Cuerdas y arpas para dibujar.

Question

Me gustaría hacer un dibujo similar al siguiente dibujado a mano:

Con etiquetas $0$, $1$, $\Psi_{L,S}$, $a_1$, $\ell_i + 2\varepsilon$, $\Psi_{L,H}$, $b_1$, $-\varepsilon$, $1 + \varepsilon$, $\Psi_{L,S}$, $a_2$, $b_N : \mathbb{N}^{*} \setminus \mathbb{N}$, $-t$, $t + 1$, y $\Psi_{L,H}$.

Las tres figuras de la línea discontinua deberían verse iguales que

sin las etiquetas numéricas, pero con las respectivas etiquetas de punto final.

Para dibujar la segunda figura, consulte una publicación anterior:¿Cómo trazar un gráfico de barras de valores en descomposición?

Las longitudes son 1/3, 1/9, 1/9, 1/27, 1/27, 1/27 y 1/27.

Cualquier código sucinto sería muy apreciado.

Answer 1

Una opción:

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

\newlength\mylen
\setlength\mylen{3pt}

\newcommand\Mdot{%
  \hspace*{2pt}\rule{1pt}{.4pt}\hspace*{2pt}}
\newcommand\Mrule[1]{\rule{#1}{0.4pt}}
\newcommand\MDot{\Mdot\Mrule{\mylen}\Mdot}
\newcommand\MSet{%
  \rule[-4pt]{.4pt}{8pt}%
  \MDot\Mrule{3\mylen}%
  \MDot\Mrule{9\mylen}%
  \MDot\Mrule{27\mylen}%
  \MDot\Mrule{9\mylen}%
  \MDot\Mrule{3\mylen}%
  \MDot%
  \rule[-4pt]{.4pt}{8pt}%
}

\begin{document}

\begin{tikzpicture}
\node[inner sep=0pt,anchor=west] (topset)
  {\MSet};
\node at ([yshift=-10pt]topset.west) {$0$};  
\node at ([yshift=-10pt]topset.east) {$1$};
\node at ([yshift=-25pt]topset.east) {$\Psi_{L,H}$};
\begin{scope}[yshift=-3cm]
\foreach \Pos/\Len in {0/3cm,1/2cm,2/2cm,3/1cm,4/1cm,5/1cm,6/1cm}
  \draw[|-|] (\Pos,0) -- ++(0,-\Len); 
\node at (6.8cm,-0.5cm) {$\dots$};
\end{scope}   
\begin{scope}[yshift=-9cm]
\node[inner sep=0pt,anchor=west] (middleset)
  {\MSet};
\node at ([yshift=-10pt]middleset.west) {$-\varepsilon$};  
\node at ([yshift=-10pt]middleset.east) {$1+\varepsilon$};
\node at ([yshift=-25pt]middleset.east) {$\Psi_{L,H}$};
\end{scope}
\begin{scope}[yshift=-14cm]
\node[inner sep=0pt,anchor=west] (bottomset)
  {\MSet};
\node at ([yshift=-10pt]bottomset.west) {$-t$};  
\node at ([yshift=-10pt]bottomset.east) {$t+1$};
\node at ([yshift=-25pt]bottomset.east) {$\Psi_{L,H}$};
\end{scope}

\draw[->] 
  ([yshift=-1cm]topset.center) -- node[right] {$a_{1}$} ++(0,-1cm);
\node at 
  ([yshift=2.5cm]middleset.center) {$\ell +2\varepsilon$};
\draw[->] 
  ([yshift=2cm]middleset.center) -- node[right] {$b_{1}$} ++(0,-1cm);
\draw[->] 
  ([yshift=-1cm]middleset.center) -- node[right] {$a_{2}$} ++(0,-1cm);
\node[rotate=90] at ([yshift=-2.5cm]middleset.center) {$\dots$};  
\draw[->] 
  ([yshift=-3cm]middleset.center) -- node[right] {$b_{N}:N\in\mathbb{N}\sp{\ast}\setminus\mathbb{N}$} ++(0,-1cm);
\end{tikzpicture}

\end{document}

Answer 2

Misma idea que @Gonzalo, implementación ligeramente diferente y con etiquetas y puntos suspensivos.

\documentclass{standalone}

\usepackage{tikz,amssymb}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}
%% Horizontal sections
% Bottom section
\node (-t) at (0,0) {$-t$};
\node (t1) at (6,0) {$t+1$};
\draw (0,.3)--(0,.8) (6,.3)--(6,.8);
\draw (.1,.55)--(5.9,.55);
\foreach \x in {.15,.55,1.25,1.65}{
  \draw[fill=black,draw=white,line width=2pt] (\x,.55) circle (.05);
  \draw[fill=black,draw=white,line width=2pt] (6-\x,.55) circle (.05);
}
\node at (5,-.5) {$\psi_{L,S}$};
% First middle section
\begin{scope}[shift={(0,4.5)}]
\node (-e) at (0,0) {$-\varepsilon$};
\node (e1) at (6,0) {$\varepsilon+1$};
\draw (0,.3)--(0,.8) (6,.3)--(6,.8);
\draw (.1,.55)--(5.9,.55);
\foreach \x in {.15,.55,1.25,1.65}{
  \draw[fill=black,draw=white,line width=2pt] (\x,.55) circle (.05);
  \draw[fill=black,draw=white,line width=2pt] (6-\x,.55) circle (.05);
}
\node at (5,-.5) {$\psi_{L,S}$};
\end{scope}
% Second middle section
\begin{scope}[shift={(0,10)}]
\draw[|-|] (0,0)--(0,-2.5);
\draw[|-|] (.5,0)--(.5,-1.25);
\draw[|-|] (1,0)--(1,-1.25);
\draw[|-|] (1.5,0)--(1.5,-.625);
\draw[|-|] (2,0)--(2,-.625);
\draw[|-|] (2.5,0)--(2.5,-.625);
\draw[|-|] (3,0)--(3,-.625);
\node at (3.5,-.3125) {$\cdots$};
\node at (5,-1.3) {$\psi_{L,H}$};
\node at (1,-2.5) {$\varphi + 2\varepsilon$};
\coordinate (b0) at (0,0);
\coordinate (b1) at (6,0);
\end{scope}
% Top 
\begin{scope}[shift={(0,12)}]
\node (0) at (0,0) {0};
\node (1) at (6,0) {1};
\draw (0,.3)--(0,.8) (6,.3)--(6,.8);
\draw (.1,.55)--(5.9,.55);
\foreach \x in {.15,.55,1.25,1.65}{
  \draw[fill=black,draw=white,line width=2pt] (\x,.55) circle (.05);
  \draw[fill=black,draw=white,line width=2pt] (6-\x,.55) circle (.05);
}
\node at (5,-.5) {$\psi_{L,S}$};
\end{scope}
%% Arrows
\draw[->,shorten >=.5cm] ($(0)!.5!(1)$) to node[right=5pt,pos=.45] {$a_1$} ($(b0)!.5!(b1)$);
\draw[->,shorten <=3cm,shorten >=1cm] ($(b0)!.5!(b1)$) to node[right=5pt,pos=.7] {$b_1$} ($(-e)!.5!(e1)$);
\draw[->] ($(-e)!.5!(e1)$) to node[right=5pt] {$a_2$} +(270:1.2);
\node at ($($(-e)!.5!(e1)$)!.33!($(-t)!.5!(t1)$)$) {$\vdots$};
\draw[->] ($($(-e)!.5!(e1)$)+(270:2)$) to node[right=5pt] {$b_N; N\in \mathbb N^*\setminus\mathbb N'$} +(270:1.2);
\end{tikzpicture}

\end{document}

Se ve como esto:

Edición rapida:Cambió la línea discontinua a puntos suspensivos y ajustó el posicionamiento.