Divergence and curl of a 2D vector field

What you are seeing: a parameterized 2D vector field drawn as a grid of arrows. The two numerical readouts are the divergence and curl evaluated at the center of the plot (or at any chosen point - here the origin). Four field families are available: radial source (uniform divergence, zero curl), uniform rotation (zero divergence, uniform curl), shear (zero divergence, constant negative curl), and saddle (both zero everywhere).

The scalar parameter $a$ scales each family uniformly. For the source family, $\nabla \cdot \mathbf{F} = 2a$ is independent of position; for the rotation family, $\nabla \times \mathbf{F} = 2a$ is similarly uniform. Watching the arrows reorganize as you slide $a$ makes the differential operators visceral.