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.
"Ideal quilt, slightly imperfect," by Andrzej K. Brodzik (Mitre Corporation, Bedford, MA)
Digital print, 24'' x 20'', 2010
Ideal quilts are Zak space representations of families of ideal sequences. Ideal sequences are sequences with certain special group-theoretical properties. In particular, ideal sequences satisfy the Sarwate bound, having both zero out-of-phase autocorrelation and minimum cross-correlation sidelobes. Construction of ideal sequences was described in the recent book, Ideal sequence design in time-frequency space. Ideal quilts are (p-1)p by (p-2)!p images, where p is a prime. As these images tend to be long and narrow, to facilitate display, they are usually divided into columns. Geometrically, an ideal quilt is a sequence of distinct permutations of the canonical image of a diagonal line. Both the overall structure of the image and the association with ideal sequences convey a strong sense of symmetry, predictability, and uniqueness. To counter-balance these qualities, the corrupting effect of tiff data compression, manifested as pixel distortion, is embedded into the image. --- Andrzej K. Brodzik