\documentclass{standalone}
\usepackage{tikz}
\usepackage{grid}

\begin{document}
\begin{tikzpicture}

% the positions of the smoothing cubes
\def\smoothingsquares{(0,0),(4,4),(-4,0),(-4,4),(-8,4),(-4,8),(0,12),(4,8),(12,12),(12,8),(16,4)}
% the positions of the bad cubes
\def\badsquares{(-0.5,0),(-1.5,0),(-2,0),(-0.5,0.5),(-1.5,0.5),(-2,0.5),(-7,4.5),(-7,5.5),(-6,4.5),(-6,5.5),(-5.5,5.5),(-5.5,5),(-5,7.5),(-5.5,7.5),(-5.5,8),(-5,8),(0,10.5),(-0.5,10.5),(0,11),(-0.5,11),(3.5,5.5),(4,5.5),(4,6),(3.5,6),(10.5,8.5),(10.5,9.5),(10.5,10.5),(10.5,11.5),(10.5,12),(11.5,12),(12.5,12),(12.5,11),(12.5,10),(12,9),(11.5,8.5),(12,9.5),(15,4),(16,4),(16,3),(15,3)}

% first fill the smearings
\foreach\pos in\smoothingsquares{
  \fillsquare{\pos}5{blue}
}

% fill the smoothing cubes
\foreach\pos in\smoothingsquares{
  \fillsquare{\pos}4{gray}
}
% fill the bad cubes
\foreach\pos in\badsquares{
  \fillsquare{\pos}{1}{green}
}

% draw grid
\grid{(-11,-3)}{0.5}{60}{36}

% stroke the smoothing squares
\foreach\pos in\smoothingsquares{
  \square{\pos}4
}

\end{tikzpicture}
\end{document}