Chaos and Images

One of the easiest way to appreciate the complexity of nonlinear dynamical (or chaotic) systems is through their visual characterizations. While the underlineing mathematical equations might be simple, the resulting pictures produced by these systems could be amazingly intricate with fine structures in arbitrary resolution. This geometrical property of chaotic systems is typically described in terms of its fractal dimension. Moreover, chaotic systems are exponentially sensitive to initial conditions. In other words, the temporal evolutions of a chaotic system with two "nearly equal" starting points will become totally uncorrelated after a finite time. The dynamical quantity which characterize this aspect of chaotic systems is called the Lyapunov Exponent. However, geometrically, there remains a degree of order amid this unpredictable nature of chaotic systems. The attractors generated by these chaotic systems are topologically invariant.

Lorenz Heartbeat by Tim Sauer - animated
Arnold Cat Movie by Evelyn Sander - animated
Spinodal Decomposition by Evelyn Sander - animated
Dynamical Shrimps by Ernest Barreto