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.
Computer graphics allows one to see both the numerical and aesthetic properties of dynamical systems. Recently I became interested in the properties of complex functions in which a complex variable is raised to a complex, rather than an integer exponent. I have also been analyzing complex polynomials that have no attracting fixed points. This image is produced by applying Newton's method for root finding to the complex function (z^(2+3i)-.09)*(z^(2-3i) -.09).The white areas are points in the complex plane where this function does not converge to any root. The background is produced using Perlin noise functions. -- Robert Spann