  Recent work has introduced the study of graphical properties of cyclic
supercharacters, functions $\mathbb{Z}/n\mathbb{Z}\to \mathbb{C}$ whose values
are exponential sums with close connections to Gauss sums and Gaussian periods.
Plots of these functions exhibit striking features, some of which have been
previously explained when the modulus $n$ is a power of an odd prime. After
reviewing this material, we initiate the graphical study of images of cyclic
supercharacters in the case of composite $n$.
