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.
"They Arrive," by Frank A. Farris (Santa Clara University San Jose, CA)
20 x 25 cm, digital aluminum print on DuraPlaq mount, 2016
Glowing globes with three types of polyhedral symmetry drift over a moonlit mountain to land on the lake. Are they wafting from the Platonic world into ours? (The patterns on the globe were created with domain colorings of meromorphic functions invariant under the actions of the three chiral polyhedral groups. In the past, I always used rectangular photographs to paint spheres, resulting in images with singularities. New techniques allow the source photograph to live on the Riemann sphere, allowing poles to be painted just as if they were zeroes. Ray tracing and manipulation of the original daytime mountain photograph were done in Photoshop.) --- Frank A. Farris