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.
"A Radin-Conway Pinwheel Lace Sampler," by Douglas G. Burkholder (Lenoir-Rhyne University Hickory, NC)
Digital Print, 50 x 50 cm, 2015
This artwork evolved from a search for beauty and patterns within Conway and Radin’s non-periodic Pinwheel Tiling of the plane by 1x2 right triangles. The Pinwheel tiling can be created by repeatedly subdividing every triangle into five smaller triangles. This lace resulted from alternately subdividing triangles and removing triangles. Triangles are removed based upon their location in the next larger triangle. First, on the macro level, the five distinctive removal rules are applied one to each row. This removal rule is especially easy to see in the bottom row. These same five rules are then applied, on the micro level, to the columns. The remaining triangles form a sampling of twenty-five styles of lace generated by the Pinwheel tiling. --- Douglas G. Burkholder