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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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valvarezapa / LCD

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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.

julia-language numerical-methods iterative-methods julia-sets numerical-analysis newton-raphson hopf-fibration lyapunov-functions lyapunov-exponents complex-dynamics fatou-sets basins-of-attraction n-cycles rational-maps
  • Updated Jul 2, 2024
  • Julia

himanshuvnm / Examples-Dynamical-Systems-in-Python

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Codes of my present and recent research work on dynamical systems in Python. In this repository, we can see a wide variety of examples of the phase-portraits of dynamical systems ranging from simple age-dependent population dynamics to the capacitor-resistor dynamical system used in electrical circuits.

python dynamical-systems julia-sets chua-circuit capacitor-resistor-dynamical-system
  • Updated Apr 24, 2024
  • Jupyter Notebook
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