A tour in the wonderland of math with python.
A collection of python scripts for drawing beautiful figures and animating interesting algorithms in mathematics.
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:.
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:
I'll use only popular python libs and build all math stuff by hand (tools like
mathemeticawill 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
anacondafor package management then you need not worry about this because anaconda will fix it for you). Note
numbais only used in a few fractal scripts in the
miscdirectory and all other projects should also work for python>=2.7.
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
glslhelpersis a helper module for running glsl programs and
miscis a collection of independent scripts), any file named
example_*.pyis an executable script that gives some output.
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 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
sudo apt-get install libgraphviz-dev
In the scripts these softwares are called in command line as
ImageMagick), etc. For Windows users you should add the directories contain these .exe files to the system
Pathenvironment 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\binto system
povray.exe, 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
uniform-tilingsproject 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.
I have learned a lot from the following people:
see the LICENSE file.