Non-Abelian Mechanical Metamaterials

An elastic material follows the principle of superposition and is impervious to the order of actuations, severely constraining the design of programmable metamaterials. Here, we introduce a non-Abelian metamaterial that is sensitive to sequential ordering of mechanical input signals. We demonstrate how to describe these materials as finite state machines, and show that the smallest non-Abelian metamaterial already encodes both logical gates and different flavours of one-bit memory. Our work establishes the groundwork for designer matter with memory.