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.
"Clover-52," by Jean-Francois Colonna (Centre de Mathematiques Appliquees, Ecole Polytechnique)
This image shows the lack of associativity for addition and multiplication inside a computer. In order to be able to obtain the exact same results over the years for a certain computation, I did include the definition of some "devices" in my own programming language, which allow the definition of the precise order of the arithmetic operations: +, -, *, and / (by the way, parentheses won't do that, for example, X=A+(B+C) does not mean T=B+C then X=A+T).
This opens the door to something very powerful: The possibility to dynamically redefine the arithmetic used when launching a program. This picture and "Clover-51" are the results of the combination of eight elementary pictures: 3-clover, 4-clover, ... ,10-clover with substitutions like (A+B) --> MAX (A,B), (A*B) --> (A+B).