Animating the Quantum Drunkard’s Walk

A recent PPCG challenge titled The Quantum Drunkard’s Walk was about a tiny drunken person for which quantum mechanics apply and who — being drunk — will randomly walk in one of the four cardinal directions each step they take.
As they experience the strange world of quanta, they can simultaneously take every path at once and their paths influence each other. The challenge then asked to output all possible positions the quantum drunkard could occupy, all paths they could take in ASCII representation.

The question also states this problem’s equivalence to a cellular automaton, when one removes the story boilerplate.
Cells in this cellular automaton are square and can occupy one of three states: empty, awake or sleeping. Each iteration, all cells change according to three rules.

  • An empty cell wakes up iff there is exactly one awake cell amongst its cardinal neighbours, else it stays empty.
  • An awake cell goes to sleep.
  • A sleeping cell continues to sleep.

Being code golf, the aim was to come up with a minimally sized source code; my attempt required 214 bytes and prints a nested array containing one-length strings (characters), as this output method is cheaper than concatenating all characters to one string.

python -rmi 200
python -rmi 200

However, one user took the challenge idea a bit further and created an animated gif showing the walk’s,¬†or cellular automaton’s, progression over time with an increasing number of iterations. My Python program shown in this post does exactly that, generating an animated gif showing the automaton’s progression. I even implemented rainbow support, possibly improving the automaton’s visual appearance.
Python source code can be downloaded and seen below.

I use the Python Imaging Library to produce all frames and use a shell call to let ImageMagick convert all frames to an animated gif. Animation parameters are taken via shell arguments, a full list of features follows (also available via the -h flag).

  • --iterations N Number of iterations (initial frame not counted)
  • --colorempty C Empty cell color (#rrggbb)
  • --colorawake C Awake cell color (#rrggbb)
  • --colorsleeping C Sleeping cell color (#rrggbb)
  • --rainbow Use rainbow colors (overrides color settings)
  • --scale N Cell square pixel size
  • --convert Execute ImageMagick’s convert command
  • --delay N Delay between frames in output image.
  • --loop N Gif loops (0 means for indefinite looping)
  • --keepfiles Do not delete files when converting
python -s 25 -md 50
python -s 25 -md 50

# Python 2.7 code; Jonathan Frech; 1st of December 2017

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Haferman Carpet

The Haferman Carpet is a fractal, which kind of looks like a woven carpet. To generate it, you start with a single black pixel and apply in each cycle a set of rules.
In each generation every pixel in the carpet will be replaced by nine pixels according to the rules. A black pixel is represented by a 0, a white one by a 1.

The rules

  • 0 \rightarrow \left( \begin{array}{ccc}1&0&1\\0&1&0\\1&0&1\end{array} \right) \text{and } 1 \rightarrow \left( \begin{array}{ccc}0&0&0\\0&0&0\\0&0&0\end{array} \right)

6 iterations of the Haferman Carpet

# Python 2.7.7 Code
# Pygame 1.9.1 (for Python 2.7.7)
# Jonathan Frech 26th of February, 2016

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Conway’s Game of Life

This program is a simulation of the famous cellular automaton created by John Conway. The so-called ‘game’ is rather a simulated evolution of cells in a two-dimensional world. Each cell can either be dead (black) or alive (white) and always has eight neighbours surrounding them. In each cycle of the simulation their state will be changed based on two simple rules, which are listed below.
Despite the rule’s simplicity, the outcomes are often very interesting and complex.
For more details on the game of life, check this Wikipedia entry.

The rules

  • A live cell can only survive with exactly 2 or 3 neighbours, or else it dies.
  • A dead cell with exactly 3 neighbours comes to life.


  • Left click turns cell at current mouse position alive
  • Right click turns cell at current mouse position dead
  • ‘r’ turns every cell dead
  • ‘q’ cycles once
  • ‘w’ cycles continuously

Moving ships JBlog! Stars

# Python 2.7.7 Code
# Pygame 1.9.1 (for Python 2.7.7)
# Jonathan Frech 12th of February, 2016

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