Gradient of scalar in 3D

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

Live Script showing an example of a function H in 3D space (x, y, and z) evaluated as a scatterplot. 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, y, and z (partial derivatives).