\begin{tikzpicture}[scale=0.66]
\begin{pgfscope}
\clip(-2,-2) rectangle (2,2);
\begin{scope}[shift={(.5,.5)}]
\draw[densely dotted] (-3,-3) grid (3,3);
\end{scope}
\draw[fill] (1,0) circle (1.5pt) node[right]
     {e};
\draw[fill] (0,1) circle (1.5pt) node[above left]
     {n};
\draw[fill] (1,1) circle (1.5pt) node[above right]
     {ne};
\draw[fill] (1,-1) circle (1.5pt) node[below right]
     {se};
\draw[thick,->] (0,0) -- (1,0);
\draw[thick,->] (0,0) -- (0,1);
\draw[thick,->] (0,0) -- (1,1);
\draw[thick,->] (0,0) -- (1,-1);
\draw[fill] (-1,0) circle (1.5pt) node[left]
     {w};
\draw[fill] (0,-1) circle (1.5pt) node[below right]
     {s};
\draw[fill] (-1,-1) circle (1.5pt) node[below left]
     {sw};
\draw[fill] (-1,1) circle (1.5pt) node[above left]
     {nw};
\draw[dashed,->] (0,0) -- (-1,-0);
\draw[dashed,->] (0,0) -- (-0,-1);
\draw[dashed,->] (0,0) -- (-1,-1);
\draw[dashed,->] (0,0) -- (-1, 1);
\end{pgfscope}

\node at (3,0) {\Large$\Rightarrow$};

\begin{pgfscope}
\begin{scope}[xshift=6cm]
\clip (-1.9,-1.9) rectangle (1.9,1.9);
\fill[gray] (-2,-2) rectangle (2,2);
\draw[step=0.5cm,line width=3pt,white]  (-2,-2) grid (2,2);
\draw[step=0.5cm,black]                 (-2,-2) grid (2,2);
\end{scope}
\end{pgfscope}
\end{tikzpicture}