Mindmaps, method to get regular circle shape for level 4 or 5

Question

I'm new on LaTeX and I started to learn it especially to design mindmap thing. My aim is to synthesize a math course with many concepts (like 40 theorems) on a mindmap able to reach level 4, 5 or 6 while optimizing its size. I did many researches and I found this topic : Mindmaps, general method to get regular/harmonious circle shape for level 3 and more

Besides, I don't find the code that allowed the author to create this beautiful mindmap. I took and modify the last piece of code of the article, made by another person, which works with the level 3 but I have some issues with the level 4, here is my code :

\documentclass[tikz,border=2]{standalone}
\usetikzlibrary{mindmap, decorations.pathmorphing}

\makeatletter
\newcount\tikz@count@leaf % count only leaf
\def\tikz@grow@concentric{
    \pgftransformreset%
    \pgftransformshift{\pgfpoint
        {\pgfkeysvalueof{/tikz/smuggle xshift}}
        {\pgfkeysvalueof{/tikz/smuggle yshift}}}
    \pgftransformrotate{
        \pgfkeysvalueof{/tikz/smuggle rotation}+
        (\pgfkeysvalueof{/tikz/sibling angle})*(\tikz@count@leaf)}
    \ifnum\pgfkeysvalueof{/tikz/nold}=0
        % this is a leaf
        \global\advance\tikz@count@leaf by1
    \else
        % this is not a leaf
        % we need to rotate it further
        \pgftransformrotate{
            (\pgfkeysvalueof{/tikz/sibling angle})*
            (\pgfkeysvalueof{/tikz/nold}-1)/2}
        \tikzset{nold/.initial=0} % reset for safty
    \fi
    \pgftransformxshift{\the\tikzleveldistance}
}

\begin{document}
\tikzset{
    smuggle rotation/.initial=0,
    smuggle xshift/.initial=0pt,
    smuggle yshift/.initial=0pt,
    Xshift/.style={xshift=#1,smuggle xshift=#1},
    Yshift/.style={yshift=#1,smuggle yshift=#1},
    Rotate/.style={smuggle rotate=#1},
    nold/.initial=0, % hint tikz the number of leaf in its descendants
    % explain: don't count a child if they have your grand-child
    branch color/.style={
        concept color=#1!white,
        every child/.append style={concept color=#1!white!30!white},
    }
}
\tikzstyle{circle connection bar}=[to path={[every circle connection bar] decorate [decoration={bent}] { -- (\tikztotarget) \tikztonodes}},
append after command={[fill=white,draw=black]}]
\begin{tikzpicture}
%    \draw foreach\i in{1,...,36}{
%       (0:0)--(\i*10:15)
%    };
    \begin{scope}[text width=1.5cm,
            mindmap,
            growth function=\tikz@grow@concentric,
            sibling angle=15,
            nodes={concept, draw=blue!30, minimum size=0cm, inner sep=1mm},
            concept color=orange!60,
            level 1/.style={
                level distance=8cm,
                minimum size=3.0cm,text width=2.5cm
            },
            level 2/.style={
                level distance=12cm,
                minimum size=2.0cm,text width=2.0cm
            },
            level 3/.style={
                level distance=15cm,
                minimum size=2.0cm,text width=2.0cm
            }
            level 4/.style={
                level distance=15cm,
                minimum size=2.0cm,text width=2.0cm
            }
        ]
        \node [root concept]{Dimension finie}
        child[nold=9]{node {EV de DF} 
            child[nold=2] {node {L. Steinitz}
                    child[nold=1] {node {T. Base intermédiaire}
                child {node {T. Base incomplète}}
                }
            child {node {P. Dim infinie}} 
            } 
        child[nold=1] {node {T. Dim de f. libres, génératrices, bonux 1}
            child{node{T. Bonux 2}}
                    }
                child {node {P. Dim d'un produit}}
        child[nold=5] {node {P. Grassman}
            child{node {P. Non généralisation de Grassman}}
            child[nold=2]{node {P. Dim de sommes directes}
                child{node {P. Supplémentaires}}
                child{node {T. Bonux 3 des supplé.}} 
                }
            child[nold=2]{node {D. Le rang}
                child{node {P. sur le rang}}
                child{node {P. Rang, lib, gén, base}}
                }
            }
            }
        child[nold=8]{node {ALM}
            child[nold=3]{ node (equity) {Equity}
                child { node {Indices}}
                child { node {Stocks}}
                child { node {ETFs}}
            }
            child[nold=3]{ node (commo) {Commodities}
                child { node {Soft commo}}
                child { node {Precious}}
                child { node {Oil/Gas}}
            }
            child {node {Assurances}}
            child {node {Caisse de retraite}}
        }
        child[nold=1]{node {Directions financieres}
            child {node {Corporate}}
        }
        child[nold=3]{node {Instrument specialists} 
            child {node {Asset Managers traditionnels}}
            child {node {Hedge funds}}
            child {node {Trading desks form other banks}}
        }
        ;
    \end{scope}
\end{tikzpicture}
\end{document}

On top of that, I wonder if it is possible to modify the level distance of the level 3 and the level 4, for having far bigger bubbles, because they seem locked to allow growth function to make a good circle.

Finally, I will put my theorems and propositions into rectangles instead of bubbles, let me know if you have any advice to optimize this style (level distance between rectangles is very hard to use because it bases itself on the rectangle's center)

Thank you for all !

Answer 1

One can cook up some growth function for that. Here is a version that stores the configuration in the aux file and uses it in the second run. It basically records how many nodes arise at a given level and uses this information for the layout. It does reconstruct the graph the code of which you are asking for qualitatively.

\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=0,
    overall xshift/.initial=0pt,
    overall yshift/.initial=0pt,
    sign/.initial=1,
    child weight/.initial=0.5,
    /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=-70,mmap/sign=-1,
            nodes={concept,align=center, text width=2.5cm,inner sep=1mm},
            concept color=orange!60,
            level 1/.style={nodes=concept,
                %every child/.append style={concept color=orange},
                level distance=5cm,
            },
            level 2/.style={%opacity=0,
                %every child/.append style={concept color=blue},
                level distance=10cm,
                minimum size=2.0cm
            },
            level 3/.style={%opacity=0,
                %every child/.append style={concept color=green!70!black},
                level distance=15cm,sibling angle=40,
                minimum size=2.0cm,
            },
            level 4/.style={%opacity=0,
                %level distance=20cm,
                minimum size=2.0cm,text width=2.0cm
            }
        ]
        \node [root concept,ball color=orange!50]{Core}
          child[branch color=yellow]{node[shading=ball] {Core-1}
            child {node {Core-1-1}
                child {node {Core-1-1-1}}
                child {node {Core-1-1-2}}
                child {node {Core-1-1-3}}
                }
            child {node {Core-1-2}
                child {node {Core-1-2-1}}
                child {node {Core-1-2-2}}
                child {node {Core-1-2-3}}
                }
            child {node {Core-1-3}
                child {node {Core-1-3-1}}
                }
            child {node {Core-1-4}
                child {node {Core-1-4-1}}
                }
            child {node {Core-1-5}
                child {node {Core-1-5-1}}
                child {node {Core-1-5-2}}
                }
            }   
          child[branch color=blue]{node[shading=ball] {Core-2}
            child {node {Core-2-1}
                child {node {Core-1-1-1}}
                child {node {Core-1-1-2}}
                }
            child {node {Core-2-2}
                child {node {Core-2-2-1}}
                child {node {Core-2-2-2}}
                child {node {Core-2-2-3}}
                child {node {Core-2-2-4}}
                }
            }   
          child[branch color=red]{node[shading=ball] {Core-3}
            child {node {Core-3-1}
                child {node {Core-3-1-1}}
                child {node {Core-3-1-2}}
                }
            child {node {Core-3-2}
                child {node {Core-3-2-1}}
                child {node {Core-3-2-2}}
                }
            child {node {Core-3-3}
                child {node {Core-3-3-1}}
                child {node {Core-3-3-2}}
                }
            child {node {Core-3-4}
                }
            }   
          child[branch color=gray]{node[shading=ball] {Core-4}
            child {node {Core-4-1}
                child {node {Core-4-1-1}}
                child {node {Core-4-1-2}}
                }
            child {node {Core-4-2}
                child {node {Core-4-2-1}}
                child {node {Core-4-2-2}}
                }
            child {node {Core-4-3}
                child {node {Core-4-3-1}}
                child {node {Core-4-3-2}}
                }
            child {node {Core-4-4}
                }
            }   
          child[branch color=orange]{node[shading=ball] {Core-5}
            child {node {Core-5-1}
                child {node {Core-5-1-1}}
                }
            child {node {Core-5-2}
                child {node {Core-5-2-1}}
                child {node {Core-5-2-2}}
                }
            child {node {Core-5-3}
                child {node {Core-5-3-1}}
                child {node {Core-5-3-2}}
                }
            child {node {Core-5-4}
                }
            child {node {Core-5-5}
                }
            }   
        ;
    \end{scope}
\end{tikzpicture}
\end{document}

In other cases one has to help manually

\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%
   \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}%
   \fi   
   \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
  \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}%
   \ifnum\myniii>0
    \pgfmathsetmacro{\pgfutil@tempa}{\pgfutil@tempa+\pgfkeysvalueof{/tikz/mmap/sign}%
     *(\tikzcountchildiii-1)*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=0,
    overall xshift/.initial=0pt,
    overall yshift/.initial=0pt,
    sign/.initial=1,
    child weight/.initial=0.5,
    /tikz/.cd,
    Xshift/.style={xshift=#1,mmap/overall xshift=#1},
    Yshift/.style={yshift=#1,mmap/overall yshift=#1},
    branch color/.style={
        concept color=#1!60,
        every child/.append style={concept color=#1!30},
    }
}

\begin{tikzpicture}
    \begin{scope}[
            mindmap,garlic growth=A,mmap/child weight=0,
            mmap/overall rotation=-45,mmap/sign=1,
            nodes={concept,align=center, text width=2.5cm,inner sep=1mm},
            concept color=orange!60,
            level 1/.style={nodes={concept},
                every child/.append style={concept color=orange},
                level distance=5cm,
            },
            level 2/.style={%opacity=0,
                every child/.append style={concept color=blue},
                nodes={concept},
                level distance=10cm,
                minimum size=2.0cm
            },
            level 3/.style={%opacity=0,
                every child/.append style={concept color=green!70!black},
                level distance=5cm,sibling angle=40,
                minimum size=2.0cm,
            },
            level 4/.style={opacity=0,
                level distance=14cm,
                minimum size=2.0cm,text width=2.0cm
            }
        ]
        \node [root concept]{Dimension finie}
          child{node {EV de DF}% [clockwise from=0]
            child {node {L.\ Steinitz}
                [clockwise from=0]
                child {node {T.\ Base interm\'ediaire}
                child {node {T.\ Base incompl\`ete}}
                }
            child {node {P.\ Dim infinie}} 
            } 
          child {node {T.\ Dim de f.\ libres, g\'en\'eratrices, bonux 1}
              [clockwise from=-20]child{node{T.\ Bonux 2}}
                      }
          child {node {P.\ Dim d'un produit}}
          child {node {P.\ Grassmann}
            [clockwise from=10]
            child{node {P.\ Non g\'en\'eralisation de Grassmann}}
            child{node {P.\ Dim de sommes directes}
                child{node {P.\ Suppl\'ementaires}}
                child{node {T.\ Bonux 3 des suppl\'e.}} 
                }
            child{node {D.\ Le rang}
                child{node {P.\ sur le rang}}
                child{node {P.\ Rang, lib, g\'en, base}}
                }
            }
            }
        child{node {ALM}
            child{ node (equity) {Equity}
                [clockwise from=40]
                child { node {Indices}}
                child { node {Stocks}}
                child { node {ETFs}}
            }
            child{ node (commo) {Commodities}
                [clockwise from=70]
                child { node {Soft commo}}
                child { node {Precious}}
                child { node {Oil/Gas}}
            }
            child {node {Assurances}}
            child {node {Caisse de retraite}}
        }
        child{node {Directions financieres}
            child {node {Corporate}}
        }
        child{node {Instrument specialists} 
            child {node {Asset Managers traditionnels}}
            child {node {Hedge funds}}
            child {node {Trading desks form other banks}}
        }
        ;
    \end{scope}
\end{tikzpicture}
\end{document}

Here a new parameter was introduced, the child weight. In the above examples it is effectively set to 0.5. It determines how much the number of children influence the angle space allocated to a level 1 node. If it is 1, then impact is maximal, in this example it is 0.

So the overall summary is that some things work, and some don't, at least not fully automatically. However, I do not think one could expect an answer to solve the problems completely. What answers on this site can do is to contribute some incremental progress. 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 (a quick search for that didn't yield results but of course I could have missed them), but this will be spared for future questions and answers.