Nesting in Graphical Representations in Physics

We develop a theoretical model for understanding one way, ``nesting,'' that space is used in graphics from within and outside physics. Nesting can be used to increase a graphic's capacity for displaying several dimensions of information, beyond the two dimensions afforded by a flat page. We use the model of nesting to analyze previously observed student difficulties with electromagnetic waves, to predict how physics students would interact with certain graphics, and to generate new multivariate graphics in physics for instruction and for research on student thinking. Finally we apply the nesting model to explain the multidimensionality of certain kinds of gestures in physics education.