Doing a bit more reading, I found out that the equations that make up the Lorenz attractor (which are derived from a simplified model of 2D fluid flow with a superimposed temperature gradient) can also be thought of as governing another physical system. Imagine a water wheel, with a number of buckets spaced evenly around the perimeter. These buckets filled at the top of the wheel. As that bucket fills, any offset will generate an imbalance, and the wheel rotates. That will rotate another bucket into position. The amount of water in that bucket is less because it spends less time under the faucet. But eventually, the buckets all fill up, the wheel is balanced, and the friction of rotation causes the motion to cease.
But now, imagine that each bucket is leaky: that some of its water drains out. What happens then? Well, it turns out that depending on the speed at which the water is pumped in and leaks out, the wheel can exhibit chaotic motion: spinning at radically different speeds and often reversing itself. Very neat. Here’s a video of one with a particularly simple design (you can google for more examples):
This would be a fun garden project.