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.
"Art of Fourier Space," by Ian Sammis (University of California, Davis)
Print of digital art, 24”x20” (framed), 2008. This is the computed Fourier transform of a constant linear measure placed on a piecewise-linear approximation to the space-filling Sierpinski Curve. The curve itself is shown in the lower-left corner. The reduced art appears gray, but in the original each pixel has a hue determined by its complex phase. The transformation was computed by the Geometric Nonuniform Fast Fourier Transform. "Over the course of earning my Ph.D., I've become fascinated by the fact that in generating images for the most utilitarian of purposes (debugging, testing hypotheses, and the like) the most useful images are usually also the most aesthetically pleasing." --- Ian Sammis (University of California, Davis) http://math.ucdavis.edu/~isammis