English: Newton map for the polynomial ${\displaystyle f:z\mapsto (z^2-2z-1)(z^2-2z+\sigma )/\sigma }$ centred at critical point ${\displaystyle 1,}$ with unit circle and the graph of the real function plotted for reference. ${\displaystyle f(1)=\frac{-4}{\sigma +1},}$ the other critical points are ${\displaystyle 1\pm \frac{1}{\sqrt{\sigma +1}}}$ with image ${\displaystyle \frac{-\sigma }{2}.}$ The roots at the centres of the basins of attraction have coordinates ${\displaystyle 2-\sigma ,}$ ${\displaystyle 1\pm i\sqrt{\sigma -1}}$ and ${\displaystyle \sigma }$ (the silver ratio).