Self-Organized Origami

In origami, form follows the sequential spatial organization of folds. This requires continuous intervention and raises a natural question: Can origami arise through self-organization? We answer this affirmatively by examining the possible physical origin for the Miura-ori leaf-folding patterns that arise naturally in insect wings, leaves, and other laminae-like organelles. In particular, we point out examples where biaxial compression of an elastically supported thin film, such as that due to differential growth, shrinkage, desiccation, or thermal expansion, spontaneously generates these patterns, and we provide a simple theoretical explanation for their occurrence.