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 image belongs to a simple Julia set, but the refined technique of Andreas Lober, who graduated from the University of Heidelberg with a degree in mathematics, converted it entirely into a creative prodigy. The coloring algorithm is simple: find the minimum value of │z│ during the iteration, deflecting lightly the values pseudo-randomly; this produces the sine waves that heighten the composition. The values are trapped during the calculation in discrete intervals; this produces the peculiar coloring that appears to be done with colored pencils. Other preferences of Andreas Lober include designing tilings that cover the plane with squares containing geometric shapes, so that they fit perfectly with the adjacent eight squares. These experiments produce tesselations of great visual impact and, in this case, variations have been used to obtain the frames contained in the image.