How can I plot sin(1/x) with a logarithmic x-axis?

Question

I would like to plot the function f(x) = sin(1/x) and it should look like this. I get this so far:

You might notice, that my image doesn't look as good as the linked one because of the axis.

How can I get a logarithmic axis for my plot?

Why does it currently produce an error with a logarithmic axis?

\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}

\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{arrows, positioning, calc, intersections}

\begin{document}

\begin{preview}
\begin{tikzpicture}
    \begin{axis}[
    axis x line=middle,
    axis y line=middle,
        width=15cm, height=15cm,     % size of the image
        grid = major,
        grid style={dashed, gray!30},
        %xmode=log,log basis x=10, % <- doesn't work:
        % ! Missing number, treated as zero.
        % <to be read again> 
        %                    p
        % l.33 ..., red, thick,samples=500] {sin(deg(1/x))};
        %                                                   
        % ? 
        % ! Emergency stop.
        % <to be read again> 
        %                    p
        % l.33 ..., red, thick,samples=500] {sin(deg(1/x))};
        %                                                   
        % !  ==> Fatal error occurred, no output PDF file produced!
        %ymode=log,log basis y=10,
        xmin=-0.7000, % start the diagram at this x-coordinate
        xmax=-0.0062, % end   the diagram at this x-coordinate
        ymin=-1,      % start the diagram at this y-coordinate
        ymax= 1,      % end   the diagram at this y-coordinate
        axis background/.style={fill=white},
        ylabel=y,
        xlabel=x,
        %xticklabels={,,},
        %yticklabels={,,},
        tick align=outside,
        tension=0.08]
      \addplot[domain=-0.700:-0.0062, red, thick,samples=500] {sin(deg(1/x))};
    \end{axis} 
\end{tikzpicture}
\end{preview}
\end{document}

If you plot it with a logarithmic y-axis it looks ... hmm ... lets call it interesting.

The latest LaTeX-Code of this plot can be found on GitHub.

Answer 1

The problem is that the logarithm isn't real for negative numbers, so you'll have to use some trickery: Plot the function for the positive domain, but flip the direction of the x axis and the sign of the tick labels:

\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}

\usepackage{pgfplots}
\pgfplotsset{compat=1.6}

\begin{document}

\begin{preview}
\begin{tikzpicture}
    \begin{axis}[
        xmode=log, % Logarithmic x axis
        xmin=0.01, xmax=1, % Positive domain...
        x dir=reverse, % ... but increasing to the left
        xticklabel=\pgfmathparse{-exp(\tick)}\pgfmathprintnumber{\pgfmathresult}, % Reverse the sign of the labels
        xticklabel style={/pgf/number format/.cd,fixed}, % Use fixed point notation
        width=15cm, height=8cm,     % size of the image
        grid = major,
        grid style={gray!30},
        ymin=-1,      % start the diagram at this y-coordinate
        ymax= 1,      % end   the diagram at this y-coordinate
        axis background/.style={fill=white},
        ylabel=y,
        xlabel=x,
        tick align=outside
     ]
      \addplot[domain=0.01:1, red, thick,samples=2000] {-sin(deg(1/(x)))};
    \end{axis} 
\end{tikzpicture}
\end{preview}
\end{document}

Answer 2

run with xelatex

\documentclass{article}
\usepackage{pst-plot}
\pagestyle{empty}
\begin{document}

\psset{xunit=10,yunit=3}
\begin{pspicture}(0.05,-1.1)(-1.05,1.1)
    \psaxes[axesstyle=frame,ticksize=0 5pt,Dx=0.2,Dy=0.5,ylabelPos=right]{->}(0,0)(0,-1.25)(-1.1,1.25)[$\log(x)$,180][$sin(1/\log(x))$,90]
    \psplot[plotpoints=10000,linecolor=red,algebraic]{-0.1}{-0.001}{sin(1/(log(1-x)))} 
    \psplot[plotpoints=1000,linecolor=red,algebraic]{-0.99}{-0.1}{sin(1/(log(1-x)))} 
\end{pspicture}

\end{document}