Trying to peer inside a crumpled ball by simulating the process in three dimensions is “mathematically nasty,” a problem that quickly pushes lab-grade computers to their limits, said Menon. And trying to reverse-engineer structure from patterns revealed upon unfolding just isn’t possible. What happens in a crumpled ball stays in a crumpled ball.
“If you’re not talking about simulation, but mathematical understanding of these things, that’s one step harder,” said Menon. “We understand the underlying equations of the mechanics of a thin sheet very well. Those have been around for a century. But solving those equations, to produce a physical understanding, is difficult even in simple cases. If you’re talking about a structure that owes its properties to 1,000 or more of these structures, interacting in complicated ways, that’s asking more than we can do now.”