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.
Æxploration (Aesthetic Exploration) is a real-time, interactive video projection. This custom software visualizes a variety of two- and three-dimensional strange attractors, allowing the viewer to control the coefficients, color, and translation of the attractor. Until recently, my goal has been to generate high quality still images of strange attractors, and my interactive software has been geared towards that purpose alone - an artist's tool that is a byproduct of the process, viewable only by myself. But recently, in the course of a single day, I made some changes to my code that completely revolutionized what I was seeing on the screen while using my software, and I am excited to share the results. The image above is a screen capture. Video is available at http://nathanselikoff.com/251/strange-attractors/aesthetic-exploration. --- Nathan Selikoff (http://www.nathanselikoff.com)