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 comes from the fusion of the three separate image files generated with the software Apophysis, designed by Mark Townsend. Each one of the files contains different types of transformations-linear, polar, and spherical-that produce a curious dialog between the vertical lines, the sinuous curves with the appearance of smoke, and the bubbling circular shapes. In this type of fractal there is only one method of coloring. Sometimes a tiny change to the color gradient can distort the image dramatically. Fractal artists, hunting for treasure, can tease out unexplored forms, but a slight difference in this or that parameter can make them pass by that secret treasure without seeing its hidden beauty. David April lives in Illinois (USA). His interest in fractals is relatively recent, but he compensates for that with an enormous enthusiasm and fascination for finding new forms.