Systematic Design of Local Rules for Directing Emergent Structure in Bottom-Up Systems

Abstract: Many biological systems collectively construct complex, adaptive, and functional architectures, where function emerges from bottom-up building processes rather than top-down planning or centralized control. However, general strategies for programming and controlling such emergent function in engineered systems remain largely unexplored. In this work, we present a systematic framework for designing local behavioral rule sets for simple builders such that, when adhered to, structures with targeted global properties emerge. Using a minimal model inspired by tent caterpillars, we study how simple agents equipped with limited sensing and no memory or global knowledge construct networked structures through local deposition of line segments. We base our framework on tuning local degrees of freedom in a complex system to alter global behavior. By identifying the degrees of freedom that influence a given property and specifying how they are tuned through local rules, we demonstrate that the corresponding global properties can be directed. We explore this through three geometric properties of the agents' resulting networks, in particular area coverage, average line density, and front curvature. We show that agents can reliably achieve targeted values for these properties while maintaining low variability in the presence of stochasticity. These results establish a generalizable approach for programming emergence in decentralized systems and suggest new pathways for designing adaptive materials and autonomous construction strategies in complex, uncertain environments.