Basins of attraction

To plot a basin of attraction for given governing equations: x^3-y = 0 ; y^3-x = 0

While solving a system of equations using any numerical method, the point to which the method converges is strongly dependent on the initial guess. The set of points that converge to a given root is called the basin of attraction of that root. It would be interesting to visualize the basins of attraction by coloring each starting point with a different color depending on which root it converges to. The different basins will thus be given different colors. The basins of attraction obtained will look like fractals.