{"id":483,"slug":"julia-sets","name":"Julia Sets","short_description":"Julia Sets are mathematical objects generally associated with fractals.","url":"https://github.com/topics/julia-sets","github_count":123,"created_by":null,"logo_url":"https://explore-feed.github.com/topics/julia-sets/julia-sets.png","released":null,"wikipedia_url":"https://en.wikipedia.org/wiki/Julia_set","related_topics":["mandelbrot","fractal"],"aliases":["julia-fractal","julia-set"],"github_url":null,"content":"\u003cp\u003eJulia 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.\nTo 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 $X$.\u003c/p\u003e\n\n\u003cp\u003eTo 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.\u003c/p\u003e\n","created_at":"2024-07-29T13:46:04.091Z","updated_at":"2026-05-28T00:16:54.687Z","topic_url":"https://awesome.ecosyste.ms/api/v1/topics/julia-sets","html_url":"https://awesome.ecosyste.ms/topics/julia-sets","projects_url":"https://awesome.ecosyste.ms/api/v1/projects?keyword=julia-sets","lists_url":"https://awesome.ecosyste.ms/api/v1/lists?topic=julia-sets"}