Change grid line dash pattern such that grid intersections look uniform

Question

We can set the appearance of the grid like follows:

\pgfplotsset{
  grid style = {
    dash pattern = on 0.05mm off 1mm,
    line cap = round,
    black,
    line width = 0.5pt
  }
}

The result may look like this:

At the intersection of the x- and y-grid-lines, this looks not very nice. What I like to see is somewhat like this (only recognize how the dash pattern is chosen differently in x- and y-direction to fit nicely):

This will produce somewhat like the first image:

\documentclass[a4paper,10pt]{scrartcl}
\usepackage[greek,english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{pgfplots}

\pgfplotsset{
  grid style = {
    dash pattern = on 0.05mm off 1mm,
    line cap = round,
    black,
    line width = 0.5pt
  }
}

\begin{document}

\begin{tikzpicture}
\begin{axis}[grid = major]
\addplot[color=red,mark=x] coordinates {
(2,-2.8559703)
(3,-3.5301677)
(4,-4.3050655)
(5,-5.1413136)
(6,-6.0322865)
(7,-6.9675052)
(8,-7.9377747)
};
\end{axis}
\end{tikzpicture}

\end{document}

Answer 1

One way to do this is to explicitly set the unit vector length of the plot to an integer multiple of the dash pattern period. If additionally the left and bottom bounds of the plot are set to a value corresponding to an integer multiple of the dash pattern period, the dash pattern will line up at the intersections:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\pgfplotsset{
  grid style = {
    dash pattern = on 0.025mm off 0.95mm on 0.025mm off 0mm, % start with half a dot to get correct centering of the pattern
    line cap = round,
    black,
    line width = 0.5pt
  }
}

\begin{document}

\begin{tikzpicture}
\begin{axis}[grid = major, xmin=2.2, ymin=-8.2, x=10mm, y=10mm]
\addplot[color=red,mark=x] coordinates {
(2,-2.8559703)
(3,-3.5301677)
(4,-4.3050655)
(5,-5.1413136)
(6,-6.0322865)
(7,-6.9675052)
(8,-7.9377747)
};
\end{axis}
\end{tikzpicture}

\end{document}