I am certainly lacking of knowledge on graph theory, computing, optimization or probably just geometry ! But just asking the brains here if a solution to the problem in title exists (without external programs?). And if not, what would be the next step(s) to automate harmonious mindmaps ?
Sequence of answers so far
Based on multiple questions on mindmaps shape automation (growcyclic circle-shape-for-level-4-or-5, circle-shape-for-level-3, nodes-alongside-a-rectangle ), Schrodinger's cat gave multiple variations on the topic and produced multiple, complex growing functions. With 2 compilations, they are automatically calculating the number of nodes at each level and adapt automatically the sibling angles based on 360/number of nodes on that level.
What works
As mentioned in a previous post, when the Mindmaps are well balanced (with a relatively equal number of nodes and children), the growing function works well and reaches the fantastic objective of focusing on content, and not so much on the organization of the nodes (wasn't it one of the original target of TeX ?).
What worked less...
The problem comes from unbalanced mindmaps with for instance level 2 without level 3 or 4. The nodes look twisted and feel like watchmaking mechanisms where you'd like to shift level 2 by clockwise X% and level 3 counterclockwise by Y% (as below) to make things nicer.
Conclusion so far (by Schrodinger's cat)
"Progress is more if someone provides a concrete idea (a specific algorithm, say) which one can build on. There are many possible modifications of the above one can explore. One particular promising one may be to marry the mindmap story to graph drawing algorithms."
I ran the following code (based on shape-for-level-4-or-5 to have an idea of the shape in limit cases and I get a strange behaviour with distance between nodes (and ever weirder without [clockwise from=0], I hardcoded the sibling angles, I cannot adapt the level distance)
\documentclass[tikz,border=9]{standalone}
\usetikzlibrary{mindmap,decorations}
\makeatletter
\newcount\tikzcountchildi
\newcount\tikzcountchildii
\newcount\tikzcountchildiii
\newcount\tikzcountchildiv
\newcount\tikzcountchildv
\newcount\tikzcountchildvi
\tikzset{garlic growth/.style={growth function=\tikz@grow@garlic,
/tikz/mmap/name=#1,mmap/#1/.is family,
mmap/initialize counts,
execute at end scope={%
\tikz@mmap@store@aux{n-i}{\the\tikzcountchildi}%
\tikz@mmap@store@aux{n-ii}{\the\tikzcountchildii}%
\tikz@mmap@store@aux{n-iii}{\the\tikzcountchildiii}%
\tikz@mmap@store@aux{n-iv}{\the\tikzcountchildiv}%
\tikz@mmap@store@aux{n-v}{\the\tikzcountchildv}%
\tikz@mmap@store@aux{n-vi}{\the\tikzcountchildvi}}},
mmap/.cd,initialize counts/.code={\tikzcountchildi=0%
\tikzcountchildii=0%
\tikzcountchildiii=0%
\tikzcountchildiv=0%
\tikzcountchildv=0%
\tikzcountchildvi=0%
}
}
\def\tikz@mmap@store@aux#1#2{%
\immediate\write\@mainaux{\string\expandafter\xdef\noexpand\csname pgfk@/tikz/mmap/\pgfkeysvalueof{/tikz/mmap/name}/#1\string\endcsname{#2}}}%
\def\tikz@mmap@get@from@aux#1#2{%
\ifcsname pgfk@/tikz/mmap/\pgfkeysvalueof{/tikz/mmap/name}/#1\endcsname
\edef#2{\csname pgfk@/tikz/mmap/\pgfkeysvalueof{/tikz/mmap/name}/#1\endcsname}%
\else
\edef#2{0}%
\fi
}
\newcount\tikzcountgrandchild
\def\tikz@grow@garlic{%
\pgfmathsetmacro{\pgfutil@tempa}{\pgfkeysvalueof{/tikz/mmap/overall rotation}}%
\ifcase\tikztreelevel
\or
\global\advance\tikzcountchildi by1\relax%
\tikz@mmap@get@from@aux{n-i}{\myni}%
\tikz@mmap@get@from@aux{n-ii}{\mynii}%
\tikz@mmap@get@from@aux{n-1-\the\tikzcountchildi}{\mynall}%
\tikz@mmap@get@from@aux{p-1-\the\tikzcountchildi}{\mypi}%
\ifnum\mynii>0
\pgfmathsetmacro{\pgfutil@tempa}{\pgfutil@tempa+\pgfkeysvalueof{/tikz/mmap/sign}%
*(\pgfkeysvalueof{/tikz/mmap/child weight}*(\mypi)*360/\mynii+%
(1-\pgfkeysvalueof{/tikz/mmap/child weight})*(\tikzcountchildi-1)*360/\myni)}%
\fi
\or
\global\advance\tikzcountchildii by1\relax%
\tikz@mmap@get@from@aux{n-ii}{\mynii}%
\tikz@mmap@get@from@aux{n-1-1}{\mynall}%
\ifnum\mynii>0
\pgfmathsetmacro{\pgfutil@tempa}{\pgfutil@tempa+\pgfkeysvalueof{/tikz/mmap/sign}%
*(\tikzcountchildii-1-\mynall/2)*360/\mynii}%
\fi
\ifnum\tikznumberofcurrentchild=1\relax
\tikz@mmap@store@aux{n-1-\the\tikzcountchildi}{\the\tikznumberofchildren}%
\tikz@mmap@store@aux{p-1-\the\tikzcountchildi}{\the\numexpr\tikzcountchildii-1}%
\tikz@mmap@store@aux{a-1-\the\tikzcountchildi-\the\tikzcountchildii}{\pgfutil@tempa}%
\fi
\or
\global\advance\tikzcountchildiii by1\relax%
\ifnum\tikznumberofcurrentchild=1\relax
\tikz@mmap@store@aux{n-1-\the\tikzcountchildi-\the\tikzcountchildii}{\the\tikznumberofchildren}%
\tikz@mmap@store@aux{p-1-\the\tikzcountchildi-\the\tikzcountchildii}{\the\numexpr\tikzcountchildiii-1}%
\fi
\tikz@mmap@get@from@aux{n-iii}{\myniii}%
\tikz@mmap@get@from@aux{a-1-1-1}{\bettera}%
\tikz@mmap@get@from@aux{n-1-1-1}{\mynall}%
\ifdim\bettera pt=0pt\relax
\else
\pgfmathsetmacro{\pgfutil@tempa}{\bettera}%
\fi
\ifnum\myniii>0
\pgfmathsetmacro{\pgfutil@tempa}{\pgfutil@tempa+\pgfkeysvalueof{/tikz/mmap/sign}%
*(\tikzcountchildiii-1-\mynall/2)*360/\myniii}%
\fi
\or
\global\advance\tikzcountchildiv by1\relax%
\tikz@mmap@get@from@aux{n-iv}{\myniv}%
\ifnum\myniv>0
\pgfmathsetmacro{\pgfutil@tempa}{\pgfutil@tempa+\pgfkeysvalueof{/tikz/mmap/sign}*(\tikzcountchildiv-1)*360/\myniv}%
\fi
\or
\tikz@mmap@get@from@aux{n-v}{\mynv}%
\pgfmathsetmacro{\pgfutil@tempa}{\pgfutil@tempa+\pgfkeysvalueof{/tikz/mmap/sign}*(\tikzcountchildv-1)*360/\mynv}%
\ifnum\mynv>0
\global\advance\tikzcountchildv by1\relax%
\fi
\or
\global\advance\tikzcountchildvi by1\relax%
\tikz@mmap@get@from@aux{n-vi}{\mynvi}%
\ifnum\myvi>0
\pgfmathsetmacro{\pgfutil@tempa}{\pgfutil@tempa+(\tikzcountchildvi-1)*360/\mynvi}%
\fi
\fi
\pgftransformreset%
\pgftransformshift{\pgfpoint{\pgfkeysvalueof{/tikz/mmap/overall xshift}}%
{\pgfkeysvalueof{/tikz/mmap/overall yshift}}}%
\pgftransformrotate{\pgfutil@tempa}%
\pgftransformxshift{\the\tikzleveldistance}%
}
\makeatother
\begin{document}
\tikzset{mmap/.cd,
name/.initial=undef,
overall rotation/.initial=00,
overall xshift/.initial=0pt,
overall yshift/.initial=0pt,
sign/.initial=1,
child weight/.initial=0,
/tikz/.cd,
Xshift/.style={xshift=#1,mmap/overall xshift=#1},
Yshift/.style={yshift=#1,mmap/overall yshift=#1},
branch color/.style={
concept color=#1!80,ball color=#1!50,
every child/.append style={concept color=#1!50},
}
}
\begin{tikzpicture}
\begin{scope}[
mindmap,garlic growth=A,
mmap/child weight=0,
mmap/overall rotation=00,
mmap/sign=-1,
root concept/.append style={ball color=blue!50, line width=1.5ex,text=red!80!black,font=\Large\bfseries\scshape,minimum size=2.5cm,text width=2.5cm,},
nodes={concept,align=center, text width=2cm,inner sep=1mm,minimum size=1.0cm,execute at begin node=\hskip0pt},
concept color=blue!50!black,
level 1/.style={nodes=concept,
every child/.append style={concept color=blue!90},
level distance=4cm,
},
level 2/.style={%opacity=0,
% nodes=concept,
every child/.append style={concept color=blue!70},
level distance=8cm,
% minimum size=1.0cm
},
level 3/.style={%opacity=0,
% nodes=concept,
every child/.append style={concept color=blue!50},
level distance=12cm,
% minimum size=1.0cm,
},
level 4/.style={%opacity=0,
% nodes=concept,
every child/.append style={concept color=blue!30},
level distance=14cm,
% minimum size=1.0cm,text width=1.0cm
}
level 5/.style={%opacity=0,
nodes=concept,
% every child/.append style={concept color=white},
level distance=16cm,
% minimum size=1.0cm,text width=1.0cm
}
]
\node [root concept]{}
child foreach \A in {1,2,3,4}{
node[] {\A}
child foreach \B in {1,2,3}{
node[] { \A-\B}
child foreach \C in {1,2,3}{
node { \A-\B-\C}
child[clockwise from=0,sibling angle=10] foreach \D in {1,2}{
node {\A-\B-\C-\D}
child[clockwise from=0,sibling angle=10] foreach \E in {1,2}{
node {\footnotesize \A-\B-\C-\D-\E}
}
}
}
}
};
\end{scope}
\end{tikzpicture}
\end{document}
