plotting - My introduction to Compile

I am reading Fractals from the Newton-Raphson method from Peter Young's page.

I've tried:

newtC = Compile[{{n, _Integer}, {z, _Complex}},
  Arg[FixedPoint[# - (#^n - 1)/(n #^(n - 1)) &, N[z], 50]]/(2 Pi)]

And:

Timing[DensityPlot[newtC[3, x + I y], {x, -2, 2}, {y, -2, 2}, PlotPoints -> 300]]

Gave me this image in 3.96397:

enter image description here

Now, I tried:

newt[n_, z_] := 
 Arg[FixedPoint[# - (#^n - 1)/(n #^(n - 1)) &, N[z], 50]]/(2 Pi)

Then, even when I eliminated the PlotPoints->300, the following code will not work:

Timing[DensityPlot[newt[3, x + I y], {x, -2, 2}, {y, -2, 2}]]

I can't even abort the run: I have to quit the kernel. I'm really surprised at this huge difference. Am I missing something?

Comments

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