by neozhaoliang

neozhaoliang / pywonderland

A tour in the wonderland of math with python.

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A Tour in the Wonderland of Math with Python

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

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About this repo

The purpose of this project is to show the beauty of math with python. It consists of several independent subprojects with each one illustrates a special object/algorithm in math. The current list is:

These topics are chosen largely due to my personal taste:

  1. They must produce appealing results.
  2. There must be some non-trivial math behind them.
  3. The code should be as simple as possible.

I'll use only popular python libs and build all math stuff by hand (tools like

will not be used here). Also I will only maintain the code for
python >= 3.6

Note: Python3.5 is deprecated now because it's a bit tricky to install the latest numba on Ubuntu16.04 for python3.5 (if you are using

for package management then you need not worry about this because anaconda will fix it for you). Note
is only used in a few fractal scripts in the
directory and all other projects should also work for python>=2.7.

A few examples:

How to use

All projects here are implemented in a ready-to-use manner for new comers. That is you can simply run the examples without tweaking any parameters once you have the dependencies installed correctly. Each subdirectory in

is a single program (except that
is a helper module for running glsl programs and
is a collection of independent scripts), any file named
is an executable script that gives some output.

List of algorithms

Here is a list of some algorithms implemented in this project:


The recommended way to install all dependencies is simply running the bash script
sudo bash

Or you can install the python libs by pip:

pip install -r requirements.txt

Open source softwares required:

  • python3-tk
    (for file dialog)
  • ImageMagick
    (for making gif animations)
  • FFmpeg
    (for saving animations to video files)
  • POV-Ray
    (for generating high quality raytracing results)
  • graphviz
    (for drawing automata of Coxeter groups)
  • Inkscape
    (optional, for convering large svg files to png)

They can all be installed via command-line:

sudo apt-get install python3-tk imagemagick ffmpeg povray graphviz inkscape


also requires
sudo apt-get install libgraphviz-dev

In the scripts these softwares are called in command line as

), etc. For Windows users you should add the directories contain these .exe files to the system
environment variables to let the system know what executables these commands refer to. For example on Windows the default location of POV-Ray's exe file is
C:\Program Files\POV-Ray\v3.7\bin\pvengine64.exe
, so you should add
C:\Program Files\POV-Ray\v3.7\bin
to system
and rename
, then you can run the scripts without any changes and everything works fine.


I have a long list of projects to do in mind and they may take a few years to accomplish:

  • Knots, inspired by knotilus but I hope I could do better than that.

  • Minimal surfaces. Implement two ways to construct minimal surfaces: either by solving Plateau's problem or use a pair of analytic functions. Render the result in POV-Ray.

  • Uniform tilings: Replace the hyperbolic module currently used in

    project by a custom one, with upper half space model added. Also find an efficient way to render the upper half space boundary images in python. Inspired by Roice's artwork.
  • Shader animations of polyhedral, euclidean, hyperbolic tilings with gears, inspired by iq' artwork.

  • Escher circle limits in svg format.

  • Shader animation of aperiodic tilings using de Bruijn's approach.

  • Draw limit roots of Coxeter groups.

  • Knots and dynamic systems.


I have learned a lot from the following people:


see the LICENSE file.

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