Algorithmic Information Dynamics of Cellular Automata

TL;DR

This paper applies Algorithmic Information Dynamics to Cellular Automata, demonstrating its ability to quantify change and sensitivity in discrete dynamical systems like Conway's Game of Life, outperforming traditional statistical measures.

Contribution

It introduces a novel application of AID to CA, showing its effectiveness in analyzing system sensitivity and perturbations beyond statistical methods.

Findings

AID effectively quantifies change in 1D and 2D CA.

AID outperforms LZW and Shannon entropy in perturbation analysis.

Potential for developing multivariate AID calculus.

Abstract

We illustrate an application of Algorithmic Information Dynamics to Cellular Automata (CA) demonstrating how this digital calculus is able to quantify change in discrete dynamical systems. We demonstrate the sensitivity of the Block Decomposition Method on 1D and 2D CA, including Conway's Game of Life, against measures of statistical nature such as compression (LZW) and Shannon Entropy in two different contexts (1) perturbation analysis and (2) dynamic-state colliding CA. The approach is interesting because it analyses a quintessential object native to software space (CA) in software space itself by using algorithmic information dynamics through a model-driven universal search instead of a traditional statistical approach e.g. LZW compression or Shannon entropy. The colliding example of two state-independent (if not three as one is regulating the collision itself) discrete dynamical systems offers a potential proof of concept for the development of a multivariate version of the AID calculus.