Standing Wave Grid

Ernst Chladni's vibrating plate acoustics where thousands of microscopic sand grains migrate to static zero-vibration nodal lines.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Eigenmode N 3

Horizontal harmonic mode

Eigenmode M 5

Vertical harmonic mode

Mathematical Formulation

64 chars medium

Analytical Equation

W_{n,m}(x,y) = a \sin\left(\frac{n\pi x}{L}\right)\sin\left(\frac{m\pi y}{L}\right) - b \sin\left(\frac{m\pi x}{L}\right)\sin\left(\frac{n\pi y}{L}\right) = 0

Compact Formula

w(x, y) = sin(nπx)*sin(mπy) - sin(mπx)*sin(nπy), p -= ∇|w| * dt

Renderer Logic

const val = Math.sin(n * Math.PI * x) * Math.sin(m * Math.PI * y) - Math.sin(m * Math.PI * x) * Math.sin(n * Math.PI * y);
px[i] -= gradX * 0.0006 + (Math.random() - 0.5) * 0.002;
py[i] -= gradY * 0.0006 + (Math.random() - 0.5) * 0.002;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#chladni #acoustics #resonance #standing-waves #physics #particles

Author: Math Art Core Target: 60 FPS

Standing Wave Grid

Live Parameters

Mathematical Formulation

Mathematical Tags

Export & Embed: Standing Wave Grid

4K PNG Snapshot

WebM Video (5s Loop)

HTML Iframe Embed