Frank A. Farris
My artistic impulse is to let the beauty of the real world shine into the realm of mathematical patterns. My method combines photographs with complex-valued functions in the plane to create images with all possible types of symmetry: Euclidean, hyperbolic, and spherical symmetries. The foundation of this body of work is explained in detail in my book Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, published in 2015 by Princeton University Press. Though I included what I thought was every possible idea about plane symmetry in my book, I continue to be amazed that there are new techniques to discover.
The rich colors of the alchemist's globes come from scenes captured with a camera that records the entire visual sphere. They tell my story of leaving home in San Jose for an autumn sabbatical in Minnesota. At the top left, we see my stairwell at home, where a stained glass window made by Hans Schepker hangs next to a quilt. Moving to the right, we find the glorious Lakewood Chapel and St. John's Abbey. Bright fall colors at the bottom left give way to another view of St. John's Abbey, and then we return home. Texture maps on the spheres use quotients of harmonic polynomials with icosahedral or octahedral symmetry. The scene is composed in Photoshop, with about 14 hours of ray-tracing.
The three windsails racing down Huntington Lake exemplify the (rotational) symmetries of the Platonic solids: icosahedron/dodecahedron, cube/octahedron, and tetrahedron. The icosahedron is painted with a frieze pattern made from sweet peas, the cube uses a California poppy. The meshes created by Maple for the tetrahedral shape were too twisted to paint with frieze patterns, so I used simple primary colors. Reflections on the water are a trick of ray-tracing in Photoshop.