  Mathematics can help analyze the arts and inspire new artwork. Mathematics
can also help make transformations from one artistic medium to another,
considering exceptions and choices, as well as artists' individual and unique
contributions. We propose a method based on diagrammatic thinking and quantum
formalism. We exploit decompositions of complex forms into a set of simple
shapes, discretization of complex images, and Dirac notation, imagining a world
of "prototypes" that can be connected to obtain a fine or coarse-graining
approximation of a given visual image. Visual prototypes are exchanged with
auditory ones, and the information (position, size) characterizing visual
prototypes is connected with the information (onset, duration, loudness, pitch
range) characterizing auditory prototypes. The topic is contextualized within a
philosophical debate (discreteness and comparison of apparently unrelated
objects), it develops through mathematical formalism, and it leads to
programming, to spark interdisciplinary thinking and ignite creativity within
STEAM.
