Pendulum Waves (2010)

I recreated this in CSS&#x2F;JS a few years ago, inspired by this video.<p><a href="https:&#x2F;&#x2F;codepen.io&#x2F;madelinw&#x2F;details&#x2F;ocnCl" rel="nofollow">https:&#x2F;&#x2F;codepen.io&#x2F;madelinw&#x2F;details&#x2F;ocnCl</a>

Without analyzing it too much this seems to be a perfect visualization of the mathematics of music theory. The lengths of string become quite a direct metaphor for the wavelengths of notes on the music scale, and seeing them move together in progressively different &quot;groups&quot; of notes I imagine closely matches traditional chord structures in different keys.<p>Quite mesmerizing, and mathematically satisfying at the same time!

If you enjoy demos like this and live in or visit San Francisco, check out the Exploratorium, which is full of amazing physical demos like this.<p><a href="https:&#x2F;&#x2F;www.exploratorium.edu&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.exploratorium.edu&#x2F;</a>

I’ve seen this demonstration at least a couple of times, once as an undergrad around 1971. I always remembered it and a few years later I was working with a minicomputer with limited I&#x2F;O so I decided to blink the row of front panel lights just to show that the program was running. I blinked each on and off with a slightly different frequency and got a similar, interesting effect.

Great to see this come up again! Here&#x27;s a simulator I wrote for it a looooong (almost 8 years!) ago: <a href="https:&#x2F;&#x2F;cs.stanford.edu&#x2F;people&#x2F;paulliu&#x2F;webapps&#x2F;pendulum.html" rel="nofollow">https:&#x2F;&#x2F;cs.stanford.edu&#x2F;people&#x2F;paulliu&#x2F;webapps&#x2F;pendulum.html</a>

Interesting to see this come up again. Here’s a small model for this system written in Haskell from a few years back:<p><a href="http:&#x2F;&#x2F;syntacticsalt.com&#x2F;blog&#x2F;2011-08-27-harmonic-motion.html" rel="nofollow">http:&#x2F;&#x2F;syntacticsalt.com&#x2F;blog&#x2F;2011-08-27-harmonic-motion.htm...</a>

It seems like the pendulums fall into a few repeating patterns. E.g. for a second it looks like a snake, for another second it looks like a double helix, and so on. The whole set cycles through each pattern and then begins again. How many patterns are there?

Now what happens when you couple the oscillators?

it looks like rotating helixes to my eye