Drawing of "dotted" yz-plane in tikz

Question

I am trying to draw my first picture in tikz and I need a small help with the following. I want to draw a family of "surfaces" that consists of all the planes parallel to yz-plane, and all the individual points on the yz-plane. I drew the planes but am struggling with the points. So what I need is to fill the yz-plane with dots. Could you give me a help to fill this gap?

Below I put my code so far:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\coordinate (O) at (0, 0, 0);
\draw[line width=0.3mm,->] (0,0,0) -- (4,0,0) node[anchor=north east]{$y$};     
\draw[line width=0.3mm,->] (0,0,0) -- (0,4,0) node[anchor=north east]{$z$};     
\draw[line width=0.3mm,->] (0,0,0) -- (0,0,7) node[anchor=east]{$x$};
\filldraw[color=blue!10!white,opacity=0.8] (0, 0, 2) -- (0, 3.5, 2) -- (2, 3.5, 2) --   (2, 0, 2) -- cycle;
\draw  (0, 0, 2) -- (0, 3.5, 2) -- (2, 3.5, 2) --   (2, 0, 2) -- cycle;
\filldraw[color=blue!10!white,opacity=0.8] (0, 0, 2.5) -- (0, 3.5, 2.5) -- (2, 3.5, 2.5) --   (2, 0, 2.5) -- cycle;
\draw  (0, 0, 2.5) -- (0, 3.5, 2.5) -- (2, 3.5, 2.5) --   (2, 0, 2.5) -- cycle;
\filldraw[color=blue!10!white,opacity=0.8] (0, 0, 3) -- (0, 3.5, 3) -- (2, 3.5, 3) --   (2, 0, 3) -- cycle;
\draw  (0, 0, 3) -- (0, 3.5, 3) -- (2, 3.5, 3) --   (2, 0, 3) -- cycle;
\filldraw[color=blue!10!white,opacity=0.8] (0, 0, 3.5) -- (0, 3.5, 3.5) -- (2, 3.5, 3.5) --   (2, 0, 3.5) -- cycle;
\draw  (0, 0, 3.5) -- (0, 3.5, 3.5) -- (2, 3.5, 3.5) --   (2, 0, 3.5) -- cycle;
\filldraw[color=blue!10!white,opacity=0.8] (0, 0, 4) -- (0, 3.5, 4) -- (2, 3.5, 4) --   (2, 0, 4) -- cycle;
\draw  (0, 0, 4) -- (0, 3.5, 4) -- (2, 3.5, 4) --   (2, 0, 4) -- cycle;
\filldraw[color=blue!10!white,opacity=0.8] (0, 0, 4.5) -- (0, 3.5, 4.5) -- (2, 3.5, 4.5) --   (2, 0, 4.5) -- cycle;
\draw  (0, 0, 4.5) -- (0, 3.5, 4.5) -- (2, 3.5, 4.5) --   (2, 0, 4.5) -- cycle;
\filldraw[color=blue!10!white,opacity=0.8] (0, 0, 5) -- (0, 3.5, 5) -- (2, 3.5, 5) --   (2, 0, 5) -- cycle;
\draw  (0, 0, 5) -- (0, 3.5, 5) -- (2, 3.5, 5) --   (2, 0, 5) -- cycle;
\filldraw[color=blue!10!white,opacity=0.8] (0, 0, 5.5) -- (0, 3.5, 5.5) -- (2, 3.5, 5.5) --   (2, 0, 5.5) -- cycle;
\draw  (0, 0, 5.5) -- (0, 3.5, 5.5) -- (2, 3.5, 5.5) --   (2, 0, 5.5) -- cycle;
\end{tikzpicture}
\end{document}

Thanks in advance!

Answer 1

I made a command \plane for the redundancies to shorten the code and added a dotted plane at x=0, using the tikzlibrary patterns and the option pattern=dots.

Note: I use \draw[fill=<color>] to draw the black border and also the filling with one command. Besides you can use rectangle to draw a rectangle between two points.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{patterns}

\begin{document}

\newcommand{\plane}[2][fill=blue!10!white]{
    \draw[opacity=0.8,#1] (0, 0, #2) rectangle (2, 3.5, #2);
}

\begin{tikzpicture}
    \coordinate (O) at (0, 0, 0);
    \draw[line width=0.3mm,->] (O) --++ (4,0,0) node[anchor=north east]{$y$};     
    \draw[line width=0.3mm,->] (O) --++ (0,4,0) node[anchor=north east]{$z$};     
    \draw[line width=0.3mm,->] (O) --++ (0,0,7) node[anchor=east]{$x$};

    \plane[draw=none,pattern=dots]{0};

    \foreach \x in {2,2.5,...,5.5}
        \plane{\x};
\end{tikzpicture}

\end{document}

Answer 2

let me convert my comment to an answer ... some how similar to dexteritas answer:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{patterns}

\usepackage[active,tightpage]{preview}% only for test
\PreviewEnvironment{tikzpicture}
    \setlength\PreviewBorder{1em}


\begin{document}
    \begin{tikzpicture}[L/.append style={line width=0.3mm,->}]
\coordinate (O) at (0, 0, 0);
\draw[L] (O) --++ (4,0,0) node[below left] {$y$};
\draw[L] (O) --++ (0,4,0) node[below left] {$z$};
\draw[L] (O) --++ (0,0,7) node[left]       {$x$};
%
\fill[pattern=dots] (O) |- (2, 3.5, 0) |- cycle;
%
\foreach \x in {2,2.5,...,5.5}
    \draw[fill=blue!10!white,opacity=0.6] (0,0,\x) |- (2,3.5,\x) |- cycle;
    \end{tikzpicture}
\end{document}