% light gray color
\definecolor{lightgray}{gray}{0.7}

% a grid with starting from #1 mesh #2 of width #3*#2 and height #4*#2
\def\grid#1#2#3#4{
  % vertical lines
  \foreach\i in{0,...,#3}{
    \draw[color=lightgray]#1++(\i*#2,0)--++(0,#4*#2);
  }
  % horizontal lines
  \foreach\j in{0,...,#4}{
    \draw[color=lightgray]#1++(0,\j*#2)--++(#3*#2,0);
  }
}

% a square centered at #1 of side #2
\def\square#1#2{
  \draw#1++(-0.5*#2,-0.5*#2)--++(#2,0)--++(0,#2)--++(-#2,0)--cycle;
}

% fill a square centered at #1 of side #2 and color #3
\def\fillsquare#1#2#3{
  \fill[color=#3]#1++(-0.5*#2,-0.5*#2)--++(#2,0)--++(0,#2)--++(-#2,0)--cycle;
}