Nonlinear dynamical systems are known to generate interesting patterns as their trajectories in phase space. This gallery includes some of these pretty patterns, most of which come from my nonlinear dynamics class.

Trajectories of the nonlinear pendulum in the phase space. The orderly yet rich pattern resembles that of a Persian carpet.
Finite time Lyapunov exponent (FTLE) of the nonlinear pendulum in the phase space.