How it works
How the Chladni Plate works
A black square plate, strewn with sand, with a frequency knob. Turn the knob onto a resonance, or draw a bow along an edge, and the sand runs off the parts that move and piles up on the lines that stand still, so the plate draws its own figure. I didn't draw any of the figures. This page is how the plate finds them.
The physics is DOM-free, so the tests run it in Node.
The plate's modes
A square plate with free edges has natural shapes it likes to vibrate in, its modes. I use the classical approximation for a free square plate, with u and v running from 0 to 1 across it:
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