Symmetry Reflects Us. It brings us “face-to-face with the grand structure of mathematics,” as Frank Farris puts it. Years ago Farris, an associate professor of mathematics and computer science at Santa Clara, bridged mathematical realms and photographic material with what he calls a “domain-coloring algorithm.” His resulting work weds waveforms to nature photography, and it has been exhibited in galleries and at universities across the country.
The book Creating Symmetry: The Artful Mathematics of Wallpaper Patterns (Princeton University Press) collects scores of his images: beginning in the familiar plane of Euclidean geometry, employing complex equations to generate rosettes, friezes, and wallpaper patterns (any pattern with translational symmetry in two independent directions). To follow the mathematical threads requires understanding calculus. The big story unfolding is the beauty of the Earth.
Here are a few of his creations. See the gallery below for some of the source photos that he transformed.