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.
"Quejido Design III," by Gary Greenfield (Prof Emeritus, University of Richmond, VA)
10.5" x 10.5" (unframed), Digital Print, 2012
Between 1968-1972 Spanish artist Manuelo Quejido collaborated with computer programmers at the University of Madrid in order to execute a series of state-of-the-art computer generated “sequence” designs consisting of patterns of disks. As an homage, Quejido Design III realizes one of these patterns using state-of-the-art agent based methods. Here, agents are virtual ants modeled after the species T. albipennis that collect dispersed grains of sand in order to form circular nest walls. By using two different colors for sand grains and by assigning to each virtual ant a center, radius, and color, a uniform density grid of sand grains self-organizes into a pattern which, up close, has no color symmetry, but from a distance is perceived of as being color preserving under various symmetry operations. -- Gary Greenfield