Emergent computing in a non-Abelian metamaterial

An elastic material that follows the linear laws of elasticity is impervious to the order of actuations due to superposition, severely constraining the design of programmable metamaterials. Here, we introduce a non-Abelian metamaterial sensitive to the sequential ordering of mechanical actuation signals as well as to the magnitude of such actuations. We demonstrate how to describe these materials as finite state machines and boolean logic circuits, encoding different flavours of one-bit memory in a single unit cell. We present a scalable framework to study such materials to understand and utilize their rich and complex behaviour. Our work sets the groundwork for multifunctional designer matter with memory.