Pattern Formation in Robotic Mechanical Metamaterial

Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be explored. As the underlying dynamics are typically complex, pattern formation is often theoretically analyzed and understood via phenomenological models, which effectively represent the causal mechanisms, but obscure the link between the small-scale interactions/processes and the observed macroscopic behavior. Moreover, efforts to prescribe the patterning response are often undercut by the experimental inaccessibility of the small-scale constituents/processes. This article demonstrates an artificial system (i.e., a robotic mechanical metamaterial) as an accessible and versatile platform within which to explore and prescribe the patterning response of non-equilibrium systems. Specifically, in varying a feedback parameter within the prescribed reaction kinetics, the robotic mechanical metamaterial alternately develops spatial and temporal oscillations in the displacement field following a perturbation of the initial quiescent, uniform state. The platform is amenable to a first-principles analytical description so that corresponding theoretical results possess qualitative and quantitative significance, and maintain connection to the specific system parameters.