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.
"Julia," by Jeffrey Stewart Ely (Lewis and Clark College, Portland, OR)
Photographic Paper, 20” X 20” , 2009. Julia sets are usually depicted two-dimensionally, either flat or as textures on other surfaces which themselves may have little to do with the Julia set. Here, we iterate the complex variable relation, new s = s^2 - 1.25 thirteen times to produce a polynomial in the original variable, s, of degree 8192. Now consider the three-dimensional surface, z = f(x,y) = |s^8192+ ... | where s = x+iy and | | denotes absolute value. This picture is the graph of (x,y, z) if z <= t and (x,y, t(t/z)^p) if z > t where t is a threshold value ~1.464 and p = (1/2)^13
"I am interested in applying computer graphical techniques to illuminate mathematical processes. Ideally, this can lead to a deeper understanding of the process, but even if no new insight is forthcoming, I am frequently mesmerized by the compelling beauty of the unusual shapes. I do not use 'canned' software. I wrote the code to first principles in the 'C' programming language. This particular image was constructed as a particle system made from 266 billion points and took 67 hours to compute." --- Jeffrey Stewart Ely (Lewis and Clark College, Portland, OR)