Mindmaps, general method to get regular/harmonious circle shape for level 3 and more

I have rewrite the grow function. Now you have to specify nold, which is the number of leaf descendants. That is, count the number of descendants who don't have any child. Cat's Xshift and Yshift are kept. But I renamed the internal overall xxxx as smuggle xxxx. Because we are smuggling the parameter over the \pgftransformreset barrier.

\documentclass[tikz,border=9]{standalone}
\usetikzlibrary{mindmap}

\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},
    }
}

\begin{tikzpicture}
    \draw foreach\i in{1,...,36}{
        (0:0)--(\i*10:15)
    };
    \begin{scope}[text width=1.5cm,align=flush center,
            mindmap,growth function=\tikz@grow@concentric,
            smuggle rotation=-30,
            sibling angle=10,
            nodes={concept},
            concept color=green!70!black,
            root concept/.append style={
                ball color=green!50,line width=1.5ex,text=green!40!black,
                font=\huge\bfseries\scshape,minimum size=4.5cm,text width=4.5cm
            },
            level 1/.style={
                level distance=8cm,font=\Large,
                minimum size=3.0cm,text width=2.5cm
            },
            level 2/.style={
                level distance=12cm,font=\large,
                minimum size=2.0cm,text width=2.0cm
            },
            level 3/.style={
                level distance=15cm,font=\large,
                minimum size=2.0cm,text width=2.0cm
            }
        ]
        \node [root concept]{Clients}
        child[nold=3,branch color=green!70]{node {Retail} 
            child {node {CGPI}} 
            child {node {Banques priv\'ees}}
            child {node {Retail banking}} 
        }
        child[nold=8,branch color=green!70]{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,branch color=green!80]{node {Directions financieres}
            child {node {Corporate}}
        }
        child[nold=3,branch color=green!70]{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}


UPDATED ANSWER to your edited question. Just define some counts for the various levels and introduce some offset angles. (More generally one will probably need to add some level-dependent additional angles, or do an automatized version, which the lowest code will get turned into at some point.) For your current example this seems to be sufficient.

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{mindmap}
\makeatletter
\newif\ifmmap@debug
\mmap@debugfalse
\newcommand{\mmap@debug@message}[1]{\ifmmap@debug
\typeout{#1}%
\fi}
\newcount\tikzcountchildi
\newcount\tikzcountchildii
\newcount\tikzcountchildiii
\newcount\tikzcountchildiv
\newcount\tikzcountchildv
\tikzcountchildi=0
\tikzcountchildii=0
\tikzcountchildiii=0
\tikzcountchildiv=0
\tikzcountchildv=0
\tikzset{Julien growth/.style={growth function=\tikz@grow@Julien,
mmap/initialize counts},
mmap/.cd,initialize counts/.code={\global\tikzcountchildi=0%
\global\tikzcountchildii=0%
\global\tikzcountchildiii=0%
\global\tikzcountchildiv=0%
\global\tikzcountchildv=0%
}
}



\def\tikz@grow@Julien{%
  \pgftransformreset% 
  \pgftransformshift{\pgfpoint{\pgfkeysvalueof{/tikz/mmap/overall xshift}}%
        {\pgfkeysvalueof{/tikz/mmap/overall yshift}}}%
  \ifcase\tikztreelevel 
  \or
    \pgfmathsetmacro{\pgfutil@tempb}{\pgfkeysvalueof{/tikz/mmap/overall rotation}%
        +\pgfkeysvalueof{/tikz/mmap/sign}*\pgfkeysvalueof{/tikz/offset angle}%
        +\pgfkeysvalueof{/tikz/mmap/sign}*\pgfkeysvalueof{/tikz/sibling angle}*\tikzcountchildi}%
    \global\advance\tikzcountchildi by1\relax%
  \or
    \pgfmathsetmacro{\pgfutil@tempb}{\pgfkeysvalueof{/tikz/mmap/overall rotation}%
        +\pgfkeysvalueof{/tikz/mmap/sign}*\pgfkeysvalueof{/tikz/offset angle}%
        +\pgfkeysvalueof{/tikz/mmap/sign}*\pgfkeysvalueof{/tikz/sibling angle}*\tikzcountchildii}%
    \global\advance\tikzcountchildii by1\relax%
  \or
    \pgfmathsetmacro{\pgfutil@tempb}{\pgfkeysvalueof{/tikz/mmap/overall rotation}%
        +\pgfkeysvalueof{/tikz/mmap/sign}*\pgfkeysvalueof{/tikz/offset angle}%
        +\pgfkeysvalueof{/tikz/mmap/sign}*\pgfkeysvalueof{/tikz/sibling angle}*\tikzcountchildiii}%
    \global\advance\tikzcountchildiii by1\relax%
  \or
    \pgfmathsetmacro{\pgfutil@tempb}{\pgfkeysvalueof{/tikz/mmap/overall rotation}%
        +\pgfkeysvalueof{/tikz/mmap/sign}*\pgfkeysvalueof{/tikz/offset angle}%
        +\pgfkeysvalueof{/tikz/mmap/sign}*\pgfkeysvalueof{/tikz/sibling angle}*\tikzcountchildiv}%
    \global\advance\tikzcountchildiv by1\relax%
  \or
    \pgfmathsetmacro{\pgfutil@tempb}{\pgfkeysvalueof{/tikz/mmap/overall rotation}%
        +\pgfkeysvalueof{/tikz/mmap/sign}*\pgfkeysvalueof{/tikz/offset angle}%
        +\pgfkeysvalueof{/tikz/mmap/sign}*\pgfkeysvalueof{/tikz/sibling angle}*\tikzcountchildv}%
    \global\advance\tikzcountchildv by1\relax%
  \fi
  \mmap@debug@message{level=\the\tikztreelevel,%
  \the\tikzcountchildi,\the\tikzcountchildii,\the\tikzcountchildiii,
  rotation=\pgfutil@tempb,sibling angle=\pgfkeysvalueof{/tikz/sibling angle}}%
  \pgftransformrotate{\pgfutil@tempb}%
  \pgftransformxshift{\the\tikzleveldistance}%
}
\makeatother
\begin{document}
\tikzset{mmap/.cd,overall rotation/.initial=0,% overall transformation of mind maps
    overall xshift/.initial=0pt,
    overall yshift/.initial=0pt,
    sign/.initial=1,% 1=clockwise,-1=counterclockwise
    /tikz/.cd,offset angle/.initial=0,
    Xshift/.style={xshift=#1,mmap/overall xshift=#1},
    Yshift/.style={yshift=#1,mmap/overall yshift=#1},
    branch color/.style={
        concept color=#1!white,
        every child/.append style={concept color=#1!white!30!white},
    }
}

\begin{tikzpicture}[node font=\sffamily]
    \begin{scope}[text width=1.5cm,align=flush center,
            mindmap,Julien growth,
            mmap/overall rotation=110,mmap/sign=-1,
            nodes={concept},
            concept color=green!70!black,
            root concept/.append style={ball color=green!50, line width=1.5ex,text=green!40!black,font=\huge\bfseries\scshape,minimum size=4.5cm,text width=4.5cm,},                   
            level 1/.style={level distance=5cm,font=\Large,minimum size=3.0cm,
                text width=2.5cm,sibling angle=65},
            level 2/.style={level distance=9cm,
                font=\large,minimum size=2.0cm,text width=2.0cm,
                    sibling angle=22},
            level 3/.style={level distance=12cm,font=\large,minimum
            size=2.0cm,text width=2.0cm,sibling angle=12,
            offset angle=50},
        ]
        \node [root concept]{Clients} 
        child[branch color=green!70]{node {Retail} 
            child[] {node {CGPI}} 
            child[] {node {Banques priv\'ees}} 
            child[] {node {Retail banking}} 
        }
        child[branch color=green!70]{node {ALM} 
            child { node (equity) {Equity}
                child { node {Indices}}
                child { node {Stocks}}
                child { node {ETFs}}
            }
            child { node (commo) {Commo--\\dities}
                child { node {Soft commo}}
                child { node {Precious}}        
                child { node {Oil/Gas}}
            }
            child[] {node {Assurances}} 
            child[] {node {Caisse de retraite}}         
        } 
        child[branch color=green!80]{node {Directions financi\'eres} 
            child[] {node {Corporate}} 
        } 
        child[branch color=green!70]{node {Instrument specialists} 
            child {node {Asset Managers traditionnels}} 
            child {node {Hedge funds}} 
            child {node {Trading desks form other banks}} 
        } 
        ;
    \end{scope}

    \begin{scope}[Xshift=-12cm,text width=1.5cm,align=flush center,
            mindmap,Julien growth,
            mmap/overall rotation=290,mmap/sign=-1,
            nodes={concept},
            concept color=yellow!70!black,
            root concept/.append style={ ball color=yellow!50, line width=1.5ex,text=yellow!40!black,font=\huge\bfseries\scshape,minimum size=4.5cm,text width=4.5cm,},                   
            level 1/.style={level distance=5cm,font=\Large,minimum size=3.0cm,text width=2.5cm,
                sibling angle=60},
            level 2/.style={level distance=9cm,font=\large,minimum
                size=2.0cm,text width=2.0cm,sibling angle=24},
        ]
        \node [root concept]{Suppliers} 
        child[branch color=yellow!70]{node {Retail} 
            child[] {node {CGPI}} 
            child[] {node {Banques priv\'ees}} 
            child[] {node {Retail banking}} 
        }
        child[branch color=yellow!70]{node {ALM} 
            child[] {node {Mutuelles}} 
            child[] {node {Assurances}} 
            child[] {node {Caisse de retraite}}         
        } 
        child[branch color=yellow!80]{node {Directions financi\'eres} 
            child[] {node {Corporate}} 
        } 
        child[branch color=yellow!70]{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}

enter image description here

OLDER ANSWER: This is some aux file hackery. The lowest code may be useful for writing an automatized version of the above code.

This code is not too serious an answer. So, yes, one can write stuff to the aux file and recover it when needed. But I definitely do not claim that this is a universally working code. Probably one has to choose the parameters differently. In order to have more than one mindmap, one needs to give the garlic growth a unique id (such as A or B). (I do not like onions, so I called this one garlic.) One has to compile this a few times.

\documentclass[tikz,border=9]{standalone}
\usetikzlibrary{mindmap,decorations}
\usepackage{xspace}
\makeatletter
\newcount\tikzcountchildi
\newcount\tikzcountchildii
\newcount\tikzcountchildiii
\tikzcountchildi=0
\tikzcountchildii=0
\tikzcountchildiii=0
\tikzset{garlic growth/.style={growth function=\tikz@grow@garlic,
/tikz/mmap/name=#1,mmap/#1/.is family,
mmap/initialize counts},
mmap/.cd,initialize counts/.code={\tikzcountchildi=0%
\tikzcountchildii=0%
\tikzcountchildiii=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{%
  \ifcase\tikztreelevel 
  \or
    \global\advance\tikzcountchildi by1\relax%
    \ifnum\tikznumberofcurrentchild=1\relax
     \tikz@mmap@store@aux{n}{\the\tikznumberofchildren}%
     \tikz@mmap@store@aux{l-1}{\the\tikzleveldistance}%
    \fi
    \tikzcountchildii=0\relax
  \or
    \global\advance\tikzcountchildii by1\relax%
    \ifnum\tikzcountchildii=1\relax
     \ifnum\tikznumberofcurrentchild=1\relax
      \tikz@mmap@store@aux{l-2}{\the\tikzleveldistance}%
     \fi
    \fi
    \ifnum\tikznumberofcurrentchild=1\relax
     \tikz@mmap@store@aux{n-\the\tikzcountchildi}{\the\tikznumberofchildren}%
     \c@pgf@counta=0\relax% loop counter
     \edef\pgfutil@tempb{0}% angle space needed for this child
     \tikz@mmap@get@from@aux{s-\the\tikzcountchildi}{\pgfutil@tempf}%    
     \pgfmathsetmacro{\pgfutil@tempf}{-\pgfutil@tempf/2}% offset
     \edef\pgfutil@tempe{0}% local rotation angle of grandchild
     \edef\pgfutil@tempg{0}% last angle space needed for grandchild
     % if there were no grandgrand children we only needed to count the children
     \pgfutil@loop
      \ifnum\c@pgf@counta<\tikznumberofchildren
       \advance\c@pgf@counta by1\relax
       \tikz@mmap@get@from@aux{n-\the\tikzcountchildi-\the\c@pgf@counta}{\pgfutil@tempa}%
        \ifnum\pgfutil@tempa=0\relax
         %\typeout{level \the\tikzcountchildi-\the\c@pgf@counta :found 0 children}
         \pgfmathsetmacro{\pgfutil@tempg}{\pgfkeysvalueof{/tikz/mmap/angle 2}}%
        \else
         %\typeout{level \the\tikzcountchildi-\the\c@pgf@counta :found \pgfutil@tempa\space children}
         \pgfmathsetmacro{\pgfutil@tempg}{max(\pgfkeysvalueof{/tikz/mmap/angle 2},%
         \pgfutil@tempa*\pgfkeysvalueof{/tikz/mmap/angle 3})}%
        \fi
        \pgfmathsetmacro{\pgfutil@tempe}{\pgfutil@tempf+\pgfutil@tempb+\pgfutil@tempg/2}%
        \tikz@mmap@store@aux{t-\the\tikzcountchildi-\the\c@pgf@counta}{\pgfutil@tempe}%
        \pgfmathsetmacro{\pgfutil@tempb}{\pgfutil@tempb+\pgfutil@tempg}%        
      \pgfutil@repeat
      %\typeout{n_1=\the\tikzcountchildi : space needed=\pgfutil@tempb}%
      \tikz@mmap@store@aux{s-\the\tikzcountchildi}{\pgfutil@tempb}%
      \ifnum\tikzcountchildi=1
       \tikz@mmap@store@aux{t-\the\tikzcountchildi}{\pgfutil@tempb/2}%
      \else
       \tikz@mmap@get@from@aux{s-\the\numexpr\tikzcountchildi-1}{\pgfutil@tempc}%
       \tikz@mmap@get@from@aux{t-\the\numexpr\tikzcountchildi-1}{\pgfutil@tempd}%
       \pgfmathsetmacro{\pgfutil@tempa}{\pgfutil@tempd+\pgfutil@tempc/2+\pgfutil@tempb/2}%
       \tikz@mmap@store@aux{t-\the\tikzcountchildi}{\pgfutil@tempa}%
      \fi 
    \fi
    %\typeout{level \the\tikzcountchildi-\the\tikzcountchildii:
    %\the\tikznumberofcurrentchild/\the\tikznumberofchildren}
    \pgfmathsetmacro{\pgfutil@tempg}{\tikznumberofchildren*\pgfkeysvalueof{/tikz/mmap/angle 2}}%
    \tikz@mmap@store@aux{s-\the\tikzcountchildi-\the\tikzcountchildii}{\pgfutil@tempg}%     
    \tikzcountchildiii=0\relax
  \or
    \global\advance\tikzcountchildiii by1\relax%
    \ifnum\tikznumberofcurrentchild=1\relax
     \tikz@mmap@store@aux{n-\the\tikzcountchildi-\the\tikzcountchildii}{\the\tikznumberofchildren}%
    \fi 
    \pgfmathsetmacro{\pgfutil@tempa}{(\tikznumberofcurrentchild-\tikznumberofchildren/2-1/2)*%
        (\pgfkeysvalueof{/tikz/sibling angle})}
    \tikz@mmap@store@aux{t-\the\tikzcountchildi-\the\tikzcountchildii-\the\tikzcountchildiii}{\pgfutil@tempa}%
  \fi
  \pgftransformreset% 
  \pgftransformshift{\pgfpoint{\pgfkeysvalueof{/tikz/mmap/overall xshift}}%
        {\pgfkeysvalueof{/tikz/mmap/overall yshift}}}%
  \tikz@mmap@get@from@aux{t-\the\tikzcountchildi}{\pgfutil@tempa}%
  \pgfmathsetmacro{\pgfutil@tempb}{\pgfkeysvalueof{/tikz/mmap/overall rotation}+\pgfkeysvalueof{/tikz/mmap/sign}*\pgfutil@tempa}%
  \pgftransformrotate{\pgfutil@tempb}%
  \tikz@mmap@get@from@aux{l-1}{\pgfutil@tempc}%
  \pgftransformxshift{\pgfutil@tempc}%
  \ifnum\tikztreelevel=1
    %\typeout{t-\the\tikzcountchildi: rotate by \pgfutil@tempb (t=\pgfutil@tempa)}
  \else
    \tikz@mmap@get@from@aux{t-\the\tikzcountchildi-\the\tikzcountchildii}{\pgfutil@tempa}%
    \pgftransformrotate{\pgfutil@tempa}%
    \tikz@mmap@get@from@aux{l-2}{\pgfutil@tempc}%
    \pgftransformxshift{\pgfutil@tempc}%
    %\typeout{level 2 rotation by \pgfutil@tempa\space and shift by \pgfutil@tempc}
    \ifnum\tikztreelevel=2
    \else
     \tikz@mmap@get@from@aux{t-\the\tikzcountchildi-\the\tikzcountchildii-\the\tikzcountchildiii}{\pgfutil@tempa}%
     \pgftransformrotate{\pgfutil@tempa}%
     \pgftransformxshift{\the\tikzleveldistance}%
    \fi
  \fi
}
\makeatother
\begin{document}
\tikzset{mmap/.cd,
    name/.initial=undef,
    overall rotation/.initial=0,
    overall xshift/.initial=0pt,
    overall yshift/.initial=0pt,
    angle 1/.initial=5,
    angle 2/.initial=25,
    angle 3/.initial=15,
    sign/.initial=1,
    /tikz/.cd,
    Xshift/.style={xshift=#1,mmap/overall xshift=#1},
    Yshift/.style={yshift=#1,mmap/overall yshift=#1},
    branch color/.style={
        concept color=#1!white,
        every child/.append style={concept color=#1!white!30!white},
    }
}

\begin{tikzpicture}
    \begin{scope}[text width=1.5cm,align=flush center,
            mindmap,garlic growth=A,
            mmap/overall rotation=135,mmap/sign=-1,
            sibling angle=40,
            nodes={concept},
            concept color=green!70!black,
            root concept/.append style={ball color=green!50, line width=1.5ex,text=green!40!black,font=\huge\bfseries\scshape,minimum size=4.5cm,text width=4.5cm,},                   
            level 1/.style={level distance=5cm,font=\Large,minimum size=3.0cm,text width=2.5cm,},
            level 2/.style={level distance=6cm,font=\large,minimum size=2.0cm,text width=2.0cm},
            level 3/.style={level distance=4cm,font=\large,minimum size=2.0cm,text width=2.0cm}
        ]
        \node [root concept]{Clients} 
        child[branch color=green!70]{node {Retail} 
            child[] {node {CGPI}} 
            child[] {node {Banques priv\'ees}} 
            child[] {node {Retail banking}} 
        }
        child[branch color=green!70]{node {ALM} 
            child { node (equity) {Equity}
                child { node {Indices}}
                child { node {Stocks}}
                child { node {ETFs}}
            }
            child { node (commo) {Commodities}
                child { node {Soft commo}}
                child { node {Precious}}        
                child { node {Oil/Gas}}
            }
            child[] {node {Assurances}} 
            child[] {node {Caisse de retraite}}         
        } 
        child[branch color=green!80]{node {Directions financi\'eres} 
            child[] {node {Corporate}} 
        } 
        child[branch color=green!70]{node {Instrument specialists} 
            child {node {Asset Managers traditionnels}} 
            child {node {Hedge funds}} 
            child {node {Trading desks form other banks}} 
        } 
        ;
    \end{scope}

    \begin{scope}[Xshift=-12cm,Yshift=3cm,text width=1.5cm,align=flush center,
            mindmap,garlic growth=B,
            mmap/overall rotation=250,mmap/sign=-1,
            nodes={concept},
            concept color=yellow!70!black,
            root concept/.append style={ ball color=yellow!50, line width=1.5ex,text=yellow!40!black,font=\huge\bfseries\scshape,minimum size=4.5cm,text width=4.5cm,},                   
            level 1/.style={level distance=6cm,font=\Large,minimum size=3.0cm,text width=2.5cm,},
            level 2/.style={level distance=6cm,font=\large,minimum
                size=2.0cm,text width=2.0cm},
            mmap/.cd,
            angle 1=5,angle 2=20,angle 3=5,
        ]
        \node [root concept]{Suppliers} 
        child[branch color=yellow!70]{node {Retail} 
            child[] {node {CGPI}} 
            child[] {node {Banques priv\'ees}} 
            child[] {node {Retail banking}} 
        }
        child[branch color=yellow!70]{node {ALM} 
            child[] {node {Mutuelles}} 
            child[] {node {Assurances}} 
            child[] {node {Caisse de retraite}}         
        } 
        child[branch color=yellow!80]{node {Directions financi\'eres} 
            child[] {node {Corporate}} 
        } 
        child[branch color=yellow!70]{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}

enter image description here

Overall I think it may make more sense to marry the graph drawing algorithms to mind map. Some spring layout or whatever. Something where an algorithm tries to find the optimal values.

ADDENDUMM: This is work in progress. If I do not succeed, which is quite possible, here is a better structured and documented base version of the code. I have not added any explicit growth function, but this is the easier part (IMHO). It stores the number of leafs in the aux file and also computes a quantity m which is explained in the code.

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{mindmap}
\usepackage[fleqn]{amsmath}
\makeatletter
\newif\ifmmap@debug
\mmap@debugtrue
\newcommand{\mmap@debug@message}[1]{\ifmmap@debug
\typeout{#1}%
\fi}
\newcount\tikzcountchildi
\newcount\tikzcountchildii
\newcount\tikzcountchildiii
\newcount\tikzcountchildiv
\newcount\tikzcountchildv
\tikzcountchildi=0
\tikzcountchildii=0
\tikzcountchildiii=0
\tikzcountchildiv=0
\tikzcountchildv=0
\tikzset{garlic growth/.style={growth function=\tikz@grow@garlic,
/tikz/mmap/name=#1,mmap/#1/.is family,
mmap/initialize counts},
mmap/.cd,initialize counts/.code={\tikzcountchildi=0%
\tikzcountchildii=0%
\tikzcountchildiii=0%
\tikzcountchildiv=0%
\tikzcountchildv=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
}
% m is the effective number of children
\def\tikz@compute@mandn#1{% #1=current level k
     \ifcase#1\relax % build up identifier : -i_1-i_2-...-i_k
     \or
      \edef\pgfutil@tempc{-\the\tikzcountchildi}% 
     \or
      \edef\pgfutil@tempc{-\the\tikzcountchildi-\the\tikzcountchildii}% 
     \or
      \edef\pgfutil@tempc{-\the\tikzcountchildi-\the\tikzcountchildii-\the\tikzcountchildiii}% 
     \or
      \edef\pgfutil@tempc{-\the\tikzcountchildi-\the\tikzcountchildii-\the\tikzcountchildiii-\the\tikzcountchildiv}% 
     \or
      \edef\pgfutil@tempc{-\the\tikzcountchildi-\the\tikzcountchildii-\the\tikzcountchildiii-\the\tikzcountchildiv-\the\tikzcountchildv}% 
     \fi
     % store the number of children of parent leaf (and the level distance)
     \ifnum\tikznumberofcurrentchild=1\relax
      \tikz@mmap@store@aux{l-#1}{\the\tikzleveldistance}%
      \tikz@mmap@store@aux{n\pgfutil@tempc}{\the\tikznumberofchildren}%
     \fi
     \ifnum\tikznumberofchildren=0\relax % no children
      \pgfmathsetmacro{\pgfutil@tempb}{\pgfkeysvalueof{/tikz/mmap/angle #1}}
     \else 
      % sum over the children 
      \c@pgf@counta=0\relax% loop counter
      \edef\pgfutil@tempb{0}% accumulate angle space m needed for this child
      \pgfutil@loop
       \ifnum\c@pgf@counta<\tikznumberofchildren
        \advance\c@pgf@counta by1\relax
        % read out the m value of child
        \tikz@mmap@get@from@aux{m\pgfutil@tempc-\the\c@pgf@counta}{\pgfutil@tempa}%
        \ifdim\pgfutil@tempa pt=0pt\relax
         \pgfmathsetmacro{\pgfutil@tempa}{\pgfkeysvalueof{/tikz/mmap/angle \the\numexpr#1+1}}%
         \mmap@debug@message{m\pgfutil@tempc-\the\c@pgf@counta=0, so added standard angle \pgfutil@tempa}
        \else
         \pgfmathsetmacro{\pgfutil@tempa}{max(\pgfkeysvalueof{/tikz/mmap/angle \the\numexpr#1+1},\pgfutil@tempa}%
         \mmap@debug@message{m\pgfutil@tempc-\the\c@pgf@counta=\pgfutil@tempa\space found and added}%
        \fi
        \pgfmathsetmacro{\pgfutil@tempb}{\pgfutil@tempb+\pgfutil@tempa}%
       \pgfutil@repeat
      \fi 
      \tikz@mmap@store@aux{m\pgfutil@tempc}{\pgfutil@tempb}%
}

\def\tikz@grow@garlic{%
  \ifcase\tikztreelevel 
  \or
    \global\advance\tikzcountchildi by1\relax%
    \ifnum\tikznumberofcurrentchild=1\relax
     \tikz@mmap@store@aux{n}{\the\tikznumberofchildren}%
     \tikz@mmap@store@aux{l-1}{\the\tikzleveldistance}%
    \fi
    \tikzcountchildii=0\relax
  \or
    \global\advance\tikzcountchildii by1\relax%
    \tikz@compute@mandn1
    \tikzcountchildiii=0\relax
  \or
    \global\advance\tikzcountchildiii by1\relax%
    \tikz@compute@mandn2
    \tikzcountchildiv=0\relax
  \or
    \global\advance\tikzcountchildiv by1\relax%
    \tikz@compute@mandn3
    \tikzcountchildv=0\relax
  \or
    \global\advance\tikzcountchildv by1\relax%
    \tikz@compute@mandn4
  \fi
  \pgftransformreset% 
  \pgftransformshift{\pgfpoint{\pgfkeysvalueof{/tikz/mmap/overall xshift}}%
        {\pgfkeysvalueof{/tikz/mmap/overall yshift}}}%
}
\makeatother
\begin{document}
\tikzset{mmap/.cd,
    name/.initial=undef,
    overall rotation/.initial=0,
    overall xshift/.initial=0pt,
    overall yshift/.initial=0pt,
    angle 1/.initial=20,
    angle 2/.initial=20,
    angle 3/.initial=20,
    angle 4/.initial=20,
    angle 5/.initial=20,
    sign/.initial=1,
    /tikz/.cd,
    Xshift/.style={xshift=#1,mmap/overall xshift=#1},
    Yshift/.style={yshift=#1,mmap/overall yshift=#1},
    branch color/.style={
        concept color=#1!white,
        every child/.append style={concept color=#1!white!30!white},
    }
}

\begin{tikzpicture}
    \begin{scope}[text width=1.5cm,align=flush center,
            mindmap,garlic growth=A,
            mmap/overall rotation=135,mmap/sign=-1,
            sibling angle=33,
            nodes={concept},
            concept color=green!70!black,
            root concept/.append style={ball color=green!50, line width=1.5ex,text=green!40!black,font=\huge\bfseries\scshape,minimum size=4.5cm,text width=4.5cm,},                   
            level 1/.style={level distance=5cm,font=\Large,minimum size=3.0cm,text width=2.5cm,},
            level 2/.style={level distance=6cm,font=\large,minimum size=2.0cm,text width=2.0cm},
            level 3/.style={level distance=4cm,font=\large,minimum
            size=2.0cm,text width=2.0cm},
            mmap/.cd,angle 1=-5,angle 2=25,angle 3=14,          
        ]
        \node [root concept]{Clients} 
        child[branch color=green!70]{node {Retail} 
            child[] {node {CGPI}} 
            child[] {node {Banques priv\'ees}} 
            child[] {node {Retail banking}} 
        }
        child[branch color=green!70]{node {ALM} 
            child { node (equity) {Equity}
                child { node {Indices}}
                child { node {Stocks}}
                child { node {ETFs}}
            }
            child { node (commo) {Commodities}
                child { node {Soft commo}}
                child { node {Precious}}        
                child { node {Oil/Gas}}
            }
            child[] {node {Assurances}} 
            child[] {node {Caisse de retraite}}         
        } 
        child[branch color=green!80]{node {Directions financi\'eres} 
            child[] {node {Corporate}} 
        } 
        child[branch color=green!70]{node {Instrument specialists} 
            child {node {Asset Managers traditionnels}} 
            child {node {Hedge funds}} 
            child {node {Trading desks form other banks}} 
        } 
        ;
    \end{scope}

    \begin{scope}[Xshift=-12cm,Yshift=3cm,text width=1.5cm,align=flush center,
            mindmap,garlic growth=B,
            mmap/overall rotation=250,mmap/sign=-1,
            nodes={concept},
            concept color=yellow!70!black,
            root concept/.append style={ ball color=yellow!50, line width=1.5ex,text=yellow!40!black,font=\huge\bfseries\scshape,minimum size=4.5cm,text width=4.5cm,},                   
            level 1/.style={level distance=6cm,font=\Large,minimum size=3.0cm,text width=2.5cm,},
            level 2/.style={level distance=6cm,font=\large,minimum
                size=2.0cm,text width=2.0cm},
            mmap/.cd,
            angle 1=5,angle 2=20,angle 3=5,
        ]
        \node [root concept]{Suppliers} 
        child[branch color=yellow!70]{node {Retail} 
            child[] {node {CGPI}} 
            child[] {node {Banques priv\'ees}} 
            child[] {node {Retail banking}} 
        }
        child[branch color=yellow!70]{node {ALM} 
            child[] {node {Mutuelles}} 
            child[] {node {Assurances}} 
            child[] {node {Caisse de retraite}}         
        } 
        child[branch color=yellow!80]{node {Directions financi\'eres} 
            child[] {node {Corporate}} 
        } 
        child[branch color=yellow!70]{node {Instrument specialists} 
            child {node {Asset Managers traditionnels}} 
            child {node {Hedge funds}} 
            child {node {Trading desks form other banks}} 
        } 
        ;
    \end{scope}
    \node[anchor=south,text width=14cm] at (current bounding box.north)
    {Let us define an array $m$ recursively as follows. For any \emph{outermost}
    leaf
    \[ 
      m_{i_1i_2\cdots i_k}=\alpha_k\;,
    \]
    where $k$ is the level and $\alpha_k$ is the level--dependent ``standard
    angle''. In the code, 
    \[
     \alpha_k=\texttt{\textbackslash pgfkeysvalueof\{/tikz/mmap/angle $k$\}}\;,
    \]
    i.e.\ the $\alpha_k$ are stored in the keys \texttt{angle $k$} in the
    \texttt{mmap} directory. If the leaf is \emph{not outermost}, $m$ is defined
    as the sum of the $m$--values of the children,
    \[ 
     m_{i_1i_2\cdots i_k}=
     \sum\limits_{j=1}^{n_\mathrm{children}}
     \max \{m_{i_1i_2\cdots i_k-j},\alpha_k\}\;.
    \]
    };
\end{tikzpicture}
\end{document}

enter image description here

I think one needs to clarify how the tree should look like. Then one can conceivably use the stored leaf counts and m entries to draw it.