\centering\begin{tikzpicture}[x=12pt,y=12pt]
{
\def\cell(#1,#2);{
\draw[fill=gray](#1,#2) rectangle +(1,1);
\draw[pattern=crosshatch, pattern color=gray] (#1,#2)++(0,1) rectangle +(1,1);
\draw[pattern=north west lines, pattern color=gray] (#1,#2)++(-2,0) rectangle +(1,1);
\draw[thick,->] (#1,#2)++(0.5,0.5) -- ++(0,0.8);
\draw[thick,->] (#1,#2)++(0.5,0.5) -- ++(-1.8,0);
}
\draw[step=1] (-1.5,0.5) grid (5.5,6.5);
\cell(1,1);
\cell(2,2);
\cell(3,3);
\cell(4,4);
}
\end{tikzpicture}