Staggered ToC Dots (KOMA-Script)

Question

This question illustrates what I'm trying to achieve: Dots in table of contents as on a chess-board

Notice that each row of dots is offset, creating a Chinese Checkers board-like pattern.

However I've tried it, and am having trouble achieving it. Is there a relatively simple way of doing this with KOMA-Script classes?

Answer 1

I found the answer in the TeXbook source code (I hope this is not a violation of copyright, as the information is publicly available. If it is I will immediately remove my answer). I'm still dissecting how it works and learning TeX, so if anyone is willing to help explain that would be great.

\documentclass{scrartcl}

% from TeXbook source: 
%  https://ctan.org/pkg/texbook?lang=en
%   /systems/knuth/dist/tex/texbook.tex

\countdef\counter=255  % define a new counter at register 255
\def\diamondleaders{\global\advance\counter by 1  % increment above counter every time this command is called
    \ifodd\counter \kern-10pt \fi  % says how far away initial dot can be, adds offset to kern (horizontal space) (?)
    \leaders\hbox to 20pt{\ifodd\counter \kern13pt \else\kern3pt \fi  % define a leader, still learning how these work
        .\hss}\hfil}  % hf
    %                ^(distance between dots)   ^  these show the ^ relative displacement between the two ??
    % from toying with the settings, I've found that adjusting 13 and 3 to the same value makes the dots a square grid
    % I assume the 20pt is the spacing between the dots, and the 13 / 3 is some additional displacement if odd of even


\RedeclareSectionCommand[toclinefill=\diamondleaders]{section}% can repeat this for sub, subsub, etc.


\begin{document}    
    \tableofcontents
    \section{Alpha}
    \section{Beta}
    \section{Gamma}
    \section{Delta}
\end{document}