The Mathematics Behind Wavy Origami Tubes

What is it about?

Origami, the traditional Japanese art of paper folding, has attracted considerable interest from researchers and engineers as a geometric framework for programming mechanical behavior. By introducing carefully designed crease patterns, it is possible to create structures that can be compactly folded, deployed when needed, or even switch between distinct stable states. In this study, we investigated an intriguing phenomenon known as shape undulation, which appears in a class of origami tessellations with regularly arranged creases. We revealed that this phenomenon is governed by an unexpected underlying mathematical structure.

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Photo by Carolina Garcia Tavizon on Unsplash

Photo by Carolina Garcia Tavizon on Unsplash

Why is it important?

The mathematics of origami is founded on a simple but powerful assumption: a sheet can bend and fold, but it cannot stretch or shear. Under this constraint, determining the possible folded shapes and motions of a crease pattern is a fundamental challenge. As crease patterns become more complex, however, the problem quickly becomes difficult to analyze. To address this challenge, we adopted a different perspective. Instead of studying the origami structure as a whole, we viewed it as a collection of interacting units and described their relationships using the language of dynamical systems. This approach revealed the mathematical principles underlying shape undulations and provided a new way to understand the behavior of complex origami structures. More broadly, treating origami as a dynamical system rather than a static geometric object may help uncover previously unknown phenomena and lead to new design principles for deployable and programmable structures.