Partial differential equations versus cellular automata for modelling combat

TL;DR

This paper demonstrates that simple partial differential equations can replicate complex cellular automaton behaviors in combat modeling, providing a deterministic alternative that explains observed phenomena without assuming agent reasoning.

Contribution

It introduces a PDE-based model that reproduces cellular automaton combat behaviors, challenging the need for agent-based reasoning assumptions.

Findings

PDE model replicates complex cellular automaton behaviors.

Deterministic equations explain spatial behaviors without agent reasoning.

Model captures decentralised self-organisation and tactical adaptation.

Abstract

We reproduce apparently complex cellular automaton behaviour with simple partial differential equations as developed in (Keane 09). Our PDE model easily explains behaviour observed in selected scenarios of the cellular automaton wargame ISAAC without resorting to anthropomorphisation of autonomous 'agents'. The insinuation that agents have a reasoning and planning ability is replaced with a deterministic numerical approximation which encapsulates basic motivational factors and demonstrates a variety of spatial behaviours approximating the mean behaviour of the ISAAC scenarios. All scenarios presented here highlight the dangers associated with attributing intelligent reasoning to behaviour shown, when this can be explained quite simply through the effects of the terms in our equations. A continuum of forces is able to behave in a manner similar to a collection of individual autonomous agents, and shows decentralised self-organisation and adaptation of tactics to suit a variety of combat situations.