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.
"Sanctuary" consists of 19 layers, each one of which contains variations of the orbit trap algorithm. The traps are geometric shapes placed in the complex plane that end iteration of a point when its orbit falls within the shape, hence the name. The shape, size, and location of the traps permit Nicholas Rougeux to control the appearance of each of the layers, which are then combined together as if they were transparencies held up to light. Nicholas Rougeux, a North American web developer, reinforces in this picture the idea of a sanctuary by including smooth curves on the sides that simultaneously create sensations of protection and welcome. The mild colors also help to obtain the objective of evoking a comfortable place where spirits are free.