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.
My mathematical art forms several large series exploring the creation of complex forms through sequences of simple operations or representations of simple relationships. The operations include geometric transformations, neighbor finding, attraction/repulsion and others. These computational processes attempt to replicate features of both geologic and organic morphogenesis. This image was created by application of a sequence of 3D geometric transformations to a collection of spheres on the faces of a hollow cube. The exact sequence to produce this image was obtained through the use of a genetic algorithm using subjective aesthetic appeal as the fitness function. -- Leo Bleicher