https://github.com/jonnyhyman/Chaos

Python
Visualizations of the connections between chaos theory and fractals through the logistic map; made for Veritasium YouTube video

Chaos

Visualizations connecting chaos theory, fractals, and the logistic map!

Written by Jonny Hyman, 2020

This code was developed for this YouTube video from Veritasium

This is not a library, but rather a collection of standalone scripts! As such, there is a bit of code duplication between scripts.

Requirements

• Python 3.6+ (tested on Python 3.6 and Python 3.7, macOS Catalina and Windows 10)
• Numpy package : pip install numpy
• Numba package : pip install numba

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Logistic Map - Interactive

python logistic_interactive.py

Additional Requirements

• PyQt5 : pip install pyqt5
• PyQtGraph : pip install pyqtgraph

This visualization creates a cobweb plot, time series graph, and bifurcation plot for visualizing the logistic map. The font pictured is "Avenir Next" which is licensed as part of macOS. Other OSes will see their default font.

Shortcuts:

• Spacebar: play/pause
• Backspace: reset view & animation

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3D Mandelbrot Set

python logistic_mandelbrot.py

Here we see the Mandelbrot set on the x-y plane, and iterations of the Mandelbrot set in the z axis. This reveals the bifurcation plot beneath the Mandelbrot set!

Final visualization is accomplished by a volume rendering of 1000x1000x1000 voxels, oversampled by 16 to reduce aliasing.

Additional Requirements

• Vispy : pip install vispy
• Matplotlib : pip install matplotlib
• PyOpenGL : pip install pyopengl
• ffmpeg if you want to auto-stitch rendered frames to .movs
  • macOS: Install homebrew then brew install ffmpeg
  • Windows: Install chocolatey then choco install ffmpeg

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Logistic Map Zoom

python logistic_zoom.py

• Vispy : pip install vispy
  • Note: The final version of the visualization used a custom version of Vispy, modified to improve the appearance of axes. I have not released this and don't plan to, but if you really need it please post in Issues a feature request.