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.
"Alternating Wood Bugs," by Frank A. Farris, Santa Clara University, CA
Ink jet on paper, 2015.
Had I used a source photograph whose colors reverse exactly when you turn it upside down, the image computed with these wallpaper waves would have exact color-reversing symmetry of type p4g/cmm. (See my book Creating Symmetry for explanation.) However, when you rotate my picture of a freshly cut pine stump, the colors only more-or-less reverse. This causes what I call "approximate color-reversing symmetry." The blond bugs marching northwest have the same outlines as the dark bugs marching northeast, but the details of the insides are quite different. --- Frank Farris