Drag anywhere — the pitch glides. Land on a tick and the sand runs to the figure; between the ticks it just trembles, scattered, the way real sand does off resonance. Use ◀ / ▶ to jump mark-to-mark. Sound starts on your first tap.
What you're looking at
Sprinkle fine sand on a metal plate and bow it, and the grains flee the parts that shake hardest and pile up along the lines that stay perfectly still — the nodes of the standing wave. Ernst Chladni showed this to Napoleon in 1809; the figures are named for him. Every note has its own geometry. Raise the pitch, the plate rings in a busier mode, and a new figure appears.
Here the plate is a square, and each mark on the slider is a resonance — a frequency at which the plate rings cleanly in one plate mode (n, m). Drive it off a resonance and there is no clean standing wave, so the grains never settle: they just tremble, scattered — which is exactly what you see between the marks. Tune onto a mark and the plate goes still along its nodal lines, and the sand runs there. Each of the couple of thousand grains is bounced by the local vibration until it strays onto a still line and stops — the classical Chladni sand model. When a figure forms, the pattern is the zero-set of
— the classical superposition of a square plate's two degenerate modes (Rayleigh, Theory of Sound, 1877). Where s = 0 the plate is still and the sand collects; where |s| is large it is thrown clear. Nothing on the plate is drawn by hand or by chance — every grain is placed by the field above.
The 3 × 7 plate — the 21
Tune onto the mark labelled 21 and the plate rings in mode (3, 7): three still lines one way, seven the other. Their product is written on the sand — a grid of 3 × 7 = 21 cells. It is the same bridge the rest of this record keeps drawing, this time you can hear it: the 3 and the 7 meeting, and what falls out is the 21. Not argued into you — bowed onto a plate and left to stand.
Honest limits
420Code/Lucid runs on one law: cite or refuse — never fake a provenance. So, plainly:
- The figures are real physics — the exact nodal lines of the square-plate standing wave, computed live, not images.
- The map from note → mode is illustrative, not literal. A real plate's resonances obey the biharmonic Kirchhoff–Love equation ∇⁴w = (ρh/D)·ω²·w, and its true eigenfrequencies depend on the metal — its stiffness D, density ρ, thickness h. We order the modes by rising complexity (n²+m² ascending) and pin each to a note of the scale, then drive it with a clean tone at that pitch. Ordered and truthful about the physics; not the measured resonance spectrum of any one plate.
- The tone is a pure sine synthesised in your browser (Web Audio). The little trace under the plate is that exact waveform, drawn — the sound, rendered.
- This is not the whole cymatic range — no finite instrument could be. A square plate has an unbounded ladder of modes (every integer pair n ≠ m), and audible sound runs from ~20 Hz to ~20 kHz. We show a legible slice: 15 resonances across about three octaves (C3–G6), ordered by rising complexity (n²+m²). Enough to feel the rule — figures crystallise at the marks, sand scatters between — without a wall of ticks you can't read.
Built on the420code's music-structure proofs (Lucid Music: scales, tuning as exact cents, deterministic performance). Chladni figures: E. F. F. Chladni, Die Akustik (1802). Square-plate modes: Lord Rayleigh, The Theory of Sound (1877). No cookies, no network, no stored answer — the plate is solved on your device the moment you move the slider.