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 ands, 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.

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"Owl King," by Nathan Selikoff (www.nathanselikoff.com), 2007What do you see? An owl, spider, space ship… something else? This artwork is a two-dimensional plot of the Lyapunov exponent of a chaotic dynamical system. The Lyapunov exponent is a measure of how chaotic the system is, and in this case, the system is a strange attractor with a four-dimensional phase space. Two of the dimensions are static, and the other two vary in the x and y directions of the image. A custom program renders four 16-bit grayscale images, which represent the different “components” of the spectrum of Lyapunov exponents. Read more at http://nathanselikoff.com/209/faces-of-chaos/owl-king. --- Nathan Selikoff

"Butterfly Effect," by Nathan Selikoff (www.nathanselikoff.com), 2007The "Butterfly Effect", or more technically the "sensitive dependence on initial conditions", is the essence of chaos. Besides the fact that this attractor looks like an abstract butterfly, the title of the piece is an homage to Edward Lorenz, a pioneer of chaos theory. It’s a quick jump from this popular understanding of chaos theory to playing with the Lorenz Attractor and learning a bit more about the math and science behind it. Read more at
http://nathanselikoff.com/236/strange-attractors/butterfly-effect. --- Nathan Selikoff

"Helios [var. 1198505515]," by Nathan SelikoffThis 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.

"SA_1188475827," by Nathan SelikoffAnother strange attractor, this one existing in three dimensions, comes to life with rich fiery colors that enhance the eastern Asian feel of the swirling lines. See more images at www.nathanselikoff.com/.

"SA_1188415571," by Nathan SelikoffThis three-dimensional strange attractor is reminiscent of Hubble images of the Eagle Nebula, though it is a purely mathematical construct. See more images at www.nathanselikoff.com/.

"Death Mask 2," by Nathan SelikoffThis artwork, from the "Faces of Chaos" series, is a two-dimensional plot of the Lyapunov exponent of a chaotic dynamical system. The Lyapunov exponent is a measure of how chaotic the system is, and in this case, the system is a strange attractor with a four-dimensional phase space. Two of the dimensions are static, and the other two vary in the x and y directions of the image. A custom program renders four 16-bit grayscale images, which represent the different "components" of the spectrum of Lyapunov exponents. These images are combined in Photoshop using a pseudo-color technique to bring out subtle coloration in the final artwork. See more images from this series at www.nathanselikoff.com/facesofchaos/.