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.
"Hyperbolic Tiling I," by Vladimir Bulatov (Corvallis, OR)
20" x 20", Digital print, 2011
This is a tiling at the infinity of hyperbolic space. The tiling is generated by reflections in 4 planes. The planes arrangement is obtained from faces of hyperbolic tetrahedron by truncating one vertex and one of opposite edges and moving points of truncation to infinity. The interplay of reflections forms circular area with infinitely many circular holes filled with two dimensional hyperbolic triangle tilings (2 3 24). To color the tiling we use different subgroups of the total symmetry group. --- Vladimir Bulatov (Corvallis, OR, http://bulatov.org)