Fatou sets in Julia (Fractals, Newton basins, Mandelbrot)
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Updated
Feb 16, 2024 - Julia
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
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.
Fatou sets in Julia (Fractals, Newton basins, Mandelbrot)
This is a program that generates a julia set with the Julia langauge using PlotlyJS. Note that I am new to Julsi so there may be some ineffeciencies.
Lyapunov Cycle Detector is a collection of algorithms destined to study the basins of attraction of rational maps (that is, the Fatou and Julia sets). In particular, the main focus of LCD is in the detection of attracting n-cycles of said rational map and in computing its basins.