>[!abstract] >The Malkus waterwheel, also referred to as the Lorenz waterwheel or chaotic waterwheel, is a mechanical model that exhibits chaotic dynamics. Its motion is governed by the Lorenz equations. While classical waterwheels rotate in one direction at a constant speed, the Malkus waterwheel exhibits chaotic motion where its rotation will speed up, slow down, stop, change directions, and oscillate back and forth between combinations of such behaviours in an unpredictable manner ("Malkus waterwheel", 2025). > >The [[Lorenz system|Lorenz equations]] are also the governing equations in Fourier space for the Malkus waterwheel (“Lorenz system”, 2025). Gleick (1987, p. 31) tells the genesis story of this contraption: >[!quote] >Lorenz described [the [[Lorenz system]]\] to Willem Malkus, a professor of applied mathematics at M.I.T. […] Malkus laughed and said, “Ed, we *know*—we know very well—that fluid convection doesn’t do that at all.” The complexity would surely be damped out, Malkus told him, and the system would settle down to steady, regular motion. > >“Of course, we completely missed the point,” Malkus said a generation later—years after he had built a real Lorenzian waterwheel in his basement laboratory to show nonbelievers. “Ed wasn’t thinking in terms of our physics at all. He was thinking in terms of some sort of generalized or abstracted model which exhibited behavior that he intuitively felt was characteristic of some aspects of the external world. He couldn’t quite say that to us, though. It’s only after the fact that we perceived that he must have held those views.” >[!tip] Idea compass >- **North** (upstream): [[Nonlinear system]]; [[Lorenz system]] >- **East** (different): — >- **South** (downstream): — >- **West** (similar): — ## References - Gleick, J. (1987). *Chaos*. Penguin Books. - Lorenz system. (2025, April 15). In *Wikipedia*. https://en.wikipedia.org/w/index.php?title=Lorenz%20system&oldid=1282204701 - Malkus waterwheel. (2025, April 15). In *Wikipedia*. https://en.wikipedia.org/w/index.php?title=Malkus%20waterwheel&oldid=1036962041