Pywonderland - A tour in the wonderland of math with python.

Overview

A Tour in the Wonderland of Math with Python

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

About this repo

The purpose of this project is to show the beauty of math with python by rendering high quality images, videos and animations. It consists of several independent projects with each one illustrates a special object/algorithm in math. The current list contains:

  • Aperiodic tilings like Penrose tiling, Ammann-Beenker tiling, etc.
  • Triology on perfectly random sampling algorithms.
    1. Domino shuffling algorithm on Aztec diamonds.
    2. Wilson's uniform spanning tree algorithm on 2d grids.
    3. Coupling from the past algorithm on lozenge tilings.
  • Hopf fibration.
  • 3D and 4D Uniform polytopes.
  • 2D uniform tilings and 3D uniform honeycombs in Euclidean, spherical and hyperbolic spaces.
  • Make gif animations of various algorithms.
  • Lots of shader animations.
  • Miscellaneous scripts like E8 root system, Mandelbrot set, Newton's fractal, Lorenz attractor, etc.

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).

Gallery

The code for some of the images are not in the master branch, they can be found in the released version.

  • Uniform 3D and 4D polytopes

  • Möbius transformations

  • 3D Euclidean uniform honeycombs and their duals

  • Gray-Scott simulation

  • 3D hyperbolic uniform honeycombs

  • Limit set of rank 4 Coxeter groups

  • Aperiodic tilings

  • 3D Fractals

  • Coxeter automata and 2D Uniform tilings

  • GIF animations of various algorithms

  • Others

Many more to be comtinued ...

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.

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.

Thanks

I have learned a lot from the following people:

License

see the LICENSE file.

Comments
  • Run pywonderland inside a Docker container

    Run pywonderland inside a Docker container

    Q: How can I work with pywonderland on my computer without installing all of the required libraries and modules into my operating system?

    A: Docker will allow you to create a Linux container running Python 3 where we can install pywonderland and all of its dependencies.

    opened by cclauss 19
  • Define raw_input() for Python 3

    Define raw_input() for Python 3

    input() is a different built-in function in Python 2 so we should not overwrite it. Also used strip() to eliminate leading or trailing whitespace in user input.

    opened by cclauss 6
  • Question about gifmaze module and pypi

    Question about gifmaze module and pypi

    Hello.

    I would lile to contribute to the gifmaze module, but I am a bit lost between the various versions of this code.

    So :

    • is this the "official" gifmaze.py source code repository ? :)
    • do you plan on publishing new version of gifmaze on pypi.org ?
    • are you willing to accept pull requests ?

    Regards

    opened by Lucas-C 4
  • [Feature request]Universal Random Structures in 2D

    [Feature request]Universal Random Structures in 2D

    Hi there, Really nice animations and super cool project! I am wondering if there is any plan to add Universal Random Structures in 2D (work by Scott Sheffield and Jason Miller). This Quanta article gives some good introduction, and there are more demo images here: http://statslab.cam.ac.uk/~jpm205/images.html

    opened by junpenglao 2
  • Suggestion: Conway's Game of Life

    Suggestion: Conway's Game of Life

    Suggesting another example. Here is a good reference for Python code implementing and explaining Conway's Game of Life: https://jakevdp.github.io/blog/2013/08/07/conways-game-of-life/

    opened by yoavram 2
  • Make fractal3d.py Python 3.8 ready

    Make fractal3d.py Python 3.8 ready

    The script fractal3d.py fails with Python 3.8, because time.clock() was removed from the Python API. (https://docs.python.org/3/whatsnew/3.8.html#api-and-feature-removals)

    In this PR i replaced time.clock() with time.process_time()

    opened by gsilvan 1
  • Use dictionary for parse_image to speed up image parsing.

    Use dictionary for parse_image to speed up image parsing.

    In parse_image, we do a membership check on colors, which is a list, and takes O(n) time. Using a dictionary is effectively a drop in replacement, but reduces lookup time to O(1), and offers a 5x speedup for the image for example4() in gifmaze/example_maze_animations (1.1421077s to 0.213111s)

    (Note that in Python 3.6+, dictionaries are ordered by default, but if you want to support 3.5 and below, OrderedDict is need)

    opened by philippeitis 1
  • Fix some bug risks and code quality issues

    Fix some bug risks and code quality issues

    Changes:

    • Remove unnecessary list comprehension
    • Make valid method a staticmethod
    • Remove unnecessary elif after return statement
    • Fix dangerous default argument.
    • Add .deepsource.toml file to file to run continuous static analysis on the repository with DeepSource

    This PR also adds .deepsource.toml configuration file to run static analysis continuously on the repo with DeepSource. Upon enabling DeepSource, quality and security analysis will be run on every PR to detect 500+ types of problems in the changes — including bug risks, anti-patterns, security vulnerabilities, etc.

    DeepSource is free to use for open-source projects, and is used by teams at NASA, Uber, Slack among many others, and open-source projects like ThoughtWorks/Gauge, Masonite Framework, etc.

    To enable DeepSource analysis after merging this PR, please follow these steps:

    • Sign up on DeepSource with your GitHub account and grant access to this repo.
    • Activate analysis on this repo here.
    • You can also look at the docs for more details. Do let me know if I can be of any help!
    opened by mohi7solanki 1
  • Error when runing e8.py

    Error when runing e8.py

    ---> 14 import cairocffi as cairo 15 import numpy as np 16 from palettable.colorbrewer.qualitative import Set1_8

    C:\Localdata\Software\PythonAnaconda\lib\site-packages\cairocffi_init_.py in () 14 import ctypes.util 15 ---> 16 from . import constants 17 from .compat import FileNotFoundError 18 from ._ffi import ffi

    ImportError: cannot import name constants

    opened by xhtp2000 1
  • docs: fix simple typo, representaion -> representation

    docs: fix simple typo, representaion -> representation

    There is a small typo in src/polytopes/polytopes/models.py.

    Should read representation rather than representaion.

    Semi-automated pull request generated by https://github.com/timgates42/meticulous/blob/master/docs/NOTE.md

    opened by timgates42 0
  • Add flake8 testing to Travis CI

    Add flake8 testing to Travis CI

    Each time someone adds code to this repo, CI automatically can run tests on it. The owner of the this repo would need to go to https://travis-ci.org/profile and flip the repository switch on to enable free automated flake8 testing on each pull request.

    opened by cclauss 0
  • (PYL-R1723) Unnecessary `else` / `elif` used after `break`

    (PYL-R1723) Unnecessary `else` / `elif` used after `break`

    Description

    The use of else or elif becomes redundant and can be dropped if the last statement under the leading if / elif block is a break statement. In the case of an elif after break, it can be written as a separate if block. For else blocks after break, the …

    Occurrences

    There is 1 occurrence of this issue in the repository.

    See all occurrences on DeepSource → deepsource.io/gh/neozhaoliang/pywonderland/issue/PYL-R1723/occurrences/

    opened by mayankgoyal-13 0
Releases(0.1.0)
Owner
Zhao Liang
My name is 赵亮 (Zhao Liang), since it's used by too many people I have to add a 'neo' prefix to sign up websites. I study and code math stuff.
Zhao Liang
Animal Sound Classification (Cats Vrs Dogs Audio Sentiment Classification)

this is a simple artificial neural network model using deep learning and torch-audio to classify cats and dog sounds.

crispengari 3 Dec 05, 2022
A compendium of useful, interesting, inspirational usage of pandas functions, each example will be an ipynb file

Pandas_by_examples A compendium of useful/interesting/inspirational usage of pandas functions, each example will be an ipynb file What is this reposit

Guangyuan(Frank) Li 32 Nov 20, 2022
Automatic packaging of the open-composite libs for OvGME

OvGME Packager for OpenXR – OpenComposite for DCS Note This repository is currently unsupported and needs to be migrated to the upstream OpenComposite

12 Nov 03, 2022
Active learning for Mask R-CNN in Detectron2

MaskAL - Active learning for Mask R-CNN in Detectron2 Summary MaskAL is an active learning framework that automatically selects the most-informative i

49 Dec 20, 2022
PyTorchVideo is a deeplearning library with a focus on video understanding work

PyTorchVideo is a deeplearning library with a focus on video understanding work. PytorchVideo provides resusable, modular and efficient components needed to accelerate the video understanding researc

Facebook Research 2.7k Jan 07, 2023
PyTorch implementation of deep GRAph Contrastive rEpresentation learning (GRACE).

GRACE The official PyTorch implementation of deep GRAph Contrastive rEpresentation learning (GRACE). For a thorough resource collection of self-superv

Big Data and Multi-modal Computing Group, CRIPAC 186 Dec 27, 2022
A system for quickly generating training data with weak supervision

Programmatically Build and Manage Training Data Announcement The Snorkel team is now focusing their efforts on Snorkel Flow, an end-to-end AI applicat

Snorkel Team 5.4k Jan 02, 2023
TagLab: an image segmentation tool oriented to marine data analysis

TagLab: an image segmentation tool oriented to marine data analysis TagLab was created to support the activity of annotation and extraction of statist

Visual Computing Lab - ISTI - CNR 49 Dec 29, 2022
TiP-Adapter: Training-free CLIP-Adapter for Better Vision-Language Modeling

TiP-Adapter: Training-free CLIP-Adapter for Better Vision-Language Modeling This is the official code release for the paper 'TiP-Adapter: Training-fre

peng gao 189 Jan 04, 2023
Official implementation of the paper "Lightweight Deep CNN for Natural Image Matting via Similarity Preserving Knowledge Distillation"

Lightweight-Deep-CNN-for-Natural-Image-Matting-via-Similarity-Preserving-Knowledge-Distillation Introduction Accepted at IEEE Signal Processing Letter

DongGeun-Yoon 19 Jun 07, 2022
Roger Labbe 13k Dec 29, 2022
This repository contains the code for the paper "Hierarchical Motion Understanding via Motion Programs"

Hierarchical Motion Understanding via Motion Programs (CVPR 2021) This repository contains the official implementation of: Hierarchical Motion Underst

Sumith Kulal 40 Dec 05, 2022
Omniscient Video Super-Resolution

Omniscient Video Super-Resolution This is the official code of OVSR (Omniscient Video Super-Resolution, ICCV 2021). This work is based on PFNL. Datase

36 Oct 27, 2022
Code for the paper "How Attentive are Graph Attention Networks?"

How Attentive are Graph Attention Networks? This repository is the official implementation of How Attentive are Graph Attention Networks?. The PyTorch

175 Dec 29, 2022
Vehicle direction identification consists of three module detection , tracking and direction recognization.

Vehicle-direction-identification Vehicle direction identification consists of three module detection , tracking and direction recognization. Algorithm

5 Nov 15, 2022
Official PyTorch implementation of "Proxy Synthesis: Learning with Synthetic Classes for Deep Metric Learning" (AAAI 2021)

Proxy Synthesis: Learning with Synthetic Classes for Deep Metric Learning Official PyTorch implementation of "Proxy Synthesis: Learning with Synthetic

NAVER/LINE Vision 30 Dec 06, 2022
AI创造营 :Metaverse启动机之重构现世,结合PaddlePaddle 和 Wechaty 创造自己的聊天机器人

paddle-wechaty-Zodiac AI创造营 :Metaverse启动机之重构现世,结合PaddlePaddle 和 Wechaty 创造自己的聊天机器人 12星座若穿越科幻剧,会拥有什么超能力呢?快来迎接你的专属超能力吧! 现在很多年轻人都喜欢看科幻剧,像是复仇者系列,里面有很多英雄、超

105 Dec 22, 2022
This repository is the official implementation of Using Time-Series Privileged Information for Provably Efficient Learning of Prediction Models

Using Time-Series Privileged Information for Provably Efficient Learning of Prediction Models Link to paper Abstract We study prediction of future out

Rickard Karlsson 2 Aug 19, 2022
Non-stationary GP package written from scratch in PyTorch

NSGP-Torch Examples gpytorch model with skgpytorch # Import packages import torch from regdata import NonStat2D from gpytorch.kernels import RBFKernel

Zeel B Patel 1 Mar 06, 2022
An implementation of Deep Forest 2021.2.1.

Deep Forest (DF) 21 DF21 is an implementation of Deep Forest 2021.2.1. It is designed to have the following advantages: Powerful: Better accuracy than

LAMDA Group, Nanjing University 795 Jan 03, 2023