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neozhaoliang
3.9K Stars 354 Forks MIT License 436 Commits 3 Opened issues

Description

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.


Build Status


UPDATE: This repo is currently under a huge reconstruction, more fancy and advanced features will be added, some dirty code will be removed. Also I will make more shadertoy live demos to help people understand the math. So you can look forward a more fantastic version :smile:.​

Known issues:

  1. The code for drawing E8 root system is not mathematically correct (though the result image looks right), I didn't take the bilinear form into account. Same reason for drawing polytope on its Coxeter plane in
    polytopes
    project.

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

sage
,
sympy
,
mathemetica
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

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

How to use

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

src/
is a single program (except that
glslhelpers
is a helper module for running glsl programs and
misc
is a collection of independent scripts), any file named
main.py
,
run_*.py
,
example_*.py
is an executable script that gives some output.

List of algorithms

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

Dependencies

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

install_dependencies.sh
.
sudo bash install_dependencies.sh

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

Note

pygraphviz
also requires
libgraphviz-dev
:
sudo apt-get install libgraphviz-dev

In the scripts these softwares are called in command line as

povray
,
ffmpeg
,
convert
(from
ImageMagick
), etc. For Windows users you should add the directories contain these .exe files to the system
Path
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
Path
and rename
pvengine64.exe
to
povray.exe
, then you can run the scripts without any changes and everything works fine.

TODO

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

    uniform-tilings
    project by a custom one (since I want to include LaTeX expressions in the images), 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.

  • Escher circle limits in svg format.

  • Knots and dynamic systems.

Thanks

I have learned a lot from the following people:

License

see the LICENSE file.

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