Equivalent Descriptions of The Julia Set
- is the smallest closed set containing at least three points which is completely invariant under .
- is the closure of the set of repelling periodic points.
- For all but at most two points, the Julia set is the set of limit points of the full backwards orbit . (This suggests a simple algorithm for plotting Julia sets, see below.)
- If is an entire function - in particular, when is a polynomial, then is the boundary of the set of points which converge to infinity under iteration.
- If is a polynomial, then is the boundary of the filled Julia set; that is, those points whose orbits under iterations of remain bounded.
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