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.
"Visual Proof," by Anne Burns (professor emerita, Long Island University, Brookville, NY)
13" x 13", digital print, 2013
"Visualization is an important aid in the study of mathematics."
Each of the disks in the 3X3 matrix of disks is a picture of the first five backward iterations of f(z)=z^n+c/z^m where c is a small positive real number. The rows represent n=2,3,4 and the columns represent m=2,3,4. The black disks in the center consist of the set of points z such that |f(z)|>1.1. The second largest sets of disks are blue; they are the inverse images of the black disks under f; ochre disks are the inverse images of blue disks; red disks are the inverse images of ochre disks, etc. First notice the n+m symmetry in each disk. Next, can you identify n and m by this pattern? Hint: choose one blue disk in each entry and count the number of pre-images closer to the center and the number of pre-images further away from the center. -- Anne Burns (http://anneburns.net)