Digitally programmable kirigami metamaterials via magnetic encoding

The vast configuration space of magnetic metamaterials, enabled by embedding reversibly orientable magnets into rotating-square kirigami pixels, remains largely unexplored beyond uniform magnetization patterns. To navigate this space, in-plane magnetic orientations are treated as binary bits, creating 2N×N possible states for an N×N lattice. A Monte Carlo approach, combined with a mapping of all configurations onto an N2-dimensional hypercube, allows for the systematic statistical enumeration of energy landscapes and single-bit reconfiguration paths. This framework classifies stability into neutral, monostable, bistable, and tristable classes, with occurrence probabilities converging to approximately 0, 0.6013, 0.3981, and 0.0006 as system size increases. Programmable responses—including tension–compression asymmetric stiffness, snap-through instability, and a two-stage absorption/locking energy dissipation mode—are demonstrated. The resulting digital, graph-based platform points to applications in soft modular robotics, impact-mitigation layers, deployable structures, and mechanical logic.