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BambOo
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Engineer, researcher, problem solver when possible :)

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\documentclass[tikz,margin=3mm]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{colormaps}
\usetikzlibrary{arrows.meta}
\pgfplotsset{
    compat=1.16,
    drawarrows/.style={
        Circle-,thick,point meta={\pgfkeysvalueof{/pgfplots/samples}-\coordindex},
        quiver={u=-x,v=-y,colored=mapped color},
        },
    customaxis/.style={
        domain=9*pi/2:pi/2,
        samples=1000,
        width=5cm,
        height=5cm,
        scale only axis,
        clip=false,
        hide axis,
        colormap/hsv,
    },
}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[customaxis]
        \addplot[drawarrows] ({cos(deg(x))},{x^2});
    \end{axis}
\end{tikzpicture}
\end{document}
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