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.
"InHotPursuit," by Mike Field (University of Houston)
"InHotPursuit" is a section of a planar repeating pattern of type cm and the pattern was generated using an iterated function system defined on the two-dimensional torus. The resulting pattern on the torus was lifted to the plane to obtain a repeating pattern. The coloring reflects an invariant measure on the attractor of the iterated function system. This image is a bit surprising for an iterated function system as the textures and detail are more suggestive of a deterministic system (the torus maps used to generate the iterated function system are quite discontinuous). The original image was created in 2003. --- Mike Field