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.
"El Nido Fractal," by Karl Kattchee (University of Wisconsin-La Crosse)
Digital Print, 10" x 16", 2009. The boundary between land and sea is complex, like a fractal. At the bottom of this drawing we have land, represented by rigid lines and shapes. At the top, there is the sea, swirling around. In between is the boundary, where the right angles gradually give way to curves. There is self-similarity, as one would expect in a fractal. "What is mathematical art? This question not only begs for criteria to make the judgment, but it also asks how math and art interact. That strange interaction is what makes math art fun for me. I almost always start with sketches on paper, but I recently began transferring them to the computer and carrying on the work electronically. As such, I can spend time experimenting with different ideas and change my mind often about what I'm doing. While I try to render mathematical ideas in my art, I also realize that the artistic process is itself a lot like the mathematical process. Sometimes the original 'problem' needs to be modified after careful 'research'. To me, the final product is a lot like a theorem." --- Karl Kattchee (University of Wisconsin-La Crosse) http://www.uwlax.edu/faculty/kattchee/