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.
This is a tessellation of Penrose tiles. In this set, there are two different tile shapes, a fat rhombus and a thin rhombus. Penrose tiles are remarkable because they can be arranged (as they are here) such that the tiling never repeats, no matter how many tiles are used. Also, each tile is filled with four pursuit curves, the dark curves from each corner to a point near the center of the tile. Imagine a mouse in each corner of the tile. At the same time, each mouse begins moving toward (pursuing) the next mouse. The tracks of the mice are pursuant curves. --- Kerry Mitchell