Local Rules for Directing the Emergence of Global Properties in Complex Structures

Abstract

From ants to caterpillars, many biological systems composed of simple builders have been observed to construct complex, adaptive, and functional architectures without requiring complete access to the global state of the structure. In these systems, global function emerges from the accumulation of local actions, as individual builders follow local rules to manipulate, modify, and deposit material in response to local environmental stimuli. This raises the question of how local rules can be selected for simple builders so that desired functions reliably emerge as a natural consequence of their interactions with their environment. We propose a systematic framework for determining such rules and demonstrate its effectiveness using a minimal model inspired by tent caterpillars and their silk networks. Using our framework, we show that local rules can be designed so that when simple builders follow them during network construction, the values of several emergent properties including area coverage, mean line density, and front curvature can be directed toward specific target values. We use a statistical approach to determine how rules can be modified to increase the probability that a useful local change occurs, the magnitude of that change, or both, so that the target property can be achieved reliably. Our results demonstrate a general strategy for linking local rules to emergent global properties in complex structures. This strategy offers a step toward fabricating functional structures using simple builders in uncertain environments where global information, precise control, and sustained human supervision are infeasible.