  Gaussian periods have been studied for centuries in the realms of number
theory, field theory, cryptography, and elsewhere. However, it was only within
the last decade or so that they began to be studied from a visual perspective.
By plotting Gaussian periods in the complex plane, various interesting and
insightful patterns emerge, leading to various conjectures and theorems about
their properties. In this paper, we offer a description of Gaussian periods,
along with examples of the structure that can occur when plotting them in the
complex plane. In addition to this, we offer two ways in which this study can
be generalized to other situations -- one relating to supercharacter theory,
the other relating to class field theory -- along with discussions and visual
examples of each. We end the paper by including some code for readers to
generate images on their own.
