JuliaSetPlot - how do I achieve nicer colors?

Question

I use the following code to generate images of Julia sets:

JuliaSetPlot[
   z^2 - 0.76 - 0.11 I, z, 
   PlotRange -> {{-1.6, 1.6}, {-1.0, 1.0}}, 
   MaxIterations -> 1000, 
   ImageResolution -> 1500
]

As you can see the colors are not too appealing. However I did code Julia sets in C# before and I know that the colors depend on the number of iterations so I tried less iterations:

This is what MaxIterations -> 100 gives me. I much prefer these colors. How can I get nicer colors while keeping a high number of iterations? I think ColorFunction or ColorFunctionScaling could get handy here but I never touched those so some help would be appreciated.

Answer 1

You can scale the values supplied

JuliaSetPlot[z^2 - 0.76 - 0.11 I, z, PlotRange -> {{-1.6, 1.6}, {-1.0, 1.0}}, 
 MaxIterations -> 1000, ImageResolution -> 1500,
 ColorFunction ->
  With[{cf = ColorData["M10DefaultFractalGradient"]},
   cf@Sqrt[#3] &
   ]
 ]