To shade a mindmap it is necessary to add a shading to the nodes.
Let's start to add a shading style different for each level; the method used is simple: different concepts will have different ball color
s.
The code:
\documentclass[a4paper,11pt]{article}
\usepackage{tikz}
\usetikzlibrary{mindmap}
\tikzset{level 1 concept/.append style={font=\sf, sibling angle=90,level distance = 25mm}}
\tikzset{level 2 concept/.append style={font=\sf, sibling angle=45,level distance = 16mm}}
\tikzset{level 3 concept/.append style={font=\sf, sibling angle=45,level distance = 17mm}}
\tikzset{every node/.append style={scale=0.6}}
\begin{document}
\begin{tikzpicture}[mindmap, concept color=blue, font=\sf\bf, text=white]
\node[concept,ball color=blue]{Root Concept}[clockwise from=315]
child [concept color=violet] {node[circle,ball color=violet] (c1){Child 1}
child {node [circle,ball color=violet](c11){Child 1-1}}
child {node [circle,ball color=violet](c12){Child 1-2}}
child {node [circle,ball color=violet](c13){Child 1-3}}
}
child [concept color=orange]{node [circle,ball color=orange](c2){Child 2}
child {node [circle,ball color=orange](c21){Child 2-1}}
child {node [circle,ball color=orange](c22){Child 2-2}}
child {node [circle,ball color=orange](c22){Child 1-3}}
};
\end{tikzpicture}
\end{document}
The result is:

Now we can start to define much complicated shadings to differentiate concepts (related answers as reference for shading: How to create a ball shading and to customize 3D lighting manually? and Is there a way to tune ball shading in TikZ ?); let's define, for example a myball
shading as:
\makeatletter
\pgfdeclareradialshading[tikz@ball]{myball}{\pgfqpoint{5bp}{10bp}}{%
color(0bp)=(tikz@ball!30!white);
color(9bp)=(tikz@ball!75!white);
color(18bp)=(tikz@ball!90!black);
color(25bp)=(tikz@ball!70!black);
color(50bp)=(black)}
\makeatother
With this definition, however, it is not possible to change color easily; that's why we need also:
\tikzoption{myball color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{myball}\tikz@addmode{\tikz@mode@shadetrue}}
to subsequently call myball color=...
.
Here is the full example:
\documentclass[a4paper,11pt]{article}
\usepackage{tikz}
\usetikzlibrary{mindmap}
\makeatletter
\pgfdeclareradialshading[tikz@ball]{myball}{\pgfqpoint{5bp}{10bp}}{%
color(0bp)=(tikz@ball!30!white);
color(9bp)=(tikz@ball!75!white);
color(18bp)=(tikz@ball!90!black);
color(25bp)=(tikz@ball!70!black);
color(50bp)=(black)}
% to make possible use "myball color=..."
\tikzoption{myball color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{myball}\tikz@addmode{\tikz@mode@shadetrue}}
\pgfdeclareradialshading[tikz@ball]{myball-left}{\pgfqpoint{5bp}{-9bp}}{%
color(0bp)=(tikz@ball!30!white);
color(15bp)=(tikz@ball!75!white);
color(25bp)=(tikz@ball!90!black);
color(40bp)=(tikz@ball!70!black);
color(70bp)=(black)}
\tikzoption{myball-left color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{myball-left}\tikz@addmode{\tikz@mode@shadetrue}}
\pgfdeclareradialshading[tikz@ball]{myball-right}{\pgfqpoint{-5bp}{-9bp}}{%
color(0bp)=(tikz@ball!30!white);
color(15bp)=(tikz@ball!75!white);
color(25bp)=(tikz@ball!90!black);
color(40bp)=(tikz@ball!70!black);
color(70bp)=(black)}
\tikzoption{myball-right color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{myball-right}\tikz@addmode{\tikz@mode@shadetrue}}
\makeatother
\tikzset{level 1 concept/.append style={font=\sf, sibling angle=90,level distance = 25mm}}
\tikzset{level 2 concept/.append style={font=\sf, sibling angle=45,level distance = 16mm}}
\tikzset{level 3 concept/.append style={font=\sf, sibling angle=45,level distance = 17mm}}
\tikzset{every node/.append style={scale=0.6}}
\begin{document}
\begin{tikzpicture}[mindmap, concept color=blue, font=\sf\bf, text=white]
\node[concept,shading=myball]{Root Concept}[clockwise from=315]
child [concept color=orange] {node[circle, myball-left color=orange] (c1){Child 1}
child {node [circle, myball-left color=orange](c11){Child 1-1}}
child {node [circle,myball-left color=orange](c12){Child 1-2}}
child {node [circle,myball-left color=orange](c13){Child 1-3}}
}
child [concept color=violet]{node [circle,myball-right color=violet](c2){Child 2}
child {node [circle,myball-right color=violet](c21){Child 2-1}}
child {node [circle,myball-right color=violet](c22){Child 2-2}}
child {node [circle,myball-right color=violet](c22){Child 1-3}}
};
\end{tikzpicture}
\end{document}
which gives:

Some remarks
A typical call is: child {node [circle, myball-left color=orange](c11){Child 1-1}}
where circle
is absolutely needed otherwise the concept will be a square.
If you try to add concept
to the node options, your ball will circled (the effect is more evident when the circle size is small).
In the previous example change the document
into:
\begin{document}
\begin{tikzpicture}[mindmap, concept color=blue, font=\sf\bf, text=white]
\node[concept,shading=myball]{Root Concept}[clockwise from=315]
child [concept color=orange] {node[concept,circle, myball-left color=orange] (c1){Child 1}
child {node [concept,circle, myball-left color=orange](c11){Child 1-1}}
child {node [concept,circle,myball-left color=orange](c12){Child 1-2}}
child {node [concept,circle,myball-left color=orange](c13){Child 1-3}}
}
child [concept color=violet]{node [concept,circle,myball-right color=violet](c2){Child 2}
child {node [concept,circle,myball-right color=violet](c21){Child 2-1}}
child {node [concept,circle,myball-right color=violet](c22){Child 2-2}}
child {node [concept,circle,myball-right color=violet](c22){Child 1-3}}
};
\end{tikzpicture}
\end{document}
This leads to:

Notice the external circle, very evident in the orange concepts.