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.
"Twice Iterated Knot No. 1," by Robert Fathauer, Tessellations Company (2008)
Third Prize, 2009 Mathematical Art Exhibition. Digital print, 19" x 12". Fathauer makes limited-edition prints inspired by tiling, fractals, and knots. He employs mathematics in his art to express his fascination with certain aspects of our world, such as symmetry, complexity, chaos, and infinity.
"The starting point for this iterated knot is a nine-crossing knot that has been carefully arranged to allow seamless iteration. Four regions of this starting knot are replaced with a scaled-down copy of the full starting knot, incorporated in such a way that the iterated knot is still unicursal. These same four regions are then replaced with a scaled-down copy of the iterated knot, resulting in a complex knot possessing self similarity." --- Robert Fathauer, Small business owner, puzzle designer and artist, Tessellations Company, Phoenix, AZ