How to emulate datavisualization's clean scientific axes in pgfplots

Question

I really like the "clean" scientific axes generated by TikZ' datavisualization library. However, since it provides quite a bit more plotting functionality, I want to give pgfplots a shot. How can i emulate datavisualizations's scientific axes=clean style in pgfplots?

---

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{datavisualization.formats.functions}

\usepackage{pgfplots}
\pgfmathsetlengthmacro\axisdefaultwidth{5cm}
\pgfmathsetlengthmacro\axisdefaultheight{\axisdefaultwidth * (sqrt(5) - 1) / 2}
\pgfplotsset{
  compat=1.17,
  scale only axis,
}

\begin{document}

With Ti\emph kZ:
\vskip 1ex
\begin{tikzpicture}
  \datavisualization [
      scientific axes=clean,
      visualize as line,
    ]
  data [format=function] {
      var x : interval [-1.5:1.5] samples 7;
      func y = \value x*\value x;
    };
\end{tikzpicture}

\vskip 4ex

With \textsc{pgfplots}:
\vskip 1ex
\begin{tikzpicture}
  \begin{axis}
    \addplot [
        domain=-1.5:1.5,
        samples=7,
      ] {x^2};
  \end{axis}
\end{tikzpicture}

\end{document}

Answer 1

It just amounts to adding some keys. Using

    axis lines=left,
    axis x line shift=1em,
    axis y line shift=1em,
    axis line style={-,very thin},
    axis background/.style={draw,ultra thin,gray},
    tick align=outside,
    xtick distance=0.5,
    ytick distance=0.5,

comes very close IMHO.

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{datavisualization.formats.functions}

\usepackage{pgfplots}
\pgfmathsetlengthmacro\axisdefaultwidth{5cm}
\pgfmathsetlengthmacro\axisdefaultheight{\axisdefaultwidth * (sqrt(5) - 1) / 2}
\pgfplotsset{
  compat=1.17,
  scale only axis,
}

\begin{document}

With Ti\emph kZ:
\vskip 2ex
\begin{tikzpicture}
  \datavisualization [
      scientific axes=clean,
      visualize as line,
    ]
  data [format=function] {
      var x : interval [-1.5:1.5] samples 7;
      func y = \value x*\value x;
    };
\end{tikzpicture}

\vskip 4ex

With \textsc{pgfplots}:
\vskip 2ex
\begin{tikzpicture}
  \begin{axis}[axis lines=left,
        axis x line shift=1em,
        axis y line shift=1em,
        axis line style={-,very thin},
        axis background/.style={draw,ultra thin,gray},
        tick align=outside,
        xtick distance=0.5,
        ytick distance=0.5,
        ]
    \addplot [
        domain=-1.5:1.5,
        samples=7,
      ] {x^2};
  \end{axis}
\end{tikzpicture}

\end{document}

Needless to say that you can change the size of the plot, and combined the above keys to a style.

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{datavisualization.formats.functions}

\usepackage{pgfplots}
\pgfmathsetlengthmacro\axisdefaultwidth{5cm}
\pgfmathsetlengthmacro\axisdefaultheight{\axisdefaultwidth * (sqrt(5) - 1) / 2}
\pgfplotsset{
  compat=1.17,
  scale only axis,
}

\begin{document}

With Ti\emph kZ:
\vskip 2ex
\begin{tikzpicture}
  \datavisualization [
      scientific axes=clean,
      visualize as line,
    ]
  data [format=function] {
      var x : interval [-1.5:1.5] samples 7;
      func y = \value x*\value x;
    };
\end{tikzpicture}

\vskip 4ex

With \textsc{pgfplots}:
\pgfplotsset{mimick datavisualization/.style={axis lines=left,
        axis x line shift=1em,
        axis y line shift=1em,
        axis line style={-,very thin},
        axis background/.style={draw,ultra thin,gray},
        tick align=outside,
        xtick distance=0.5,
        ytick distance=0.5,
        major tick length=2pt}}
\vskip 2ex
\begin{tikzpicture}
  \begin{axis}[mimick datavisualization,unit vector ratio=1 1 1,
    xmin=-1.5,xmax=1.5,width=5.6cm]
    \addplot [semithick,
        domain=-1.5:1.5,
        samples=7,
      ] {x^2};
  \end{axis}
\end{tikzpicture}
\end{document}