论文标题
高斯时期的画廊
A Gallery of Gaussian Periods
论文作者
论文摘要
高斯时期是一定的统一根源，其研究的历史可以追溯到高斯在代数理论和数字理论中的开创性工作。最近，已经揭示了高斯时期的大规模图以展示引人注目的视觉模式，其中一些在第二名作者的先前工作中探索了其中一些。在2020年，第一位命名作者制作了一个新的应用程序，即\ texttt {高斯时期}，该应用程序使任何人都可以比以前更有效地创建这些图。在本文中，我们介绍了高斯时期，使用新应用程序创建的当前插图，并总结了数学如何控制一些视觉特征，包括在早期工作中无法解释的颜色。
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, \texttt{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.
