Draw a contour in the left plane and the running value of the integral ∫ f(z) dz = Σ f(zk)·Δzk traces out in the right plane — its endpoint is the value of the integral. The green and cyan ticks show how f(z) turns the tangent directions dz=1 and dz=i.
A modern JavaScript + Canvas port of a 1998 Java applet by Terence Tao
(originally IntegApp.java / IntegGrid.java).
Draw a closed loop and watch the sum return (or not) to 0.