Implementations of self-reconfigurable robotics rearrange modules through a planned, deterministic reconfiguration path. Reconfiguration is achieved using active module locomotion or manipulation. Here we propose a form of self-reconfigurable robotics based on passive, stochastic self-organization. Solid-state cellular units exploit "Brownian motion" in their environment and require no local power or locomotion ability. This form of reconfiguration avoids many of the barriers that prevent self-reconfigurable robotics from extending to large numbers and small scales. We demonstrate working prototypes and discuss preliminary analytical and computational models for analyzing the scalability of this concept.