First example:
Image[
With[{s = N[2 Pi], r = N[Range[-4, 4, 8/299]]},
Map[{Arg[#]/s,
1, (# Conjugate[#])^0.33 &[Times @@ Sin[s ReIm[#]]]} &,
Mod[#/LogGamma[Abs[#]^-10.5] (1 + I Sin[s/2 Abs[#]]), 2] &[
Outer[Complex, r, r]], {2}]], ColorSpace -> "HSB"]
Here’s the result:
Second example:
Image[
With[{s = N[2 Pi], r = N[Range[4/3, -4/3, -8/1497]]},
Map[{Arg[#]/s,
1, (# Conjugate[#])^0.33 &[Times @@ Sin[s ReIm[#]]]} &,
Mod[Log[(1 + Abs[#])/(1 - Abs[#])]^0.25 # (-0.5 + I 0.1 Abs[#]),
2] &[Outer[Complex, r, r]], {2}]], ColorSpace -> "HSB"]
Here’s the result:
Sugesstion for Mathematica 13:
ComplexPlot could have the option ColorFunction → “CyclicReIm” additionaly to the existing ColorFunction → “CyclicReImLogAbs”, then these above functions could be expressed directly in ComplexPlot.
Some more functions generated with the code above (coffee beans?):
somehow hypnotic:
and even more whisked:
and simple again:
