Two-dimensional memories: from return point memory to return line memory

When large hysteretic systems like crumpled sheets or particle packings are driving with a global field like compression or sheer, they exhibit return-point memory (RPM) – the system's ability to remember at which value(s) the drive reversed (turned). However, what about when the driving is two-dimensional? Here, we experimentally investigate what aspects of the driving are remembered by using two coupled Nitinol springs that each exhibit RPM, and controlling their compression independently. We find that the turning-points are remembered as curves whose shape depends on the coupling. Together, our work presents multi-dimensional driving as a new avenue to explore and understand the memory formation in complex systems.