Mathematics for dancing laser beam
- Context: Undergrad
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I would say that these are strange attractors that are dealt with in chaos theory. The more regular shapes are closed paths in the vector fields of ordinary differential equations, basically also attractors.
Back in undergrad, I made a 2-D laser deflection mirror that I could drive in the horizontal axis with a lower-frequency waveform (like 50Hz-100Hz), and I drove the music signal into the vertical deflection circuit. You could adjust the horizontal sinusoid to get the best Lissajous figures for each particular piece of (rock) music. Very fun...sergiokapone said:
https://en.wikipedia.org/wiki/Lissajous_curve
sergiokapone
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Well, if there were always Lissajous curves, then everything is fine. But sometimes closed curves are obtained, which are far from similar to such figures.
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It looks as if there are just two cycles of X and Y, as I can see ends to the pattern. The existence of an enclosed area means the two waves are out of phase, having a quadrature component. It looks as if they are the same frequency, as we do not see a figure-of-eight in the pattern, but the wave shapes look non sinusoidal, maybe rectified sine wave.
berkeman said:
BTW, this was one of the better musical pieces for the laser show in our dorm room, and this thread reminded me of it so I had to post it. It's also the song that I get in my head when I'm pushing the cadence of my mountain bike (MTB) to keep a high pedal cadence.
Set your Lissajous laser deflection at 60Hz horizontal and turn up the vertical and the audio!
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