How draw “nested” mathemathical sets?

Question

I want to represent mathematical sets of number (R,Z,N) using nested circles like this:

This was very quickly created with gimp, but I am trying to do it properly in tikz but having some issue mainly to place circles and associated labels. I need a solution able to scale. What placement strategy should I use, I tried with

above =2

etc but it doesn't scale properly ?

Answer 1

Here's one option using circle \nodes and the positioning library to place the labels; scale=<factor>,transform shape gives you scaling:

\documentclass{article} 
\usepackage{amssymb} 
\usepackage{tikz} 
\usetikzlibrary{positioning}

\tikzset{set/.style={draw,circle,inner sep=0pt,align=center}}

\begin{document} 

\begin{tikzpicture}
\node[set,fill=blue!20,text width=3cm,label={[below=85pt of rea,text opacity=1]$\mathbb{R}$}] 
  (nat) at (0,-0.4)  (rea) {};
\node[set,fill=red!20,text width=2cm,label={[below=55pt of int]$\mathbb{Z}$}] 
  (int) at (0,-0.2)  {};
\node[set,fill=olive!20,text width=1cm] (nat) at (0,0) {$\mathbb{N}$};
\end{tikzpicture}

\begin{tikzpicture}[scale=0.7,transform shape]
\node[set,fill=blue!20,text width=3cm,label={[below=85pt of rea]$\mathbb{R}$}] 
  (nat) at (0,-0.4)  (rea) {};
\node[set,fill=red!20,text width=2cm,label={[below=55pt of int]$\mathbb{Z}$}] 
  (int) at (0,-0.2)  {};
\node[set,fill=olive!20,text width=1cm] (nat) at (0,0) {$\mathbb{N}$};
\end{tikzpicture}

\begin{tikzpicture}[scale=2.5,transform shape]
\node[set,fill=blue!20,text width=3cm,label={[below=85pt of rea]$\mathbb{R}$}] 
  (nat) at (0,-0.4)  (rea) {};
\node[set,fill=red!20,text width=2cm,label={[below=55pt of int]$\mathbb{Z}$}] 
  (int) at (0,-0.2)  {};
\node[set,fill=olive!20,text width=1cm] (nat) at (0,0) {$\mathbb{N}$};
\end{tikzpicture}

\end{document}

Answer 2

Here is a solution using positioning, fit, and backgrounds libraries.

The preamble:

\documentclass{standalone}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{positioning,fit,backgrounds}

The \drawnestedsets macro:

\newcommand\drawnestedsets[4]{
  % initial position
  \def\position{#1}
  % number of sets
  \def\nbsets{#2}
  % list of sets
  \def\listofnestedsets{#3}
  % reversed list of colors
  \def\reversedlistofcolors{#4}

  % position and draw labels of sets
  \coordinate (circle-0) at (#1);
  \coordinate (set-0) at (#1);
  \foreach \set [count=\c] in \listofnestedsets {
    \pgfmathtruncatemacro{\cminusone}{\c - 1}
    % label of current set (below previous nested set)
    \node[below=3pt of circle-\cminusone,inner sep=0]
    (set-\c) {$\mathbb{\set}$};
    % current set (fit current label and previous set)
    \node[circle,inner sep=0,fit=(circle-\cminusone)(set-\c)]
    (circle-\c) {};
  }

  % draw and fill sets in reverse order
  \begin{scope}[on background layer]
    \foreach \col[count=\c] in \reversedlistofcolors {
      \pgfmathtruncatemacro{\invc}{\nbsets-\c}
      \pgfmathtruncatemacro{\invcplusone}{\invc+1}
      \node[circle,draw,fill=\col,inner sep=0,
      fit=(circle-\invc)(set-\invcplusone)] {};
    }
  \end{scope}
}

The document:

\begin{document}
\begin{tikzpicture}
  \drawnestedsets{0,0}{4}{N,Z,R,C}{lime,orange,yellow,cyan}

  \begin{scope}[font=\tiny]
    \drawnestedsets{2,0}{3}{N,Z,R}{orange,yellow,cyan}
  \end{scope}
\end{tikzpicture}
\end{document}

Edit: Here is an horizontal variant with ellipses:

And the code (note: the \drawnestedsets macro is a modified version):

\documentclass{standalone}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{positioning,fit,backgrounds,shapes.geometric}

\newcommand\drawnestedsets[4]{
  % initial position
  \def\position{#1}
  % number of sets
  \def\nbsets{#2}
  % list of sets
  \def\listofnestedsets{#3}
  % reversed list of colors
  \def\reversedlistofcolors{#4}

  % position and draw labels of sets
  \coordinate (circle-0) at (#1);
  \coordinate (set-0) at (#1);
  \foreach \set [count=\c] in \listofnestedsets {
    \pgfmathtruncatemacro{\cminusone}{\c - 1}
    % label of current set (below previous nested set)
    \node[right=3pt of circle-\cminusone,inner sep=0]
    (set-\c) {$\mathbb{\set}$};
    % current set (fit current label and previous set)
    \node[ellipse,inner sep=0,fit=(circle-\cminusone)(set-\c)]
    (circle-\c) {};
  }

  % draw and fill sets in reverse order
  \begin{scope}[on background layer]
    \foreach \col[count=\c] in \reversedlistofcolors {
      \pgfmathtruncatemacro{\invc}{\nbsets-\c}
      \pgfmathtruncatemacro{\invcplusone}{\invc+1}
      \node[ellipse,draw,fill=\col,inner sep=0,
      fit=(circle-\invc)(set-\invcplusone)] {};
    }
  \end{scope}
}

\begin{document}
\begin{tikzpicture}
  \drawnestedsets{0,0}{4}{N,Z,R,C}{lime,orange,yellow,cyan}

  \begin{scope}[font=\tiny]
    \drawnestedsets{0,-1}{3}{N,Z,R}{orange,yellow,cyan}
  \end{scope}
\end{tikzpicture}
\end{document}