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+---
+aliases: julia-fractal, julia-set
+display_name: Julia Sets
+short_description: Julia Sets are mathematical objects generally associated with fractals.
+topic: julia-sets
+logo: julia-sets.png
+wikipedia_url: https://en.wikipedia.org/wiki/Julia_set
+related: mandelbrot, fractal
+---
+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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