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.
"Branched Manifold," by Juan G. Escudero (Universidad de Oviedo, Spain)
Digital Print, 20"x20", 2010
A cell complex is defined in the analysis of the cohomology of tiling spaces. It contains a copy of every kind of tile that is allowed, with some edges identified for the 2D case, and the result is a branched surface. When the tiling does not force the border, collared tiles can be used. Here the triangles with the same shape, color and orientation represent the same tile in the complex. The manifold appears in the cohomology computations of an octagonal pattern belonging to a random tiling ensemble introduced by the author in the context of mathematical quasicrystals. --- Juan G. Escudero