Origami and the Emergence of Hybrid Diagrams

The paper discusses the emergence of hybrid diagrams in the context of origami practice with respect to the study of the crease pattern, a particular diagram that can be associated with any origami model. We introduce the expression “hybrid diagram” to refer to a 2D diagram that embeds physical parts of the origami model and information about transformations occurred in space, or to an origami model on which attempts to grasp parts of the crease pattern appear. We focus on some university students working with the crease pattern for a given origami model. A first analysis of the work of these students allows for a preliminary characterization of hybrid diagrams: they encapsulate relations between the 3D model and the crease pattern and reveal the entanglement of diagrammatic activity with the gestural and the material. Drawing on the cognitive perspective of semiotic representations by R. Duval and diagrammatic thinking by C. Peirce, we interpret the emergence of hybrid diagrams as relevant to the conversion between different (mathematical) registers.