The Coffee Automaton - Quantifying the Rise and Fall of Complexity in Closed Systems

A reproduction of the paper The Coffee Automaton - Quantifying the Rise and Fall of Complexity in Closed Systems.

This codebase started from the given code in the paper and was updated to python 3 with few changes to improve experiment speed. Moreover some additional feature were added such as a fluid-like automaton, different smoothing functions, and different initial states.

A drop of milk in coffee

Fine	Coarse	Adjusted coarse

Entropy, Complexity and Sophistication

Fine	Coarse	Adjusted coarse

Reproduced results

Paper figure:

Reproduced figures:

Note that in our codebase and for the sake of accuracy and generalisation, we replaced "complexity" by the "coarse_3" size and "entropy" by the "fine" size.

Interacting	Non-Interacting
Interacting automaton takes more step because we count steps when two identical cells are choosen to be swaped, but results are fairly similar for both complexity and entropy.	Non-interacting automaton results couldn't be reproduced, even in loglog scale we cannot see any sign of complexity increase during the experiment even if the entropy is identical.

Added Features

Circular initial state

Instead of starting with a half coffee / half milk initial state we called updown. You can now initialize a circle of milk in the center and coffee all around, called the circular initial state.

Updown	Circular

Other smoothing functions

• Generalisation of the coarse-graining function to $k\in N^*, k>2$ categories. In the paper, they take 3 for the initial coarse-graining and 7 for the adujsted coarse-graining.
• Differences [0.5 if f(x) == x else x] for each coarse-graining.
• Differences Mask [f(x) == x] for each coarse-graining.

Fine	Coarse_3	Coarse_7	Coarse_11	Diff_3	Diff_7	Diff_11	Mask_3	Mask_7	Mask_11

Fluid automaton

Interacting	Non-Interacting	Fluid

Installation

Using pip

pip install git+https://github.com/MathisFederico/coffeematon.git

From source

git clone https://github.com/MathisFederico/coffeematon.git

Then inside the worspace:

pip install -e .

Quickstart

Launch an experiment

python -m coffeematon --help

Plot a graph from a csv results file

python -m coffeematon.plot_results --help

Generate a gif from bitmaps

python -m coffeematon.generate_gifs --help

Results

Initial state	Automaton type	Size	Graph
Updown	Interacting	100
Updown	Interacting	200
Circular	Interacting	100
Circular	Interacting	200
Updown	Fluid	100
Updown	Fluid	200
Circular	Fluid	100
Circular	Fluid	200
Updown	Non-Interacting	100
Updown	Non-Interacting	200
Circular	Non-Interacting	100
Circular	Non-Interacting	200