Newton raphson method, scaling at fractal boundaries and mathematica

The basins of convergence of cubic polynomials having real roots are studied using the Newton Raphson iterative method. The limiting value for the ratio of basin segments for equispaced roots is explained. An algorithm is presented for computing the basin boundaries on the real axis which obviates the necessity of taking recourse to extensive search. MATHEMATICA programs have been developed to help in the above study and also to depict the basins in the complex plane.