Nestability

Nestability is the property of an object, structure, or system that permits the placement or accommodation of another instance of the same type within it, typically through scaling, orientation, or recursive nesting. In practice, nestability often implies a hierarchical or self-similar organization in which each element can contain a smaller element of the same form, possibly to a finite depth.

In physical design, nestability appears in packaging and storage systems, such as nesting containers or bento boxes, and in the quintessential matryoshka or nesting doll. The concept also appears in geometric packing, where figures are designed so that one can be translated, rotated, and scaled to fit inside another without overlap.

In mathematics and computer science, nestable structures include sets under inclusion, sequences of nested intervals, and recursive data structures such as lists of lists or trees. Nesting is central to recursive definitions and to data representations like JSON or XML, where a container can hold elements that themselves are containers.

Nestability is often constrained by size, orientation, or other compatibility requirements, and is analyzed in terms of depth (how many levels can be nested) and fit (whether an inner instance can be contained after applying allowed transforms). In manufacturing, nestability affects material efficiency and cutting optimization.

See also nesting, recursion, containment, hierarchical data structures, packing.