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Recreating this image of an atomic set

TeX - LaTeX Asked by Ramanujan on April 19, 2021

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}

One Answer

As @Symbol 1 said, It seems that the plot corresponds to the real part of three successive elements + the convex hull.

I've tried it in Matlab and the closest graph corresponds to [cos(2*pi*f+phi),cos(4*pi*f+phi),cos(6*pi*f+phi)] and phi=pi/2 and f in [0,1]

Here is the result:

enter image description here

This is generated by the following Matlab code:

f=0:0.01:1;
phi=pi/2;
xx=cos(2*pi*f+phi);
yy=cos(4*pi*f+phi);
zz=cos(6*pi*f+phi);

[k1] = convhull(xx,yy,zz);
trimesh(k1,xx,yy,zz)

hold on
plot3(cos(2*pi*f+phi),cos(4*pi*f+phi),cos(6*pi*f+phi),'r','linewidth',2)

with Jet colormap option.

You can use matlab2tikz to get the LaTeX code and you can plot it using pgfplots package. Here is my attempt:

enter image description here

I've modified the Latex code:

  • removed the plot of the three elements (red curve in the previous illustration)
  • Changed opacity from 1 to 0.95.

Here is the LaTeX main file:

documentclass[border=0.2cm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.11}

begin{document}

  input{atomicSet}

end{document}

and the illustration file, named atomicSet.tex:

begin{tikzpicture}

begin{axis}[%
width=3.743in,
height=2.983in,
scale only axis,
colormap/jet,
xmin=-1,
xmax=1,
ymin=-1,
ymax=1,
zmin=-1,
zmax=1,
view={-37.5}{30},
grid,
]
addplot3[area legend,opacity=0.95, table/row sep=crcr, patch, shader=flat corner, fill=white, patch table with point meta={%
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}]
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};
end{axis}

end{tikzpicture}%

Correct answer by LaTeXdraw-com on April 19, 2021

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