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.
"Starfruit," by David MakinDavid Makin is a British computer programmer born in North Wales, who loves fractal geometry and science fiction. The majority of his work comes from his investigations into the use of coloring algorithms. In this case he employed three algorithms applied to a Julia set. The first of his algorithms, named "MMF3-Turning Points," generated the starred forms that characterize the image and suggested the title of the shape immediately to him (the starfruit is a tropical fruit whose cross section produces a five-pointed star). With the second algorithm, "MMF3-Orbital Waves," he used the idea of complementing the first layer with the handsome curved lines that accentuate the set. At this point he proceeded to include the third algorithm, "MMF3-Alternative fBm II," which provides a more organic texture. Finally, David Makin took considerable time in combining the three layers with color palettes and the algorithms described that produced the final result.