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.
"NeuralNet," by Mike Field (University of Houston)
"NeuralNet" is is part of the generating tile of a planar repeating pattern of type pgg. Repeating patterns of this type have no reflection symmetries but do have many glide reflection symmetries as well as translational symmetries and two-fold centers of rotation. The absence of reflectional symmetries often leads to very fluid and dynamic patterns. The coloring reflects the density of the invariant measure. --- Mike Field