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.
"Map of Invariability I," by Conan Chadbourne (San Antonio, TX)
60 x 60 cm, archival digital print, 2016
My work is motivated by a fascination with the occurrence of mathematical and scientific imagery in traditional art forms, and the mystical, spiritual, or cosmological significance that is often attached to such imagery. The Klein Quartic is a genus-three Riemann surface which can be covered by a regular tessellation of 24 heptagons. In this image, the Klein quartic is projected into the Poincaré disk, and this heptagonal tessellation is given a regular 8-coloring. Each triplet of heptagons of any given color is fixed by a subgroup of order 21 of the full automorphism group of the surface. --- Conan Chadbourne