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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:

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?

The docs have a similar example.

– J. M.'s ennui – 2015-11-21T16:51:53.843