Remembering a Shape --- Assembling a Memory

Recently we have been developing a new connection between self-assembly and neural networks, where a multi-component particle system with specified interaction rules between its components is mapped onto a multi-state Hopfield neural network model. Within this framework, a fixed interaction pattern of neurons representing a ``memory'' maps to particle interactions encoding a certain structure. Properties of neural networks motivate new types of questions: Can the interaction energies of particles code for multiple structures at the same time? Can stored structures be retrieved by throwing in a nucleation seed (i.e., a small assembly of particles) and have it complete into the desired stored structure? Can we define a capacity, i.e., a maximal number of structures that can be retrieved with limited error? We investigate these questions using numerical simulations of different types of building blocks with short-range interactions.