newt = Compile[{{n, _Integer}, {z, _Complex}}, 
      Arg[FixedPoint[# (n-1+#^(-n))/n &, z, 35]]];NewtFrac[n_]:=ListDensityPlot[Table[newt[n,b+a I],{a,-1.1,1.1,0.005},{b,1.1,-1.1,-0.005}],
Mesh->False,
DisplayFunction->Identity,
PlotRange->All,
ColorFunction->Hue,
Frame->False];

NewtFrac[5]