A waterwheel with leaky buckets undergoes chaotic motion. Our wheel is about 1 meter in diameter and was fabricated with wood in our shop. The little buckets are citronella candle holders with ¼” holes drilled out of the bottom. The sump pump was purchased from the local hardware store. A ball valve at the faucet regulates the water flow. The wheel and pump both sit in a concrete mixing tub.
In nature, chaotic behavior readily occurs in turbulent flows and in large-scale weather patterns, but scaling these systems to a laboratory or classroom setting is far from trivial. The idea of building a waterwheel as a discrete, mechanical example of a chaotic system was proposed and realized by Willem Malkus, Louis Howard, and Ruby Krishnamurti in the early 1970s. According to Edward Lorenz, their original design “was a precision instrument, suitable for controlled laboratory experiments.” Our design is simpler and geared more towards pedagogical impact than experimental fidelity, but we think you will find it charming and instructive nonetheless.
For more details on our setup, including links to download some of the clips of the wheel in motion, see sciencedemonst...