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.
"Basilica," by Anne Burns (professor emerita, Long Island University, Brookville, NY)
Digital print, 2014
The Julia Sets of z^n + c are familiar objects to mathematicians. In particular c=-1 yields the well-known "Basilica". Adding a term d/z(z^2-1) introduces three poles: z=0, z=-1, z=1. The orbits of initial points near the poles rapidly diverge to ∞; for very "small" (real, positive) d, amazingly, the boundary of the set of points whose orbit escapes (the Julia Set) contains an infinite number of tiny decorations resembling the decorations on the original "Basilica". --- Anne Burns