Chladni Plate: Standing-Wave Sand Patterns (2D)

This 2D companion renders the same Chladni standing-wave field as the 3D version — f(x,y) = sin(nπx/L)sin(mπy/L) − sin(mπx/L)sin(nπy/L) — from directly overhead on a plain Canvas2D context, which makes the nodal-line geometry easier to read than an orbiting 3D scene. Drag the drive-frequency slider and watch the mode numbers (n,m) step through 21 discrete pairs, each producing a different figure as up to 6,000 sand-grain particles descend the gradient of |f(x,y)| and pile up along the zero-crossings. A separate vibration-intensity control scales how hard the grains shake near antinodes before they settle, and the live readout panel tracks the current mode, particle count, the fraction of grains that have already reached a node, their average residual speed, and elapsed simulation time.