Gradient of scalar in 2D

Comparing the surface plot of the scalar function to the quiver plot of its gradient vector function

Live Script showing an example of a function H in 2D space (x and y) evaluated as a surface plot in 3D. The gradient of H is a vector field with arrows pointing to and away from local maxima and minima, respectively, and magnitudes (relative arrow length) corresponding to the change in H with respect to change in x and y (partial derivatives).