Although thin films are typically manufactured in planar sheets or rolls, they are often forced into three-dimensional shapes, producing a plethora of structures across multiple length scales [1]. A key challenge is to understand the overall gross shape that is selected, and how it constrains the fine features, such as wrinkles, crumples, or creases. Here, we study a thin-membraned balloon as a prototypical system. We discover a surprising simplicity: the complex three-dimensional shape can be predicted by modeling each of its cross-sections as a string in an effective confining potential [2]. Our results establish a route to combine global and local features consistently over an enclosed surface, which could aid the design of inflatable structures, or provide insight into biological patterns.

[1] Paulsen, Annual Review of Condensed Matter Physics vol. 10, 431 (2019).

[2] He, Démery, & Paulsen, PNAS 120, e2216786120 (2023).