brainwagon "There is much pleasure in useless knowledge." — Bertrand Russell

22Mar/110

The Chaotic Lorenz Water Wheel

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.

22Mar/110

Chua chaotic oscillator

Over sushi this evening, Tom mentioned "Chua's circuit", or "Chua's oscillator". I knew that I had seen this somewhere before, but failed to remember that Chua was also the guy who first theorized about the memrister: a circuit element whose resistance is proportional to the sum of the charges that has been passed through it. Chua first imagined this circuit back in 1983, and it is probably one of the most well studied and well understood chaotic circuits ever proposed. It's also quite simple. The page linked here should a simple circuit, with just a single op amp and a handful of other discrete components. I'll ponder it some more:

Chua chaotic oscillator.

22Mar/110

My own animation of the Lorenz Attractor

I've been working on a script or two for generating intros for some of my little YouTube videos, and thought that maybe something like an animation of the Lorenz strange attractor might make a somewhat interesting background. A little tweaking, and I produced the following example (only 10 seconds long, and with some Morse as the background):



You'll probably see this (or something similar) on front of future videos.

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