Propagation of Information through Origami Folding: A Graph-Theoretic Approach

Origami structures are a network of vertices connected to their neighbors through shared creases with preferred fold angles and rotational stiffnesses. As a result of the nonlinear and nonlocal interplay of the crease mechanics, crease geometries, and vertex topologies, origami structures are generally multistable. Here multistability naturally leads to a network embedding: the equilibrium configurations as the network’s vertices and the folding paths between them as the edges. The multiple layers of network complexity inherent in origami enable new ways to mechanically store and process information. To identify the network embedding, we use numerical optimization and minimum energy path methods. Specifically, we find and classify both stable states and folding paths between states. Then using shape metrics, we identify intermediate branching points and bifurcations where fold paths intersect. The graph representation which emerges leads to insights on the stability and propagation of mechanical information from one stable state to the next. Understanding the links between crease pattern design and the propagation of mechanical information will be key to effectively utilizing origami as a design paradigm and “compiler” for unconventional and network-theoretic computing.