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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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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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