Wrinkles have been in the limelight for their theoretical importance in understanding geometric nonlinearities in elasticity and also for their practical significance in emerging engineering applications such as lithography-free micropatterning Yet, despite decades of study, a general predictive theory of confinement-induced wrinkling remains elusive. Such a theory would enable the creation of targeted yet reconfigurable wrinkle patterns and could identify the broadest possible class of wrinkle morphologies that can be obtained through geometrically incompatible confinement."

Source : Nature Physics (Aug. 2022)

The mathematics of wrinkling and crumpling are so notoriously complex that even sophisticated computer modeling techniques fail to accurately predict how a surface will fold up. The paper cited above managed to find solutions for some 'flat' scenarios.

In many 'real world' situations, however, there are too many variables (and quasi-random effects) to construct accurate models.

Further reading : A state variable for crumpled thin sheets, Communications Physics volume 1, article number: 70

From collapsed hulls of ships to discarded mathematical theorems written on a white piece of paper, many thin sheets end their life cycle as crumpled heaps. Nevertheless, the dynamics by which an initially flat sheet develops into a disordered and elaborate three-dimensional network of folds are often considered a hallmark example of disordered and complex system"