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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Double-Slit Experiment

Light is a fascinating thing in our universe. We perceive it as color, warmth and vision. Yet it does things one may not expect it to do. One of the experiments that called for a better physical model of light was the double slit experiment. In this experiment, a laser is shone through two closely adjacent slits and projected on the screen behind. Using old physical models, one would expect to see one or maybe two specs of light on the screen, when in reality there appear alternating dark and bright spots.

To explain why this seemingly strange phenomenon is occurring, one can either see light as photons and comprehend that a photon presumably follows every possible path there is in the entire universe and then — through it being observed — randomly chooses one path and thus creates stripes (according to the theory of quantum mechanics) or one can see light as simply being a wave.

For more information on the double-slit experiment, I refer to this Wikipedia entry.

The animation shown below describes light as a wave. The green vectors represent the light wave’s phase at the points on the light beam, the yellow vector represents the addition of both of the slit’s light beam’s phase when hitting the screen and the red dots at the screen represent the light’s brightness at that point (defined by the yellow vector’s length).
To create the animation, Python and a Python module called PIL were used to create single frames which were then stitched together by ImageMagick to create an animated gif.

Double-Slit Simulation (probably loading...)

# Jonathan Frech, 18th of January 2017
#          edited 19th of January 2017
#          edited 22nd of January 2017
#          edited 27th of January 2017

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