Why does the field point this way?

Pick a vector field. Hover any point to see the local vector, the numerically estimated Jacobian, and a plain-language diagnosis: is this point a source, a sink, a rotation, a saddle? The color shows the direction of the field; the arrows show magnitude and heading.

Vector field

Rendering…
hover the field
Arrows = direction + relative magnitude. Color = heading (hue) & magnitude (brightness). Scroll to zoom, drag to pan, double-click to reset. Shift+scroll changes arrow density.
f(x,y)
—
g(x,y)
—
div F = ∂f/∂x + ∂g/∂y
—
curl F = ∂g/∂x − ∂f/∂y
—
speed |F|
—
det J = λ₁λ₂
—
trace J = λ₁+λ₂
—
eigenvalues
—

Local analysis

outward inward field

Hover over the field to analyze a point.