An example of a dynamical plane associated with a value of the parameter is shown in protocol Figure 2(a), where three different basins of attraction appear, two of them of the superattractors 0 and �� and the other of z = 1, that is, a fixed attractive point. It can be observed how the orbit (in yellow in the figure) converges asymptotically to the fixed point. Also in Figure 2(b), the behavior in the boundary of the disk of stability of z = 1 is presented, where this fixed point is parabolic. An orbit would tend to the parabolic point alternating two ��sides�� (up and down of the parabolic point in this case). Figure 2Dynamical planes for �� verifying |�� ? 16| �� 64.The generation of dynamical planes is very similar to the one of parameter spaces.

In case of dynamical planes, the value of parameter �� is constant (so the dynamical plane is associated with a concrete element of the family of iterative methods). Each point of the complex plane is considered as a starting point of the iterative scheme, and it is painted in different colors depending on the point which it has converged to. A detailed explanation of the generation of these graphics, joint with the Matlab codes used to generate them, is provided in Section 3.In Figure 3(a), a detail of the region around �� = 0 of P1 can be seen. Let us notice that region around the origin is specially stable, specifically the vertical band between ?4 and 1 (see also Figure 3(b)). Figure 3Around the origin.In fact, for �� = 0, the associated dynamical plane is the same as the one of Newton’s, that is, it is composed by a disk and its complementary in .

Around the origin is also very stable, with two connected components in the Fatou set. When �� = 16, z = 1 is not a fixed point (see Theorem 2) and ?1,1 define a periodic orbit of period 2 (see Figure 4(a)). The singularity of this value of the parameter can be also observed in Figure 4(b), in which a dynamical plane for �� = 15.9 ? 0.2i is presented, showing a very stable behavior with only two basin of attraction, corresponding to the image of the roots of the polynomial by the M?bius map. Figure 4Around �� = 16.It is also interesting to note in Figure 3(a) that white figures with a certain similarity with the known Mandelbrot set appear. Their antennas end in the values �� = ?4 and �� = 1, whose dynamical behavior is very different from the near values of the parameter, as it was shown in Lemma 3.A similar procedure can be carried out with the free critical points, z = cri, i = 3,4, Brefeldin_A obtaining the parameter planes P2, shown in Figure 5. Figure 5Parameter space P2 associated with z = cri, i = 3,4.As in case of P1, the disk of repulsive behavior of z = 1 is clear, and inside it different ��bulbs�� appear, similar to disks.