Not exactly an answer to the question, but it is fun.
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{backgrounds}
\begin{document}
\begin{tikzpicture}
\draw[yellow,yslant=0.5] (0,0) rectangle (2,2);
\node[yslant=0.5,anchor=center,opacity=0.3] at (1,1.5) {\includegraphics[width=2cm,height=2cm]{example-image-a}};
\draw[magenta,yslant=-0.5] (-2,2) rectangle (0,0);
\node[yslant=-0.5,anchor=center,opacity=0.3] at (-1,1.5) {\includegraphics[width=2cm,height=2cm]{example-image-b}};
\begin{scope}[on background layer]
\draw[orange,yslant=-0.5] (0,2) rectangle (2,4);
\node[yslant=-0.5,anchor=center,xshift=0cm,yshift=1cm,opacity=0.3] at (1,1.5) {\includegraphics[width=2cm,height=2cm]{example-image-b}};
\draw[green,yslant=0.5,,xshift=-2cm,yshift=2cm] (0,0) rectangle (2,2);
\node[yslant=0.5,anchor=center,xshift=-2cm,yshift=2cm,opacity=0.3] at (1,1.5) {\includegraphics[width=2cm,height=2cm]{example-image-a}};
\draw[blue,yslant=-0.5,xslant=1] (-2,0) rectangle (0,2);
\node[yslant=-0.5,anchor=center,xshift=0cm,yshift=2cm,xslant=1,opacity=0.3] at (-0,-1) {\includegraphics[width=2cm,height=2cm]{example-image-a}};
\end{scope}
\draw[red,yslant=-0.5,xslant=1] (-4,2) rectangle (-2,4);
\node[yslant=-0.5,anchor=center,xshift=0cm,yshift=4cm,xslant=1,opacity=0.3] at (-0,-1) {\includegraphics[width=2cm,height=2cm]{example-image-a}};
\end{tikzpicture}
\end{document}

A brute-force attempt with pgfplots
: there are surely better ways. :-)
The "coarseness" of the texture can be adjusted using the samples
key value. For this fine of a texture, LuaLaTeX must be used (dynamic memory allocation). For samples=100
or fewer, any modern engine can be used.
\IfFileExists{luatex85.sty}{%
\RequirePackage{luatex85}%
}{}
\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
view={0}{90},
hide axis=true,
samples=200,
colormap={papyrus}{
cmyk(0cm)=(0.00,0.08,0.24,0);
cmyk(1cm)=(0.00,0.08,0.24,0.05)
},
]
\addplot3[surf,shader=interp] {rand};
\end{axis}
\end{tikzpicture}
\end{document}

Best Answer
It takes ages.