A Tour in the Wonderland of Math with Python

A collection of python scripts for drawing beautiful figures or animating interesting algorithms in mathematics.

About this repo

Please visit the website for this repository to see how to use these scripts and get more information of the math behind them.

I'm building the docs so that there will be more usage & math explanations for each program.

The history commits are deleted (sorry for this) but will not be deleted any more.

This repository will be always under construction since there are too many interesting things in math that can be shown by code. Pull requests, issues, questions, and suggestions are all welcomed!

Warning: I'll not maintain support for python<=2.7 any more, please run the code with python>=3.

Contents

• Mandelbrot Set
• Julia Set
• Newton Fractal
• Icosahedral Kaleidoscope
• Fractal Tree
• Reaction-Diffusion Simulation
• The E8 Pattern
• The Modular Group
• Generalized Penrose Tilings
• Domino Shuffling Algorithm Animation
• Wilson's Uniform Spanning Tree Algorithm Animation
• Coupling From The Past And Lozenge Tilings
• Todd-Coxeter Algorithm And 4D Polytopes
• Möbius Transformations In Hyperbolic 3-Space

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Mandelbrot Set

[Code] [Doc]

[Back to Top]

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Julia Set

[Code] [Doc]

[Back to Top]

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Newton Fractal

[Code] [Doc]

[Back to Top]

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Icosahedral Kaleidoscope

[Code] [Doc]

[Back to Top]

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Fractal Tree

[Code]

[Back to Top]

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Reaction-Diffusion Simulation

[Code] [Doc] [Pmneila's Javascript Animation]

[Back to Top]

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The E8 Pattern

[Code] [Doc] [Wiki]

[Back to Top]

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The Modular Group

[Code] [Doc] [Wiki]

[Back to Top]

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Generalized Penrose Tilings

[Code] [Doc]

[Back to Top]

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Domino Shuffling Algorithm Animation

[Code][Doc]

[Back to Top]

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Wilson's Uniform Spanning Tree Algorithm Animation

[Code] [Doc] [Mike Bostock's Javascript Animation]

[Back to Top]

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Coupling From The Past And Lozenge Tilings

[Code] [Doc]

[Back to Top]

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Todd-Coxeter Algorithm And 4D Polytopes

[Code] [Doc]

[Back to Top]

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Möbius Transformations In Hyperbolic 3-Space

[Code] [Doc]

[Back to Top]

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Programs to come:

• Fractals with orbit trap
• 2D hyperbolic tilings (Escher's circle limit)
• 3D hyperbolic honeycombs
• Hopcroft's minimization algorithm

Dependencies

Python libs: pip install -r requirements.txt.

Softwares:

• ImageMagick
• FFmpeg
• POV-Ray