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.
"Peer Below the Surface - No. 65.270," by Leo S. Bleicher (Cepheus Information Systems, San Diego, CA)
Digital print of 3D model on photographic paper, 23” x 19”, 2009. Serial coordinate transformations interleaving symmetry preserving and symmetry breaking operations yield a stunning variety of forms. A sequence of fourteen such operations in 3D create this shape from the unit square. Small spheres are initially an array of 40000 normals to the surface at a distance of 0.05. Larger spheres represent hierarchical clustering centroids of the normals in their final positions. Sequences are selected with a genetic recombination function using esthetic appeal as the fitness function. This transformation sequence begins with a cylindrical transform around the z-axis, and finishes with a spherical coordinate transform and rotation around the y-axis. These images are from 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. --- Leo S. Bleicher (Cepheus Information Systems, San Diego, CA) http://porterbleicher.g2gm.net/computed-paintings/