Creating Symmetry: The Artful Mathematics of Wallpaper Patterns
Reviews, software, and errata
Based on a course I taught at Carleton College in 2011, this book develops the thesis that humans like to look at shapes generated by solutions to partial differential equations, the sensual waves that compose all periodic phenomena.
According to Doris Schattshneider, author of M. C. Escher: Visions of Symmetry, "This unique book takes an entirely new approach to creating images with symmetry. The pictures are compelling and Farris presents the material in an inviting manner. He leads readers into interesting areas of mathematics not usually encountered in undergraduate courses, and rarely, if ever, encountered as a way to study symmetry."
Learn more at the Princeton University Press site for the book. And if you read the book, be sure to consult my (unfortunately long) list of errata.
In 2016, thanks to a grant entitled SymmetryWorks! obtained by Bill Barker, students at Bowdoin College wrote a software suite to implement the algorithms in the book. In 2018, SCU student Carolyn Liu updated the package, which relies on libraries from QtCreator. The best way to investigate this code is through her GitHub site.
I would be happy to collaborate with anyone wishing to implement these algorithms. The definitive GUI for wallpaper functions has not been written. Recently, I have been using Octave code specialized to wallpaper patterns, which I am happy to share privately.
I have been delighted by the critical reception of the book. It pleases me to think that many readers report being surprised to learn something new about a topic they assumed they already knew thoroughly. The book was awarded the Alpha Nu Sigma Book Award in 2019 and received an Honorable Mention from the PROSE Awards in 2016. Many reviews are available, but probably the most significant one, by James A. Walker, appeared in the Notices of the American Mathematical Society.