\documentclass{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=1.9}
\pgfplotsset{
    /pgfplots/colormap={pink}{color(0cm)=(purple); color(1cm)=(pink!80!purple); color(2cm)=(pink!90); color(3cm)=(pink) }
}

\begin{document}

\begin{tikzpicture}
    \begin{axis}[
            view={0}{10},
            axis equal,
            axis lines=none,
            colormap name =pink,
        ]
        \addplot3[
            surf,
            shader=faceted,
            samples=50,
            domain=0:2*pi,y domain=0:2*pi,
            z buffer=sort,
        opacity=0.15]
        (
        {(sin(deg(x)))^3*cos(deg(y))},
        {(sin(deg(x)))^3*sin(deg(y))},
        {(13*cos(deg(x))-5*cos(2*deg(x))-2*cos(3*deg(x))-cos(4*deg(x)))/16}
        );
    \end{axis}
\end{tikzpicture}

\end{document}

    
\documentclass{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=1.9}
\pgfplotsset{
    /pgfplots/colormap={pink}{color(0cm)=(purple); color(1cm)=(pink!80!purple); color(2cm)=(pink!90); color(3cm)=(pink) }
}

\begin{document}

\begin{tikzpicture}
    \begin{axis}[
            view={0}{10},
            axis equal,
            axis lines=none,
            colormap name =pink,
        ]
        \addplot3[
            surf,
            shader=faceted,
            samples=50,
            domain=0:2*pi,y domain=0:2*pi,
            z buffer=sort,
        opacity=0.15]
        (
        {(sin(deg(x)))^3*cos(deg(y))},
        {(sin(deg(x)))^3*sin(deg(y))},
        {(13*cos(deg(x))-5*cos(2*deg(x))-2*cos(3*deg(x))-cos(4*deg(x)))/16}
        );
    \end{axis}
\end{tikzpicture}

\end{document}