Curl Vector Field

Incompressible fluid flow computed from the discrete mathematical curl of a continuous 2D scalar potential field.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Streamline Particles 1200

Particle density

Flow Velocity 2.2

Particle advection speed

Field Scale 0.0035

Vorticity wave scale

Mathematical Formulation

70 chars medium

Analytical Equation

\mathbf{v} = \nabla \times \psi = \left( \frac{\partial \psi}{\partial y}, -\frac{\partial \psi}{\partial x} \right), \quad \nabla \cdot \mathbf{v} = 0

Compact Formula

vx = (N(x, y+ε) - N(x, y-ε)) / 2ε, vy = -(N(x+ε, y) - N(x-ε, y)) / 2ε

Renderer Logic

const vx = (noise2D(nx, ny + eps + t) - noise2D(nx, ny - eps + t)) / (2 * eps);
const vy = -(noise2D(nx + eps, ny + t) - noise2D(nx - eps, ny + t)) / (2 * eps);
px[i] += vx * speed * 8;
py[i] += vy * speed * 8;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#curl #vector-field #solenoidal #fluid-dynamics #physics #incompressible

Author: Math Art Core Target: 60 FPS

Curl Vector Field

Live Parameters

Mathematical Formulation

Mathematical Tags

Export & Embed: Curl Vector Field

4K PNG Snapshot

WebM Video (5s Loop)

HTML Iframe Embed