%https://tex.stackexchange.com/a/356984/2288

\documentclass{article}

\usepackage{pgfplots}
\usepackage{siunitx}

\usepackage[
a4paper , margin = 10 mm ,
]{geometry}

\begin{document}
\centering

\pagestyle{empty}



% http://tex.stackexchange.com/a/15002/100384
\newcommand*{\getlength}[2]{%
   % Convert to `cm` and round to two fractional digits:
   \pgfmathsetmacro#1{round(0.0351459804*#2)}%
}

\rotatebox{90}{
    \begin{tikzpicture}
        % a factor for measures, since pfplots produces slightly bigger images than defined
        %   in width/height. This can be used to adjust that problem manually
        \pgfmathsetmacro{\factor}{0.90}

        % we will need some length in `cm`, without units, and rounded
        \getlength{\yMax}{\factor*\textwidth}
        \getlength{\xMax}{\factor*\textheight}

        \begin{axis}[
            set layers,
            width=\factor\textheight, height=\factor\textwidth,
            x = 1cm, y = 1cm,
            %axis lines = middle,
            %xlabel = {t\lbrack\si{\second}\rbrack},
            %ylabel = {x\lbrack\si{\metre}\rbrack},
            %x label style = {anchor = north west, font = \scriptsize},
            %y label style = {anchor = north east, font = \scriptsize, shift={(0,0.5cm)}},
            %xtick={0,1,...,\xMax},
            %ytick={0,1,...,\yMax},
            minor xtick={0,0.1,0.2,...,\xMax},
            minor ytick={0,0.1,0.2,...,\yMax},
            tick style = {line width = 0.6pt, black!40!white},
            minor tick style = {draw = none},
            ticklabel style = {draw = none},
            xticklabels=\empty,
            yticklabels=\empty,
            axis line style = {-latex},
            grid = both,
            minor grid style={line width=0.3pt, black!40!white},
            grid style={line width=0.6pt, black!40!white},
            ymin=0, ymax=\yMax,
            xmin=0, xmax=\xMax,
            ]

            % now manually draw the 0.5cm grid on the grid layer
            \begin{pgfonlayer}{axis grid}
                \draw[line width=0.45pt, step=0.5cm, black!40!white] (axis cs: 0, 0) grid (axis cs: \xMax, \yMax);
            \end{pgfonlayer}
        \end{axis}
    \end{tikzpicture}
}

\end{document}