English: Newton map for the polynomial ${\displaystyle f:z\mapsto z^{4}-z^{3}-1}$ centred at ${\displaystyle {\tfrac {1}{4}},}$ with unit circle and the graph of the real function plotted for reference. The critical points are ${\displaystyle 0}$ (of order 2) and ${\displaystyle {\tfrac {3}{4}}}$ (with image ${\displaystyle {\tfrac {-283}{256}}}$), the roots at the centres of the basins of attraction have approximate coordinates ${\displaystyle -0.81917,}$ ${\displaystyle 0.21945\pm 0.91447i\,}$ and ${\displaystyle 1.38028}$ (the second Pisot number χ).