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 artwork is based on a rendering of a strange attractor, and is inspired by extreme ultraviolet images of our sun. Helios is part of the "Aesthetic Explorations of Attractor Space" series, more of which can be seen at www.nathanselikoff.com/strangeattractors/.
Underlying each image in this series of work is a two-dimensional plot of the "typical behavior" of a chaotic dynamical system. Of course, there is nothing typical about a strange attractor, as it is chaotic and has a fractal structure. The base images are computed with a set of iterated functions, which serve as a numerical approximation to integrating the underlying differential equations. The iterated functions contain four coefficients, which are controlled by sliders in interactive custom software and control the appearance of the attractor. Once a particular form is settled on, it is rendered as a high-resolution 16-bit grayscale image. Finally, in Photoshop, the render is colorized using gradient mapping and edited to enhance contrast, control composition, and add special effects. The number in the artwork title encodes the moment at which the attractor was "discovered" and archived for rendering.