# How to plot fractals created with Newton's method [duplicate]

I'm quite a beginner using Mathematica. I'd like to plot the fractals of higher degree polynomials.

I have an example for z^3 - 1 which looks like this:

F[z_] := z^3 - 1;
NewtonRaphsonStep[z_] := z - F[z]/F'[z]
NoOfIterations = 6;
GridSize = .01
MatrixPlot[
Table[
θ = Arg[Nest[NewtonRaphsonStep, i + j I, NoOfIterations] /.
{Indeterminate -> 10}];
If[θ > 1.8, 1, If[θ < -1.8, 2, 0]],
{j, -2., 2., GridSize}, {i, -2., 2., GridSize}],
Mesh -> None, Mesh -> False, ImageSize -> {500, 500},
ColorRules -> {2 -> Red, 0 -> Orange, 1 -> Pink}]


And this works just fine. But for z^4 - 1 and higher degrees, I don't know how to plot the fractal, I'm not sure how to handle more roots.

• Have you searched on this site? Have you seen this and other related posts? – Michael E2 Nov 29 '15 at 21:06

Here is a simpler ListDensityPlot version using FixedPoint and avoiding indeterminate values by choosing a step size which skips 0 + 0 I. It is also much faster by mapping over precomputed coordinates.
ListDensityPlot[Arg @ FixedPoint[NewtonRaphsonStep, #] & /@ 