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.
"Crocheted Lorenz manifold, detail," by Hinke Osinga, in collaboration with Bernd Krauskopf, Department of Engineering Mathematics, University of Bristol (www.enm.bris.ac.uk/staff/hinke/crochet/)
Dr. Hinke Osinga and Professor Bernd Krauskopf (Engineering Mathematics, University of Bristol) have turned the famous Lorenz equations into a beautiful real-life object, by crocheting computer-generated instructions of the Lorenz manifold: all crochet stitches together define the surface of initial conditions that under influence of the vector field generated by the Lorenz equations end up at the origin; all other initial conditions go to the butterfly attractor that has chaotic dynamics.
The photograph shows a particularly nice detail of the intriguing geometry of the Lorenz manifold. The wire running through the crocheted work illustrates one of the paths on the surface that end at the origin.
For more information, the crochet pattern and mounting instructions, see: http://www.enm.bris.ac.uk/staff/hinke/crochet/.