Experiments in Lyapunov Space
In my Faces of Chaos series, I seek to visualize a chaotic dynamical system, using a unique mapping of the Lyapunov exponent to the image plane. Tiled Faces is one result of this exploration, and its 1,024 images combine to reveal the “face” of the four-dimensional system’s chaotic behavior. This emergent figuration draws the viewer in, closer to the surface, where a myriad of individual “faces” are revealed. Because I approach the challenge of representing four dimensions from an aesthetic perspective, I am free to bring the underlying equations to light, to visually and intuitively understand them. Tiled Faces juxtaposes order and chaos, artistic sensibility and mathematical depth, within its pixels and pigments.
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. More details are available on the Tech Notes page for this series.