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.
"View of the platycosm -a2, decorated with AMS, " by Charles Gunn (Technisches Universität Berlin, Germany)
18" x 18", print of computer image, 2013
"I enjoy exploring two- and three-dimensional tessellations -- euclidean, spherical and hyperbolic, especially the "insider's" view of such spaces. I have been experimenting recently with alternative perspective rendering based on a spherical canvas surrounding the viewer. "
This is an insider's view of the platycosm -a2. ("Platycosm" is John Conway's term for a compact euclidean 3-manifold.) This platycosm is generated by a translation, a glide reflection and a screw motion with order-2 rotational part, in three mutually perpendicular directions. The fundamental domain is a cube, whose edges are rendered via the textured beams. The "geometry" consists of the initials AMS, in honor of one of the hosting orgranizations of the art show. The image is rendered conformally from the viewable sphere of an insider positioned in the scene. I sometimes call this "six-point perspective" rendering since one may see vanishing points not just in the x,y, and z directions but also in the -x, -y, and -z directions. --- Charles Gunn (http://page.math.tu-berlin.de/~gunn)