is the set of points near which the iterates of the function behave chaotically.\nIt is the complement of the [[Fatou set|C0N0XGC6GK]], where the iterates form a [[normal family|JTVWRXXAKM]].\nFor a map of degree at least $2$ it is a nonempty compact set.\nThe map sends it onto itself, and it is often a fractal.\nJulia sets are the central objects of [[complex dynamics|BQQZ0ZCGQF]].\n\n## Explanations\n\n### L1 human\n\nIterate a rule such as $z \\mapsto z^2 + c$ and colour each starting point by what its orbit does.\nIn some regions nearby starting points keep behaving alike; this is the Fatou set.\nThe Julia set is the border where tiny changes of the starting point can change the long-run behaviour completely.\nFor $z \\mapsto z^2$ the Julia set is the unit circle: inside it orbits go to $0$, outside they go to infinity.\nFor most values of $c$ the border is no longer a smooth curve but an intricate fractal.\n",
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