Modelling the Collective Building of Complex Architectures in Social Insects with Lattice Swarms

Abstract

In this paper we present a formal model of distributed building inspired by wasp colonies. We characterize a set of distributed stigmergic algorithms that allow a swarm of simple agents to build coherent nest-like structures. The agents that constitute the swarm of builders move randomly on a 3D lattice and can deposit elementary bricks. The agents do not communicate, have no global representation of the architecture they are building, do not possess any plan or blueprint and can only perceive the local configuration of matter surrounding them. Only a few of these configurations are stimulating, that is, trigger a building action. The aim of this paper is not to prove that this model is an accurate model of how wasps behave, but rather to show (i) that such behavioural algorithms can produce coherent biological-like architectures, (ii) that these architectures, if they are to be generated with these behavioural algorithms, require algorithms with specific “coordination” properties, and (iii) finally that algorithms possessing these specific properties produce in turn only very specific, coherent architectures. In effect, we found an empirical one to one correspondence between biological-like architectures and “coordinated algorithms”. Coordinated algorithms rely on a partition of the shape to be built into modular subshapes; if a swarm of agents is to build a given coherent architecture, the shape has to be decomposed into a finite number of?!building steps, with the necessary condition that the local stimulating configurations that are created at a given stage differ from those created at a previous or a forthcoming building stage so as to avoid disorganization of the whole building activity. Moreover, shapes generated with non-coordinated algorithms, for instance when stimulating configurations corresponding to the subshapes overlap and may subsequently affect the overall building process, are unstable, the same given rule table will produce very dissimilar architecture in different stimulations. Finally, architectures generated under such conditions were found not to resemble any known biological architecture. We believe that our study constitutes a first step towards a deeper understanding of the origins of natural shapes in terms of the logical constraints that may have affected the evolutionary path.