The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.
Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.
"The Alchemist's Shelf," by Frank A. Farris, Santa Clara University, CA
Digital print on aluminum, 51 x 61 cm, 2017
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. --- Frank A. Farris