Unfolding

Unfolding refers to the act of opening or expanding something that has been folded, rolled, or compacted. In everyday use it describes the physical process of spreading a folded object into a flat or extended state, such as unfurling a map, a garment, or origami. The term is also used metaphorically to describe the gradual development or revelation of events, ideas, or narratives.

In geometry and related disciplines, unfolding describes the transformation of a three-dimensional object into a two-dimensional representation. The most common form is the net of a polyhedron: a connected arrangement of polygonal faces laid out flat, obtained by cutting along edges and unfolding the surface. Unfoldings are used in design, manufacturing, and education to study shape, surface area, and constructibility.

In computer science and functional programming, unfold is a dual to fold: a corecursive process that builds a data structure from a seed value by repeatedly applying a function to generate the next element and the next seed. Unfold is used to produce lists, trees, or streams lazily and can express sequences or recursive data structures succinctly.

Biology uses unfolding to describe processes such as protein unfolding or denaturation, in which a folded biomolecule loses its native structure under changing conditions. In narrative arts, unfolding describes the way a plot or argument reveals itself over time. Across disciplines, unfolding captures the idea of transition from compact or latent form to an expanded, flattened, or more explicit state.