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Chaos! (Science Advent 3)

(Every day until Christmas, I’ll be posting a science-related image.)

Day 3

A "strange attractor" produced by a pendulum subjected both to a driving force and a brake. The balance between these opposing forces produces an obvious pattern that never repeats itself.

A “strange attractor” produced by a pendulum subjected both to a driving force and a brake. The balance between these opposing forces produces an obvious pattern that never repeats itself.

Colloquially, “chaotic” means random, but that’s not what it implies in a scientific context. Take the image above: this is a plot of the velocity of a pendulum as a function of its position, taken over many cycles. A normal pendulum would describe a circle (or more accurately a slow spiral inward as air resistance slows the pendulum down), but this is not ordinary. In fact, I constructed this pendulum as a teaching demonstration at my last job, though unfortunately I didn’t take a photo of it. It consisted of a metal disk suspended by its top edge, attached to a pulley. This pulley allowed me to drive the pendulum’s swing using a motor; additionally, I placed a magnetic brake near the disk. By adjusting the rate the motor worked and the distance between disk and magnet, I could control whether the pendulum swung freely, slowed to a stop, or engaged in the weird behavior above.

The diagram shows a pattern, but a non-repeating one. This shape is known as a strange attractor: the pendulum won’t deviate from the basic carnival-mask pattern, but it won’t ever trace over precisely the same path. Strange attractors show up in many systems where there is a similar push-pull between opposing influences. Pendulums such as the one I built are useful in that we can control exactly what goes into them; real-world examples are often far more complex, even as they exhibit similar behaviors.

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