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.
"Evolution of the Twin Tornados, " by Hartmut F. W. Höft (professor emeritus, Eastern Michigan University, Ann Arbor, MI)
7.5" x 9" (10.5" x 12" framed), archival photographic digital paper, 2013
"I like to experiment with simple planar geometric figures. Starting with one outline I move it, rotate it, and change its proportions. "
In this picture 12 images are arranged in a spiral. A primordial sea in the center starts the process. One parameter of the spine function increases, then stays constant, while the other increases and then decreases again. As the sequence progresses along the spiral the spine function increases in complexity so that the images billow out like clouds and then start separating into two funnels as the second parameter decreases again. Each image on the spiral is composed of 289 ellipses with a closed spine curve though it does not appear to be closed since the axes of the elipses decrease to zero at the bottom. The graphics were rendered in Mathematica 8 and printed on archival, photographic digital paper. --- Hartmut F. W. Höft (http://people.emich.edu/hhoft/)