Biruta Kresling is a Paris-based architect and independant researcher on folded structures—specifically how nature folds and unfolds tree leaves, tortoise shell bamboo, turbinate mollusk shells, the air sac of the hawkmoth Achaerontia atropos, and other biological structures. In this video clip from NOVA’s The Origami Revolution, she demonstrates the Kresling-Pattern, the spontaneous “buckling under torsional load.” Kresling proposes that this buckling is not a failure of the materials but a model from nature that can be understood and designed for in science and engineering.
By experiments with thin-walled cylinders in paper or in polypropylene, it was discovered that a “natural” pattern – analogous to that of the hawkmoth – arises under torsional load. In the experiments a thin-walled sheet is wrapped around two coaxial mandrels, leaving a gap. When the mandrels are twisted, highly regular self-organized folding pattern appears, across the gap, formed by inclined and elongated parallelograms (mountain-folds), divided on their long diagonal by a valley-fold. For any given gap size there is a left-hand or right-hand twist-buckling pattern.
In addition to the cylinder experiment, she demonstrates how a cone, when smashed, can fold itself into a structure that seems to mimic the spiral geometries of a pinecone or mollusk shell.
For more in-depth exploration into folded structures, check out the film Independent Lens: Between the Folds, and these two excellent books: Folding Techniques for Designers: From Sheet to Form and Paper Sculpture: Fluid Forms.