, 11 tweets, 4 min read Read on Twitter
I strongly suspect this video is so cool because of the Nyquist-Shannon Sampling Theorem. What is that? I’m glad you asked! 🤓 1/N
2/ The theorem says (very loosely) that when you convert an image of a real object into a digitized signal, the digital samples have to occur at least twice as fast as the fastest thing happening in the real object. This is standard nerdism in engineering. en.m.wikipedia.org/wiki/Nyquist–S…
3/ A millipede is a real object. A video is a digitized signal. So if anything in the millipede is happening faster than the frames of the video (divided by two) then something BAD can happen. This bad thing is called... Aliasing! en.m.wikipedia.org/wiki/Nyquist–S…
4/ We are all familiar with aliasing. When you see a wheel or propeller spinning in a movie it may seem to spin forward, then backward, then forward again. That is aliasing. You can see it in this video (disclaimer: I just found this in a quick search)
5/ A wheel is a circular object so the aliasing seems to make it spin the wrong rate. A millipede on the other hand is a linear object so the aliasing will make the ripples along its body seem the wrong length: longer/bumpier. See video, same disclaimer.
6/As a result, the legs in the shadow seem to have regions where they are all off the ground separated by regions where they touch the ground. That isn’t real. It’s aliasing in an under-sampled video. It also makes the millipede look like it’s hopping instead of flowing smoothly.
7/ That cyclic pattern of legs above the ground then on the ground is a wave with a wavelength equal to about 6 body segments.
8/ I made a mistake, above. The cyclic pattern of legs on the ground is real. Each is a single snapshot of a millipede. What is aliased is the smooth flow from one such pic to the next, making it look like the millipede is hopping. This pic came from here:
9/ So I dunno. Maybe I’m wrong about that. It’s just a hunch the ripples along the body are some multiple faster than the 30 frame per second video, plus a little, so the video sees the “beat frequency” making it look like the millipede hops up and down.
10/ If I’m correct, that hopping is called a “beat frequency”. It is the small difference between two fast frequencies. Fast leg motion sampled by a video frame rate (not fast enough) gives a slow hopping motion. Another example of a beat frequency...
11/ is the throbbing sound you often hear in a 2-engine passenger jet. The engine turbines spin extremely fast, but one turbine often spins slightly faster than the other so the difference is a very small amount. You hear it as a slow throbbing sound.
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