Self-organized criticality in aquatic robot swarm.

Self-organized criticality (SOC) provides a universal framework for understanding the emergence of scale-invariant behaviors in complex systems, yet its physical realization in programmable artificial systems remains challenging. We present an aquatic robot swarm, in which individuals interact via optical attraction and hydrodynamic repulsion, demonstrating key SOC features: avalanches with sizes and durations following power-law distributions, stability of scaling exponents under system upscaling, and self-organized evolution toward a steady state independent of system parameters. In the presence of external stimuli, the system not only maintains criticality but also spontaneously forms directed structures and exhibits adaptive behaviors such as collective pushing, showcasing emergent capabilities arising from local interactions. This work provides a controllable experimental platform for studying SOC in dynamic physical environments and provides insights for developing adaptive autonomous swarm systems that require minimal programming.