Abstract
Newton's method is often employed to numerically find a root of the equation p(z) = 0 (1-3). A root of p(z) = 0 is the limit of a sequence (zk) of complex numbers generated by this method with a proper initial guess z0 . Therefore, each of its roots plays the role of an attractor (attractive fixed point) when Newton's method is applied to solve the equation p(z) = 0. In other words, the three roots are competing with each other to attract z0. The set of starting points whose generated sequences converge to a root forms a basin of attraction for Newton's method. It is well-known that the boundary of each basin of attraction is the Julia set of Newton's method.
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