Diagrama de árbol al revés

Question

Amigos, he intentado configurar el siguiente diagrama con los comandos tikzpicture\node\child pero no logro dibujarlo. ¿Puedes ayudarme?

Gracias.

\documentclass[tikz,margin=2mm]{standalone}
\usetikzlibrary{trees,arrows}
\begin{document}
\tikzstyle{level 1}=[level distance=30mm, sibling distance=30mm]
\tikzstyle{level 2}=[level distance=30mm, sibling distance=15mm]
\tikzstyle{level 3}=[level distance=20mm]
\begin{tikzpicture}[grow=right,-,=angle 60]
%\begin{scope}[yshift=0]
  \node {$f_{0,0}$}
    child {node {$f_{2,2}$}
      child {node {$f_{3,2}$}
        child[-] {node{$x_{3}$}}  
      }
      child {node{$f_{3,1}$}
        child[-] {node{$x_{2}$}}  
      }
    }
    child {node {$f_{2,1}$}
      child {node{$f_{3,2}$}
        child[-] {node{$x_{1}$}}  
      }
      child {node{$f_{3,1}$}
        child[-] {node{$x_{0}$}}  
      }
    };
%\end{scope}
\begin{scope}[yshift=-6cm]
  \node {$f_{1,2}$}
    child {node {$f_{2,2}$}
      child {node {$f_{3,2}$}
        child[-] {node{$x_{7}$}}  
      }
      child {node {$f_{3,1}$}
        child[-] {node{$x_{6}$}}  
      }
    }
    child {node {$f_{2,1}$}
      child {node {$f_{3,2}$}
        child[-] {node{$x_{5}$}}
      }
      child {node {$f_{3,1}$}
        child[-] {node{$x_{4}$}}  
      }
    };
\end{scope}

\end{tikzpicture}
\end{document}

Answer 1

Como menciona Alan Munn, esto no es realmente un árbol,una matriz puede ser una mejor opción. Estas matrices se pueden producir de forma bastante cómoda con tikz-cd. Para encerrar algunas subexpresiones en los elementos de la matriz, se puede utilizar \subnodelo que viene con tikzmark.

\documentclass{article}
\usepackage[margin=1in]{geometry}   
\usepackage{mathtools}
\usepackage{tikz-cd}
\usetikzlibrary{shapes.geometric,tikzmark,fit}
\begin{document}
\newcommand{\ARR}{\arrow[ul]\arrow[dl]}
\begin{tikzcd}[column sep=1ex,row sep=0pt,
    every arrow/.append style={dash,shorten >=-2pt,shorten <=-2pt},
    /tikz/remember picture]
 x_1 & \subnode{red}{y_1} & & & & & \\
  &  & \subnode{orange}{y_{21}}=\dfrac{y_{2}-y_{1}}{x_2-x_1} \arrow[ul]\arrow[dl] & & & & \\
 x_2 & y_2 & &  \subnode{yellow}{y_{321}}=\dfrac{y_{32}-y_{21}}{x_3-x_1} \arrow[ul]\arrow[dl] & & \\
  &  & y_{32}=\dfrac{y_{3}-y_{2}}{x_3-x_2} \arrow[ul]\arrow[dl]& & 
  \subnode{green}{y_{4321}}=\dfrac{y_{432}-y_{321}}{x_4-x_1} \arrow[ul]\arrow[dl] & \\
 x_3 & y_3 & &  y_{432}=\dfrac{y_{43}-y_{32}}{x_4-x_2} \arrow[ul]\arrow[dl] & & \subnode{blue}{y_{54321}}=\dfrac{y_{5432}-y_{4321}}{x_5-x_1}\arrow[ul]\arrow[dl] \\
  &  & y_{43}=\dfrac{y_{4}-y_{3}}{x_4-x_3} \arrow[ul]\arrow[dl]& & 
  y_{5432}=\dfrac{y_{543}-y_{432}}{x_5-x_2} \arrow[ul]\arrow[dl] & \\
 x_4 & y_4 & & y_{543}=\dfrac{y_{54}-y_{43}}{x_5-x_3} \arrow[ul]\arrow[dl]  & & & \\
  &  &y_{54}=\dfrac{y_{5}-y_{4}}{x_5-x_4} \arrow[ul]\arrow[dl]& && & \\
 x_5 & y_5 & & & & & \\
\end{tikzcd}
\begin{tikzpicture}[remember picture,overlay]
\foreach \X in {red,green,blue,orange,yellow}
 {\node[draw,ellipse,inner ysep=-2pt,inner xsep=-4pt,fit=(\X),color=\X]{};}
\end{tikzpicture}
\end{document}

Answer 2

El siguiente MWE (que es una versión ligeramente modificada y adaptada de unrespuesta anterior similar mía) podría servir como punto de partida:

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}

\begin{document}


\begin{tikzpicture}[grow=left, 
                    sibling distance=50pt,
                    level distance=2cm,
                    edge from parent path={(\tikzparentnode.west) -- (\tikzchildnode.east)}]
    \node {$y_{21} = \dfrac{y_2 - y_1}{x_2 - x_1}$}
    child {node {$y_1$}}
    child {node {$y_2$}}
    ;
\end{tikzpicture}
\end{document}

Aquí hay una variante coloreada:

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}

\usetikzlibrary{shapes}

\newcommand{\highlighted}[2]{\tikz[remember picture,baseline=-2pt]\node[rounded rectangle,draw=#1,text=black,anchor=center]{$#2$};}

\begin{document}

\begin{tikzpicture}[grow=left, 
                    sibling distance=50pt,
                    level distance=2cm,
                    edge from parent path={(\tikzparentnode.west) -- (\tikzchildnode.east)}]
    \node {$\highlighted{orange}{y_{21}}{} = \dfrac{y_2 - y_1}{x_2 - x_1}$}
    child {node{\highlighted{red}{y_1}}}
    child {node {$y_2$}}
    ;
\end{tikzpicture}

\end{document}

Answer 3

\documentclass[tikz,margin=2mm]{standalone}
\usetikzlibrary{trees,arrows}
\begin{document}
\tikzstyle{level 1}=[level distance=30mm, sibling distance=30mm]
\tikzstyle{level 2}=[level distance=30mm, sibling distance=15mm]
\tikzstyle{level 3}=[level distance=20mm]
\begin{tikzpicture}[grow=right,-,=angle 60]
%\begin{scope}[yshift=0]
  \node {$f_{0,0}$}
    child {node {$f_{2,2}$}
      child {node {$f_{3,2}$}
        child[-] {node{$x_{3}$}}  
      }
      child {node{$f_{3,1}$}
        child[-] {node{$x_{2}$}}  
      }
    }
    child {node {$f_{2,1}$}
      child {node{$f_{3,2}$}
        child[-] {node{$x_{1}$}}  
      }
      child {node{$f_{3,1}$}
        child[-] {node{$x_{0}$}}  
      }
    };
%\end{scope}
\begin{scope}[yshift=-6cm]
  \node {$f_{1,2}$}
    child {node {$f_{2,2}$}
      child {node {$f_{3,2}$}
        child[-] {node{$x_{7}$}}  
      }
      child {node {$f_{3,1}$}
        child[-] {node{$x_{6}$}}  
      }
    }
    child {node {$f_{2,1}$}
      child {node {$f_{3,2}$}
        child[-] {node{$x_{5}$}}
      }
      child {node {$f_{3,1}$}
        child[-] {node{$x_{4}$}}  
      }
    };
\end{scope}

\end{tikzpicture}
\end{document