Interacting Behavior and Emerging Complexity

TL;DR

This paper empirically investigates how interactions between simple cellular automata influence the evolution of complexity, revealing that interactions can generate and modulate complexity in emergent systems.

Contribution

It introduces a novel empirical framework for quantifying complexity changes through interactions of cellular automata, highlighting intrinsic properties and robustness of different rules.

Findings

Interactions can increase complexity in cellular automata.

Some rules are more fragile or robust to global interactions.

Complexity is partly intrinsic to the interaction rules themselves.

Abstract

Can we quantify the change of complexity throughout evolutionary processes? We attempt to address this question through an empirical approach. In very general terms, we simulate two simple organisms on a computer that compete over limited available resources. We implement Global Rules that determine the interaction between two Elementary Cellular Automata on the same grid. Global Rules change the complexity of the state evolution output which suggests that some complexity is intrinsic to the interaction rules themselves. The largest increases in complexity occurred when the interacting elementary rules had very little complexity, suggesting that they are able to accept complexity through interaction only. We also found that some Class 3 or 4 CA rules are more fragile than others to Global Rules, while others are more robust, hence suggesting some intrinsic properties of the rules independent of the Global Rule choice. We provide statistical mappings of Elementary Cellular Automata exposed to Global Rules and different initial conditions onto different complexity classes.