Artificial Life techniques – specifically, multiagent-based models and evolutionary learning algorithms – provide a powerful new approach to understanding some of the fundamental processes of War.

This chapter introduces a simple artificial “toy model” of combat called EINSTein. EINSTein is designed to illustrate how certain aspects of land combat can be viewed as self-organized, emergent phenomena resulting from the dynamical web of interactions among notional combatants. EINSTein’s bottom-up, synthesist approach to the modeling of combat stands in stark contrast to the more traditional top-down, or reductionist, approach taken by conventional military models, and it represents a step toward developing a complex systems theoretic toolbox for identifying, exploring, and possibly exploiting self-organized, emergent collective patterns of behavior on the real battlefield. A description of the model is provided, along with examples of emergent spatial patterns and behaviors.


ILACHINSKI, Andrew, 2009. EINSTein. In: Artificial Life Models in Software. Springer. p. 259–315.

In 1914, F. W. Lanchester introduced a set of coupled ordinary differential equations – now commonly called the Lanchester equations (LEs) – as models of attrition in modern warfare [1]. In the simplest case of directed fire, for example, the LEs embody the intuitive idea that one side’s attrition rate is proportional to the opposing side’s size: […]

Similar ideas were proposed around that time by Chase [2] and Osipov [3]. These equations are formally equivalent to the Lotka-Volterra Equations used for modeling the dynamics of interacting predator–prey populations [4]. Despite their relative simplicity, the LEs have since served as the fundamental mathematical models upon which most modern theories of combat attrition are based and are to this day embedded in many “state-of-the art” military models of combat. Taylor [5] provided a thorough mathematical discussion.

[…] On the other hand, as is typically the case in the more general setting of nonlinear dynamical system theory, knowing the “exact” solution to a simplified problem does not necessarily imply that one has gained a deep insight into the problem. […]