A Tour in the Wonderland of Math with Python

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

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!

Contents

• Mandelbrot Set
• Julia Set
• Domino Shuffling Algorithm Animation
• Icosahedral Kaleidoscope
• Newton Fractal
• The E8 Pattern
• The Modular Group
• Generalized Penrose Tilings
• Wilson's Uniform Spanning Tree Algorithm Animation
• Reaction-Diffusion Simulation
• The 120-cell
• Lorenz Attractor Animation
• 2D Hyperbolic Tilings
• 3D Hyperbolic Honeycombs

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Mandelbrot Set

Mandelbrot 集 [View Code]

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Julia Set

Julia 集 [View Code]

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Domino Shuffling Algorithm Animation

多米诺洗牌算法 [View Code] [Arctic Cirlce Phenomena] [Wiki]

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Icosahedral Kaleidoscope

正二十面体万花筒 [View Code] [View Webm Animation]

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Newton Fractal

Newton 迭代分形 [View Code] [Wiki]

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The E8 Pattern

李代数 E8 的根系 [View Code] [Wiki]

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The Modular Group

模群的基本域 [View Code] [Wiki]

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Generalized Penrose Tilings

彭罗斯铺砌 [View Code] [Wiki]

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Wilson's Uniform Spanning Tree Algorithm Animation

Wilson 一致生成树算法 [View Code] [Wiki] [Mike Bostock's Javascript Animation]

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Reaction-Diffusion Simulation

反应扩散方程模拟 [View Code] [Wiki] [View Webm Animation] [Pmneila's Javascript Animation]

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The 120-cell

120 胞腔 [View Code][Wiki]

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Lorenz Attractor Animation

洛伦兹吸引子动画 [View Code][View Webm Animation]

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2D Hyperbolic Tilings

Poincare 双曲铺砌 [View Code]

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3D Hyperbolic Honeycombs

双曲蜂巢 [View Code]

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Dependencies

Python libs:

$ pip install -r requirements.txt

numpy, matplotlib, scipy, cairo, palettable, tqdm, numba, pyglet, vapory

Softwares:

ImageMagick, FFmpeg, POV-Ray