newton[z_] := z - f[z]/f'[z]

    plot :=
      ListDensityPlot[Arg@FixedPoint[newton, #, 50] & /@
        Table[i + j I, {j, -2., 2., 0.011}, {i, -2., 2., 0.011}],
       ColorFunction -> "Rainbow"]

    f[z_] := z^3 - 1; plot

[![enter image description here][1]][1]


    f[z_] := z^5 - 1; plot

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/xIlxW.jpg
  [2]: https://i.sstatic.net/oUveM.jpg