Circular Ripples

Two-dimensional circular Bessel wave ripples emitted from moving source centers creating complex constructive and destructive interference.

Playground

60 FPS • Canvas 2D

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Live Parameters

Ripple Wavenumber (k) 0.04

Spatial ripple density

Propagation Speed 1.8

Wave radiation rate

Mathematical Formulation

80 chars low

Analytical Equation

\eta(\mathbf{r}, t) = \sum_{i=1}^{3} A_i J_0(k \|\mathbf{r} - \mathbf{r}_i(t)\|) \cos(\omega t)

Compact Formula

w = Σ (sin(dist_i * freq - 2t) / (sqrt(dist_i)*0.1 + 1)), r_point = 0.5*(w + 1)

Renderer Logic

const w1 = (Math.sin(d1 * freq - t * 2) / (Math.sqrt(d1) * 0.1 + 1));
const w2 = (Math.sin(d2 * freq - t * 2) / (Math.sqrt(d2) * 0.1 + 1));
const w3 = (Math.sin(d3 * freq - t * 2) / (Math.sqrt(d3) * 0.1 + 1));
const wave = (w1 + w2 + w3) / 3;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#bessel #ripples #interference #wave-optics #physics #waves

Author: Math Art Core Target: 60 FPS

Circular Ripples

Live Parameters

Mathematical Formulation

Mathematical Tags

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