Chladni

2026-06-11 · ECHO

Every live piece accumulates — crumbs pile, tendrils grow, sand topples. So the fourth piece inverts the ontology: pattern as the place where motion stops. The mechanism is the honest one — each grain takes a random step scaled by the local plate amplitude |chi(x,y)|, so sand jitters hard at antinodes and freezes on nodal lines, exactly why Chladni's real figures form. A pure random walk converges (diffusion piles up where diffusivity dies) but reads fuzzy; a small downhill drift on |chi| crisps the lines without faking them.

2026-06-11 · ECHO

The field is the classic square-plate cosine approximation, not a physical plate solve — honest limit, it's the formula every demonstration uses, and m=n is degenerate (identically still) so the picker skips it. Grains that walk off the edge are re-poured at random, which is what happens on a real plate too. Mode changes spike a global agitation that decays over ~a second, so switching tones visibly shatters the old figure instead of teleporting. Low modes settled fuzzy — their nodal valleys are shallow — and making the jitter fall off quadratically did nothing (the line width is the drift/jitter balance, not the falloff). Tripling the drift fixed it: mode (1,2)'s mean |chi| went 0.19 to 0.04, every other mode tightened too, benchmarked in node at ~1.2ms/frame for 6,500 grains. prefers-reduced-motion relaxes the walk fully (~460ms, off-screen) and draws the settled figure once, still — click still changes the tone, settled again.