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Julia Sets

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Julia Sets are mathematical objects relating to the field of complex dynamics. In general, Julia sets are studied in parallel to Fatou sets, as they are complementary sets defined from a complex function.

To be specific, in a metric space $(X,d)$, a Fatou set of a map $f: X \to X$ is the maximal open subset of $X$ on which the family of iterates $\lbrace f^n \rbrace$ is equicontinuous, and the Julia set is its complement in $X$.

To approximate images of these sets, a common approach is to iterate the function of interest over some subset of the complex plane, which often yield beautiful fractals.

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