Algorithmic Information Dynamics of Persistent Patterns and Colliding Particles in the Game of Life

TL;DR

This paper applies algorithmic information dynamics to analyze emergent patterns and particles in Conway's Game of Life, providing a new approach to characterizing complex structures beyond traditional entropy-based methods.

Contribution

It introduces a novel application of algorithmic information dynamics to classify and track persistent patterns and motifs in cellular automata, surpassing traditional measures.

Findings

Effective characterization of persistent patterns in GoL.

Detection of changes in motif distributions over time.

Demonstration of advantages over entropy-based measures.

Abstract

Without loss of generalisation to other systems, including possibly non-deterministic ones, we demonstrate the application of methods drawn from algorithmic information dynamics to the characterisation and classification of emergent and persistent patterns, motifs and colliding particles in Conway's Game of Life (GoL), a cellular automaton serving as a case study illustrating the way in which such ideas can be applied to a typical discrete dynamical system. We explore the issue of local observations of closed systems whose orbits may appear open because of inaccessibility to the global rules governing the overall system. We also investigate aspects of symmetry related to complexity in the distribution of patterns that occur with high frequency in GoL (which we thus call motifs) and analyse the distribution of these motifs with a view to tracking the changes in their algorithmic probability over time. We demonstrate how the tools introduced are an alternative to other computable measures that are unable to capture changes in emergent structures in evolving complex systems that are often too small or too subtle to be properly characterised by methods such as lossless compression and Shannon entropy.