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.
"Thorns" is a bounded symmetric pattern in the plane with symmetry Z_5. It is a visual representation of the invariant measure on the attractor of a rational Z_5-equivariant planar map. The original image was created in 1996 and was perhaps my first serious attempt to investigate ways one could use methods based on symmetry, dynamics and chaos to achieve artistic ends. --- Mike Field