Drawing a 3D manifold with gridlines in TikZ

Question

I'd like to draw an arbitrary 3D manifold, such as this, with gridlines and labeled axis, using TikZ:

There are a few similar posts here and elsewhere, but nothing that quite achieves what I'm looking for.

Answer 1

pgfplots offers such plots.

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots} % package used to draw plots  
\pgfplotsset{compat=1.17}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[trig format plots=rad]
        \addplot3 [surf,fill=white,domain=0:6,point meta=1] {(1+sin(x/2))*sin(x)*cos(y)};
    \end{axis}
\end{tikzpicture}
\end{document}