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.
"Exploring Complex Domain Functions Using Domain Coloring," by Konstantin Poelke and Konrad Polthier, Free University of Berlin
Honorable Mention, Illustration - 2011 Visualization "Vizzies" Challenge (National Science Foundation). This illustration represents one example of a complex function. Such functions are mathematical relationships that incorporate both real and imaginary numbers, such as the square root of -1. To create this visualization, researchers at the Free University of Berlin assigned each complex number in their equation to a spot on a color wheel. The farther numbers get from zero, the brighter they are (white regions approach infinity). The result packs two dimensions of information (hue and brightness) into each point in the image. See 2011 Vizzie Winners