Fig. 1 Illustration of the chaotic waterwheel, from chapter 9 of S.H. Strogatz (1994) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering

Water drips in steadily in the top cups. When the inflow of water is small enough to drip out of the cup immediately, no torque is exerted on the wheel and it does not move: the diffusive equilibrium of the Lorenz equations. When water pours in a little faster, the top cups fill with water, a torque is exerted on the wheel and it starts to rotate. The wheel quickly settles into an equilibrium with a constant speed, the rate of inflow is small enough for the cups to be empty once they are in the top position. Either direction is possible corresponding to the two convective equilibria of the Lorenz equations. When the inflow becomes even larger, the steady rotation becomes unstable. The cups are filled very quickly when they are in the top position, they exert a large torque on the wheel and it accelerates. Due to the high speed of the wheel, the cups at the top receive hardly any water and the few cups which do contain a large amount of water hardly have the time to loose it before they are in top position again. The wheel can do two things now: either inertia is large enough so that the wheel overshoots and makes another rotation in the same direction, or inertia is too small and the wheel stops and rotates in the opposite direction. This latter possibility corresponds to a trajectory of the Lorenz model in its chaotic regime, hopping from one wing of the attractor to the other.