How can I get a nice gray-scaling in this 3D-plot?

Question

I was able to customize an online example to my needs, but now I am stuck with the coloring. It would be great, if the function 5*x*sin(2*deg(x)) * y*(1-y) would be in gray-scale and the half-space which so far is yellow -> black.

How can I do this? Thank you in advance.

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{width=7cm,compat=1.8}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[grid=major,view={210}{30}, 
         xtick={0,1},
 xticklabels={{1},{0}},
  ytick={0,1},
  yticklabels={{$A$},{$a$}},
   ztick={0,1},
 zticklabels={{0},{$H$}},
    ]
    \addplot3+[mesh,scatter,samples=10,domain=0:1] 
        {5*x*sin(2*deg(x)) * y*(1-y)};

\addplot3 [data cs=cart,surf,domain=0:1,samples=2, opacity=0.5]
      {0.5};        

    \end{axis}
\end{tikzpicture}
\end{document}

Answer 1

You can add an appropriate color map.

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{width=7cm,compat=1.8}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[grid=major,view={210}{30}, 
         xtick={0,1},
 xticklabels={{1},{0}},
  ytick={0,1},
  yticklabels={{$A$},{$a$}},
   ztick={0,1},
 zticklabels={{0},{$H$}},colormap/blackwhite
    ]
    \addplot3+[mesh,scatter,samples=10,domain=0:1] 
        {5*x*sin(2*deg(x)) * y*(1-y)};

\addplot3 [data cs=cart,surf,domain=0:1,samples=2, opacity=0.5,point meta=0]
      {0.5};        

    \end{axis}
\end{tikzpicture}
\end{document}