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.
"Ammann Scaling (2006)," by Edmund Harriss (University of Leicester)
Printed on Canvas 24" x 24". The Ammann-Beenker tiling is the eight-fold sibling of the more famous, five-fold Penrose rhomb tiling. It was discovered independently by R. Ammann and F. Beenker. Like the Penrose tiling, the Ammann-Beenker can be constructed by two particular methods. The first method is uses the substitution rule, and the second method is to construct the tiling as a planar slice of a four dimensional lattice (in much the same way that a computer draws a line using the pixels of its screen) and then project this to the plane. See more information at www.mathematicians.org.uk/eoh/Art/Ammann_Text.pdf. This was a commission for the School of Mathematical Sciences at Queen Mary. It is one of a pair with Ammann Squares, exploring aspects of the Ammann-Beenker Tiling. It appeared in the June 2007 issue of Notices of the AMS. --- Edmund Harriss