Chaos - 100 Times Lorenz Attractor

The mathematician E. Lorenz originally discussed the set of ordinary differential equations today called Lorenz system in the context of meteorologistic prediction of weather phenomena [1]. The set of equations read
dx/dt = a(y - x),
dy/dt = x(b - z) - y, and
dz/dt = xy - cz.
This system experiences chaotic dynamics at a = 10, b = 28, and c = 8/3. The corresponding attractor is often called Lorenz attractor.

The video illustrates the geometry of the attractor in (x, y, z)-space and its chaotic nature by showing the trajectories of 100 different and originally closely neighbored initial conditions. The sensitive dependence typical for chaos becomes well visible after only a few oscillations.

[1] E. N. Lorenz, Deterministic Nonperiodic Flow, J. Atmospheric Sci. 20 2, 130 (1963).