Various functions and code samples centered around Chaos and Fractals. This was made by C. Simal and J. Mohet as part of their 2019-2020 Master's Course Chaos et Déterminisme at Unamur.
Most of the code is in Julia. In order to run it, we recommend you use JuliaPro as it allows using Julia in a workflow similar to Matlab. Users coming from Matlab should check out this page for a detailed list of the differences between both languages. Some code is in Octave/Matlab
Once you've installed Julia and downloaded the code, you will need to install several community packages. Thankfully, this can be done very easily by running dependencies.jl. If you want a quick introduction to the basics of Julia, we recommend you look at introduction.jl first.
The code was initially developed on Julia 1.2.0, but was tested without issues on Julia 1.3.0 (the latest Julia release at the time of writing)
dependencies.jl: Installation script for community packages.
introduction.jl: Introductory script for users unfamiliar with Julia.
FractalDimensions.jl: Implementations of the box counting dimension and the correlation dimension, along with some companion functions.
sierpinsky.jl: Simple script that generates an approximation of the Sierpinsky triangle and tests the fractal dimension functions from FractalDimensions.jl on it.
mandelbrot.jl: Script implementing functions for generating arbitrary Julia and Mandelbrot sets, and plot them as images.
bifurcationdiagramlogistic.m: Bifurcation diagram of the logistic map in Octave/Matlab
logisticmap.m: Orbits of the logistic map in Octave/Matlab
lyapunovexp.m: Computation of the Lyapunov exponent of orbits of the logistic map. (In Octave/Matlab)
rossler.jl: Script for integrating the rössler equations and do various operations on the resulting solution.