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.
A parametric surface like the one shown here is defined by mapping two variables into three-dimensional space. This surface was the result of playing with the points on a sphere, perturbing them in different directions by some sinusoidal functions. The surface is rendered so as to appear to be lit from different positions by differently colored point lights. Coded in Processing. --- Daniel Gries (Hopkins School, New Haven, CT)