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Julia Sets

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.

GitHub: https://github.com/topics/julia-sets
Wikipedia: https://en.wikipedia.org/wiki/Julia_set
Related Topics: mandelbrot, fractal,
Aliases: julia-fractal, julia-set,
Last updated: 2024-10-28 00:11:08 UTC
JSON Representation

https://github.com/chakravala/fatou.jl

Fatou sets in Julia (Fractals, Newton basins, Mandelbrot)

chaos complex-numbers fractal-algorithms fractal-images fractals julia-set julia-sets mandelbrot newton-fractals newtons-method nonlinear numerical-analysis recursion root-finding

Last synced: 19 Jan 2025

https://github.com/chakravala/Fatou.jl

Fatou sets in Julia (Fractals, Newton basins, Mandelbrot)

chaos complex-numbers fractal-algorithms fractal-images fractals julia-set julia-sets mandelbrot newton-fractals newtons-method nonlinear numerical-analysis recursion root-finding

Last synced: 29 Nov 2024

https://github.com/MicheleFiladelfia/fractals-cli

Multiplatform fractals explorer 🌌

burning-ship cli collaborate fractal github julia-sets mandelbrot mandelbrot-explorer mandelbrot-fractal mandelbrot-set terminal-based tty

Last synced: 05 Nov 2024

https://github.com/pysrc/fractal

Draw fractal image by python.

fractal ifs julia-sets l-system mandelbrot-sets

Last synced: 12 Dec 2024

https://github.com/justinlubin/fractastic

Fractastic is a simple and approachable fractal generator written in C.

fractals julia-sets mandelbrot-sets

Last synced: 18 Nov 2024

https://github.com/paramrathour/nonlinear-dynamics

Files related to my Summer of Science Report on Nonlinear Dynamics

barnsley-fern bifurcation chaos chaos-game fractals henon-map index-theory julia-sets linearization logistic-map lorenz-attractor lorenz-equation lotka-volterra-model lyapunov-exponents mandelbrot-sets newton-fractal rossler-attractor sir-model stability stochastic-system

Last synced: 28 Jan 2025

https://github.com/ekzhang/webgl-julia-viewer

Real-time Julia Set renderer right in your browser, accelerated with WebGL

fractal julia-sets webgl

Last synced: 12 Oct 2024

https://github.com/zbendefy/julia4d

4D Julia set renderer

computeshader fractal gpu graphics julia julia-sets mandelbrot opengl raytracer raytracing

Last synced: 16 Nov 2024

https://github.com/prantlf/mandelbrot-set

Web components and a web worker for painting Julia and Mandelbrot sets on a web page.

custom-elements julia julia-sets mandelbrot mandelbrot-set web-components

Last synced: 05 Dec 2024

https://github.com/owainkenwayucl/fractals

Python (some Julia!) tools for generating fractals

julia-sets julialang mandelbrot numpy python3

Last synced: 28 Jan 2025

https://github.com/tvumcc/fractal-factory

A project showcasing 2D and 3D fractals with emphasis on interactivity and customizability

2d 3d fractals godot julia-sets l-systems mandelbrot

Last synced: 12 Oct 2024

https://github.com/rhaeguard/visualizations

cool visualizations made with the Canvas API

boids-simulation canvas2d cellular-automata falling-sand game-of-life julia-sets mandelbrot-fractal rule-110 sorting-visualization times-table ulam-spiral

Last synced: 18 Jan 2025

https://github.com/rileyjshaw/fractal

😵‍💫 Visual fractal explorer (Julia/Mandelbrot/Burning Ship sets)

fractal gpu julia-sets shader webgl

Last synced: 01 Feb 2025

https://github.com/kiwijuice56/java-fractals

A fractal exploration program to render and navigate fractals in realtime

buddhabrot burning-ship fractal fractal-rendering fractals graphics interactive-visualizations java julia julia-sets mandelbox mandelbrot newton-fractal sierpinski-triangle tricorn

Last synced: 02 Feb 2025

https://github.com/omerkel/fractals

Rendering Fractals like Hilbert curves, Julia sets and Mandelbrot sets in various techniques.

fractals glsl-shaders hilbert-curve julia-sets jupyter-notebook mandelbrot-sets matplotlib numpy webgl-shader

Last synced: 04 Jan 2025

https://github.com/sofianedjerbi/animatedjulia

A fast Rust solution animating the continuity between Julia sets in high-quality.

fractals julia-sets mandelbrot rust

Last synced: 01 Jan 2025

https://github.com/porglezomp/julia

A parallel realtime Julia set renderer in Rust

fractals julia-sets real-time rendering rust

Last synced: 20 Dec 2024

https://github.com/himanshuvnm/examples-dynamical-systems-in-python

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.

capacitor-resistor-dynamical-system chua-circuit dynamical-systems julia-sets python

Last synced: 25 Dec 2024