Endless forms most beautiful: how to program materials using geometry, topology and singularities

The dream of programmable matter is to create materials whose physical properties (shape, moduli, response to perturbations, etc.) can be changed on the fly. For many years, my group has been thinking about how to program flat sheets that fold up into three dimensional shapes, most recently by exploiting the principles of origami design. Unfortunately, a combinatorial explosion of folding pathways makes robust folding particularly challenging. In this talk, I will discuss how this pluripotency arises from the topology of the configuration space. This suggests a broader understanding of a larger class of materials spanning from folding forms to spring networks to mechanical structures that perform computational logic.