Use this construction to explore the convergence of an initial point in the complex plane to one of three roots in a cubic polynomial using Newton's Method. Move points A, B and C to change the roots of the polynomial and move point C1 to change the initial point. Nine iterations of Newton's Method are performed with C10 being the final point. The color of C1 represents the root to which it will converge. Right-click point C1 and turn tracing on as you move the point to see basins of color representing the basins of convergence for each root.

What do you notice as you drag point C1 along boundary areas of the basins?