Bloom patterns: radially expansive, developable and flat-foldable origami

This paper introduces bloom patterns as a family of radially expansive, flat-foldable, and developable origami patterns, many of which are rotationally symmetric. Two main definitions are presented for bloom patterns. The generalized definition is a minimum set of conditions based on the most defining characteristics found in bloom patterns, and is designed to minimize the possibility of excluding undiscovered origami patterns that could be classified as bloom patterns. The standardized definition restricts the generalized definition to more specific characteristics of bloom patterns, which enables a systematic framework that describes, analyses, and constructs bloom patterns. A classification scheme for bloom patterns is identified based on their intrinsic characteristics, and several types of bloom patterns are analysed. The distinct helical nature that characterizes bloom patterns is documented with the helical model. A set of compatibility conditions is derived to help determine if a valid bloom pattern can be constructed based on the standardized definition. Finally, applications of bloom patterns are discussed.