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.
"Mossy Frogs and Granite Bugs Spiral on a Globe," by Frank A. Farris, Santa Clara University, CA
Digital print on aluminum, 24" x 20", 2015
The pattern in the background of this image does not exactly have color-reversing symmetry. The source photograph of granite and moss is only vaguely color-reversing when you turn it upside down: the greens turn into grays. Still, when I used it with a formula that would yield color-reversing symmetry, it led to the two similar-but-different shapes: frogs and bugs. Then I wound the pattern onto a sphere in a spiral pattern. I added the purple haze by hand, using Photoshop. --- Frank A. Farris