Massive Shape Formation in Grid Environments

Shape formation mechanism plays an essential role in many natural processes, involving the formation and evolution of living or non-living structures, and shows potential applications in many emerging domains. In existing research and practice, there still lacks a shape formation mechanism that manifests efficiency, scalability, and stability at the same time. Inspired by phototaxis observed in nature, we propose a self-organized approach for the massive formation of connected shapes in grid environments. The key component of this approach is an artificial light field superimposed on a grid environment, which is determined by the positions of all agents and at the same time drives all agents to change their positions, forming a dynamic mutual feedback process. To evaluate the effectiveness of this approach, we conduct a set of simulations, involving 156 shapes from 16 categories, comparing with four baseline methods. The results show that: (1) our approach outperforms the three semi-/decentralized non-optimal baselines in efficiency, scalability, and stability; (2) compared to the centralized optimal baseline, our approach exhibits considerable decreases in the absolute completion time on diverse shape formation tasks, indicating a better efficiency and scalability of our approach.