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.
Superimposition of Polar Surfaces-2, by Dejenie A. Lakew
Superimpositions of polar surfaces. Equations:
rho = 2cos(3exp sin 3[theta])*exp sin 3[theta]*exp(sin 3(exp sin 3[theta])),
rho = exp(sin 3(exp sin 3[theta]),
rho = -3cos(3exp sin 3[theta])*exp sin 3[theta]*exp(sin 3(exp sin 3[theta]))
with compositions of tilts and turns.
Here the first polar surface is the derivative of the second surface and the third surface is a spatial reflection of the first through the origin with wire frames, but with a larger spatial radius.