Abstract
Gaussian periods are certain sums of roots of unity whose study dates back to Gauss’s seminal work in algebra and
number theory. Recently, large scale plots of Gaussian periods have been revealed to exhibit striking visual patterns,
some of which have been explored in the second named author’s prior work. In 2020, the first named author produced
a new app, Gaussian periods, which allows anyone to create these plots much more efficiently and at a larger
scale than before. In this paper, we introduce Gaussian periods, present illustrations created with the new app, and
summarize how mathematics controls some visual features, including colorings left unexplained in earlier work.
