Something I'm thinking about and may comment on a bit later:
In a landmark 1987 essay,“Why a Diagram Is (Some- times) Worth Ten Thousand Words,” Herbert Simon and Jill Larkin argue that a diagram is fundamentally computational, and that the graphical distribution of elements in spatial relation to each other supported “perceptual inferences” that could not be properly structured in linear expressions, whether these were linguistic or mathematical. They state at the outset that “a data structure in which information is indexed by two-dimensional location is what we call a dia- grammatic representation.” They argue that the spatial features of diagrams are directly related to a concept of location, and that location performs certain functions. Locations exercise constraints and express values through relations, whether a machine or human being is processing the instructions. Larkin and Simon were examining computational load and efficiency, so they looked at data representations from the point of view of a three part process: search, recognition, and inference. Their point was that visual organization plays a major role in diagrammatic structures in ways that are unique and specific to these graphical expressions. In particular, they bring certain efficiency into their epistemological operations because the information needed to process information is located “at or near a locality” so that it can be “assessed and processed simultaneously.”
Johanna Drucker, Graphesis: Visual Forms of Knowledge Production, Harvard University Press, 2014, pp. 106-107.