Visualizes a multivariable function z=f(x,y) as a gridded surface. Then it animates partial derivatives by taking x- and y-slices through a moving point and shrinking the step h in the difference quotient (holding the other variable fixed). Finally it shows the gradient vector ∇f, a rotating displacement Δx, and the first-order change approximation Δf ≈ ∇f·Δx, comparing linear prediction to the actual surface step.
Pure Canvas2D; blocky aesthetic via 4px snapping and squared markers. Surface uses a lightweight projected grid (no fills) for speed. Animation cycles through 4 stages (~3.8s) and uses easing to shrink h toward 0 for the limit interpretation. Gradient/dot-product shown in a 2D inset plus a predicted-vs-actual step on the surface.