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.
"Three-Fold Development, " by Robert Fathauer (Tessellations, Phoenix, AZ)
13" x 13" x 13", ceramics, 2013
Best textile, sculpture, or other medium
2014 Mathematical Art Exhibition
"I'm endlessly fascinated by certain aspects of our world, including symmetry, chaos, and infinity. Mathematics allows me to explore these topics in distinctive artworks that I feel are an intriguing blend of complexity and beauty. "
This sculpture is based on the first five generations of a fractal curve. The starting point is a circle, and the first iteration produces a three-lobed form. With each iteration, the number of lobes is tripled. The spacing between features is essentially constant throughout a layer, while the three-fold symmetric boundary of the curve becomes increasingly complex. A hexagonal version of this curve is found in Benoit Mandelbrot's book "The Fractal Geometry of Nature". This hyperbolic surface is reminiscent of naturally-occurring corals. It was inspired in part by a 3D-printed model created by Henry Segerman. (For more information on this work see http://mathartfun.com/shopsite_sc/store/html/Art/FractalCurveSculp.html . --- Robert Fathauer (http://robertfathauer.com)