#StackBounty: #tikz-pgf #pgfplots #tikz-3dplot Recreating this image of an atomic set

Bounty: 50

On slide 24 of this talk one finds this image

enter image description here

which is supposed to depict the atomic set e^{i phi} [ 1, e^{2 pi i f}, e^{4 pi i f}, … e^{2 (n – 1) pi i f}]^T for phi in [0, 2 pi) and f in [0, 1).
I am suspecting that only the real parts of the first three components of the vector is plotted for different phi values but that is not quite it.

I would be grateful if someone could identify what exactly is plotted and how to achieve the colouring on the surface.

MWE

documentclass[tikz]{standalone}
usepackage{pgfplots}

begin{document}

begin{tikzpicture}
        begin{axis}[grid = major, view={-30}{30}]
        addplot3[variable=t,samples = 60,domain=0:1]
        ({cos(2 * pi * deg(t))},{cos(4 * pi * deg(t))}, {cos(6 * pi * deg(t))});
        end{axis}
    end{tikzpicture}
end{document}


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