The Gaussian Periods app is now available on the Mac app store!
The app allows one to plot Gaussian periods quickly. I originally conceived of it as a tool for for quick exploratory analysis, i.e. to help make conjectures about graphical features of Gaussian periods. A newer feature allows one to download layers to produce customized, aesthetically pleasing images, e.g. in Adobe Photoshop. For example, that is how I made all the images in my joint paperA Gallery of Gaussian Periods with S. R. Garcia. In the summer of 2021, undergraduate Nat Milnes made many improvements to the package, in preparation for deploying it to the app store. Here is the description from the app store:
This app produces beautiful mathematical images. Everyone from novices to experts can use this app, whether purely for fun or for exploratory analysis. In response to a parameters input by the user, the app plots Gaussian periods, certain complex numbers that play important roles in mathematics. The app enables you to view them at large scale, even plotting millions of points. You indicate parameters defining the Gaussian periods, as well as additional data, namely parameters for color and the size of the points to be plotted. You have the option to download the image (as a 2, 4, or 8k png) or to download distinct layers to produce customized, aesthetically pleasing images, for example in Adobe Photoshop. For more information, see A Gallery of Gaussian Periods, by E. E. Eischen and S. R. Garcia, as well as the information at http://www.elleneischen.com/gaussianperiods.html
Some tips:
1. The images in the window of the app consist of Gaussian periods, like discussed in the paper A Gallery of Gaussian Periods. To save the image, click "Export PNG."
2. For more control over the appearance of the layers in images, click "Export Layers." If you open them in photoshop, you can change the colors and order in which they are layered.
3. Questions? Suggestions? Comments? Please email me at myfirstinitialmylastnameATuoregonDOTedu.
4. Have fun, and enjoy!