I Mathematics for dancing laser beam

AI Thread Summary
The discussion centers on the mathematical principles behind the shapes produced by dancing laser beams, particularly focusing on Lissajous curves and their relation to chaos theory and ordinary differential equations. Participants share experiences of using a 2-D laser deflection mirror to create visual patterns synchronized with music, adjusting frequencies for optimal results. There is a mention of how closed curves can appear that differ from typical Lissajous figures, indicating complex wave interactions. The conversation also touches on the importance of phase relationships between the waves and their impact on the resulting patterns. Overall, the thread highlights the intersection of mathematics, music, and visual art in creating dynamic laser displays.
sergiokapone
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Is there a math that describes these shapes at least one frequency?
 
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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.
 
sergiokapone said:
Is there a math that describes these shapes at least one frequency?
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...

https://en.wikipedia.org/wiki/Lissajous_curve
 
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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.
 
sergiokapone said:
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.
Can you e-mail the person who created that figure and other similar figures? Perhaps they would share their setup details with you.
 
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.
 
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berkeman said:
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...

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. :smile:

Set your Lissajous laser deflection at 60Hz horizontal and turn up the vertical and the audio!


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