Currently, I am working of creating some tricky complex color function. I need the original values, not scaled, so I indicated ColorFunctionScaling->False, but result is incorrect.

Here is a simplified code for show the problem:

ExceptNegAng[rad_] := If[rad < 0, 2 Pi + rad, rad];
ComplexColorFunction[argf_] := Hue[ExceptNegAng[argf]/(2 Pi)];
ComplexPlot[z, {z, -1 - I, 1 + I}, 
ColorFunction -> {ComplexColorFunction[#8] &, None}, 
ColorFunctionScaling -> False]

After run, we get:

enter image description here

Why is there a white(transparent) line on the plot?

How to fix ComplexColorFunction?

  • 1
    $\begingroup$ Your problem is the usage of Arg respectively the slot #8. From the doc: Arg[z] has a branch cut discontinuity in the complex z plane running from -[Infinity] to 0. Cooler is PieChart[Table[Style[1, Hue[h, s, 1]], {s, 0, 1, .1}, {h, 0, 1, .1}]] from the documentation. Exclusions->None is correct. $\endgroup$ Mar 10, 2020 at 9:38

1 Answer 1


Add the option Exclusions -> None to get

enter image description here


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