The first official "chaos machine" is easy to make

Illustration for article titled The first official chaos machine is easy to make

Do you want to make a truly chaotic system? It's not as hard as you think. In fact, you could probably set up the first official chaos machine ever made in your shower.


The Butterfly Effect, before it was a movie, was a phenomenon discovered by Edward Lorenz. A professor of meteorology at MIT, Lorenz created a computer model that printed out a set of weather patterns based on certain initial conditions that Lorenz typed in. When he very slightly altered the initial conditions, he was surprised to see how widely the results varied. That got him thinking about chaos.

Chaos is marked by an absence of predictable patterns. Many systems, and certainly the most-studied ones, eventually settle down into a predictable sequence of behavior. Chaotic ones will never fall into a pattern — and they do this by involving multiple variables, all dependent on each other. Sounds complicated, right? But when Lorenz started thinking of different devices that might exemplify this behavior, he came up with a very simple little chaos machine called the Lorenzian Waterwheel.


Picture a wheel suspended above the ground, like a Ferris Wheel. Rather than cars with seats, it has buckets. Water rains down on the top bucket, and when the bucket fills, it will slowly descend, turning the wheel and giving the downpour more buckets to fill. That alone will settle into a regular motion. Lorenz added something simple — holes in the bottom of the buckets. If the water pours down slowly, the top bucket will drain before it tips the wheel. At most, the wheel will spin regularly. If the water gushes down fast enough, on the other hand, things get chaotic.

Each bucket is affected by the amount of water in the rest of the buckets, and their position on the wheel, both of which are changing all the time. If the top buckets fill up enough, the wheel spins one way. If it spins too far, it goes backwards and can change direction completely. It can settle down in a place for a long time, only to get started up again. No matter how long we wait, the wheel never acquires a predictable motion. It will always be chaotic. Get just a bit more complicated than the wheel of a mill, and you officially have a machine that models chaos forever.

And an amazing bath and shower toy. Why isn't anyone marketing this?

[Via Chaos: Making a New Science, The Chaotic Wheel]


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Stephan Zielinski

Chaotic systems aren't necessarily particularly complicated; their distinguishing characteristic is sensitive dependence on initial conditions. Example: the double pendulum:

Which looks like it should be easy enough to model— it's just one pendulum hanging from another, and pendulums are easy, eight?— but it's mathematically intractable. (Digital simulation available at… .)