Faces of Chaos

Experiments in Lyapunov Space

This artwork captures the essence of a chaotic dynamical system by visualizing its 4-dimensional parameter space. The X and Y of the whole image map to two coefficients, while the X and Y of each of the 1,024 individual images contained therein map to the other two coefficients.

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Tiled Faces	Purchase
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Archival Inkjet Print

The framing and matting pictured above is a simulation of the actual presentation chosen for the Art of Digital Show 2007 and does not quite do it justice. The piece will be in San Diego for a month, and I did not have a chance to photograph it before shipping. The archival inkjet print was hand-torn and traditionally framed with a double mat coming up against the deckle edge and a beautiful contemporary wooden frame.

The following images are each one of those 1,024 "faces," chosen because they lean towards figurative images and away from pure abstraction. I decided to add color to the initially grayscale images through a technique described in the Technical Information section.

In the Resources section below, there are links and information that were useful to me in the process of coding the software for this digital art series.

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Chinese Warrior	Purchase
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Owl King	Purchase
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Death Mask 1	Purchase
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Death Mask 2	Purchase
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Technical Information

Custom software was developed to calculate the Lyapunov exponent of a chaotic dynamical system over a range of its four parameters. The raw data from this 4-dimensional parameter space was fed to another program to generate thousands of individual images, where X and Y represent two of the four coefficients. Every single pixel in these images gets its value from the calculation of the Lyapunov exponent of the strange attractor generated by the four coefficients it represents. The second program outputs four 16-bit grayscale images, which represent the different “components” of the spectrum of Lyapunov exponents. These images were combined in Photoshop using a pseudo-color technique to bring out subtle coloration in the final images.

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Resources

The following resources were very helpful and inspirational in my exploration of lyapunov space and in the development of my software and artwork.

Lyapunov Exponent Spectrum Software and Lecture Notes by J.C. Sprott

Extracting beauty from chaos by Andy Burbanks

Lyapunov Exponents by Jan Thor

Lyapunov fractal on Wikipedia

Lyapunov Space and Lyapunov Exponent from The Chaos Hypertextbook

Z-Lyapunov by Georges Rosset

C code for numerical calculation of the Lyapunov exponent by Paul Bourke

Complexity and 'art': Lyapunov graphs by Diethard Janßen

Markus-Lyapunov Fractals by Charles Vassallo

Lyapunov Exponents Lab Report by Earl F. Glynn II

Lyapunov Space - A Software Developer's Odyssey by Bill Storage

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