[Tex/LaTex] Highlighting some nodes of a TikZ binomial tree

highlightingnodestikz-pgftikz-trees

In this binomial tree I have 4 columns of nodes.

I want the entire last column to be highlighted with light blue, and perhaps a border around this highlighting. Something like a opaque blue-ish rectangle or thin oval highlighting the entire last column of nodes.

Just started with TikZ and nothing is working so far.

I'm using pdfLaTeX.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}

   \begin{tikzpicture}[>=stealth,sloped]
      \matrix (tree) [%
        matrix of nodes,
        minimum size=1cm,
        column sep=3.5cm,
        row sep=1cm,
      ]
      {
                &                    &                     &  $^\tau S_0$     \\
                &                    &  $^{2\Delta t}S_0$  &              \\
                & $^{\Delta t}S_0$   &                     &  $^\tau S_1$     \\
        $^0S_0$ &                    &  $^{2\Delta t}S_1$  &              \\
                & $^{\Delta t}S_1$  &                      &  $^\tau S_2$     \\
                &                    &  $^{2\Delta t}S_2$  &              \\
                &                    &                     &  $^\tau S_2$     \\
      };
      \draw[->] (tree-4-1) -- (tree-3-2) node [midway,above] {$p$};
      \draw[->] (tree-4-1) -- (tree-5-2) node [midway,below] {$1-p$};
      \draw[->] (tree-3-2) -- (tree-2-3) node [midway,above] {};
      \draw[->] (tree-3-2) -- (tree-4-3) node [midway,below] {};
      \draw[->] (tree-5-2) -- (tree-4-3) node [midway,above] {};
      \draw[->] (tree-5-2) -- (tree-6-3) node [midway,below] {};

    \draw[->] (tree-2-3) -- (tree-1-4) node [midway,above] {};
      \draw[->] (tree-2-3) -- (tree-3-4) node [midway,below] {};
      \draw[->] (tree-4-3) -- (tree-3-4) node [midway,above] {};
      \draw[->] (tree-4-3) -- (tree-5-4) node [midway,below] {};
      \draw[->] (tree-6-3) -- (tree-5-4) node [midway,above] {};
      \draw[->] (tree-6-3) -- (tree-7-4) node [midway,below] {};

    \end{tikzpicture}

\end{document}

Best Answer

Here are two solutions. First solution uses column 4 style to add a border and to fill each node in fourth column of your matrix. Second solution uses fit and background libraries to put a new node on background fitting tree-1-4 and tree-7-4 nodes.

enter image description here

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{matrix,fit,backgrounds}
\begin{document}
\begin{tikzpicture}[>=stealth,sloped]
  \matrix (tree) [%
  matrix of nodes,
  minimum size=1cm,
  column sep=3.5cm,
  row sep=1cm,
  % fill and draw each node of fourth column 
  column 4/.style={nodes={draw,fill=cyan!30,rounded corners}},
  ]
  {
            &                  &                   & $^\tau S_0$ \\
            &                  & $^{2\Delta t}S_0$ &             \\
            & $^{\Delta t}S_0$ &                   & $^\tau S_1$ \\
    $^0S_0$ &                  & $^{2\Delta t}S_1$ &             \\
            & $^{\Delta t}S_1$ &                   & $^\tau S_2$ \\
            &                  & $^{2\Delta t}S_2$ &             \\
            &                  &                   & $^\tau S_2$ \\
  };
  \draw[->] (tree-4-1) -- (tree-3-2) node [midway,above] {$p$};
  \draw[->] (tree-4-1) -- (tree-5-2) node [midway,below] {$1-p$};
  \draw[->] (tree-3-2) -- (tree-2-3) node [midway,above] {};
  \draw[->] (tree-3-2) -- (tree-4-3) node [midway,below] {};
  \draw[->] (tree-5-2) -- (tree-4-3) node [midway,above] {};
  \draw[->] (tree-5-2) -- (tree-6-3) node [midway,below] {};

  \draw[->] (tree-2-3) -- (tree-1-4) node [midway,above] {};
  \draw[->] (tree-2-3) -- (tree-3-4) node [midway,below] {};
  \draw[->] (tree-4-3) -- (tree-3-4) node [midway,above] {};
  \draw[->] (tree-4-3) -- (tree-5-4) node [midway,below] {};
  \draw[->] (tree-6-3) -- (tree-5-4) node [midway,above] {};
  \draw[->] (tree-6-3) -- (tree-7-4) node [midway,below] {};

  % put a new node on background fitting (tree-1-4) and (tree-7-4) nodes
  \begin{scope}[on background layer]
    \node[fit=(tree-1-4)(tree-7-4),
    fill=blue!20,rounded corners,draw=blue,line width=1pt]{};
  \end{scope}
\end{tikzpicture}
\end{document}

Edit: Here is another method to position your nodes (using positioning instead of matrix).

enter image description here

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning,fit,backgrounds}
\begin{document}
\begin{tikzpicture}[>=stealth,sloped]
  \tikzset{
    on grid,
    node distance=1cm and 3.5cm,
    col4/.style={fill=cyan!20,draw,rounded corners},
    every node/.style={minimum size=1cm},
  }
  % first column
  \node (n-0-0) at (-5,-3) {$^0S_0$};

  % second column
  \node[above right=of n-0-0] (n-1-0) {$^{\Delta t}S_0$};
  \node[below right=of n-0-0] (n-1-1) {$^{\Delta t}S_1$};

  % third column
  \node[above right=of n-1-0] (n-2-0) {$^{2\Delta t}S_0$};
  \node[below right=of n-1-0] (n-2-1) {$^{2\Delta t}S_1$};
  \node[below right=of n-1-1] (n-2-2) {$^{2\Delta t}S_2$};

  % fourth column
  \node[col4,above right=of n-2-0] (n-3-0) {$^{\tau}S_0$};
  \node[col4,below right=of n-2-0] (n-3-1) {$^{\tau}S_1$};
  \node[col4,below right=of n-2-1] (n-3-2) {$^{\tau}S_2$};
  \node[col4,below right=of n-2-2] (n-3-3) {$^{\tau}S_2$};

  \draw[->] (n-0-0) -- (n-1-0) node [midway,above] {$p$};
  \draw[->] (n-0-0) -- (n-1-1) node [midway,below] {$1-p$};
  \foreach \col in {1,2}{
    \pgfmathtruncatemacro{\nextcol}{\col+1}
    \foreach \line in {0,...,\col}{
      \pgfmathtruncatemacro{\nextline}{\line + 1}
      \draw[->] (n-\col-\line) -- (n-\nextcol-\line);
      \draw[->] (n-\col-\line) -- (n-\nextcol-\nextline);
    }
  }

  \begin{scope}[on background layer]
    \node[fit=(n-3-0)(n-3-3),inner sep=.5em,
    fill=blue!20,rounded corners,draw=blue,line width=1pt]{};
  \end{scope}
\end{tikzpicture}
\end{document}

Related Solutions

[Tex/LaTex] Highlight a group of nodes in a tikz tree

You can use Jake's answer to padded boundary of convex hull and layers:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows,backgrounds,calc,trees}

\pgfdeclarelayer{background}
\pgfsetlayers{background,main}


\newcommand{\convexpath}[2]{
[   
    create hullnodes/.code={
        \global\edef\namelist{#1}
        \foreach [count=\counter] \nodename in \namelist {
            \global\edef\numberofnodes{\counter}
            \node at (\nodename) [draw=none,name=hullnode\counter] {};
        }
        \node at (hullnode\numberofnodes) [name=hullnode0,draw=none] {};
        \pgfmathtruncatemacro\lastnumber{\numberofnodes+1}
        \node at (hullnode1) [name=hullnode\lastnumber,draw=none] {};
    },
    create hullnodes
]
($(hullnode1)!#2!-90:(hullnode0)$)
\foreach [
    evaluate=\currentnode as \previousnode using \currentnode-1,
    evaluate=\currentnode as \nextnode using \currentnode+1
    ] \currentnode in {1,...,\numberofnodes} {
  let
    \p1 = ($(hullnode\currentnode)!#2!-90:(hullnode\previousnode)$),
    \p2 = ($(hullnode\currentnode)!#2!90:(hullnode\nextnode)$),
    \p3 = ($(\p1) - (hullnode\currentnode)$),
    \n1 = {atan2(\y3,\x3)},
    \p4 = ($(\p2) - (hullnode\currentnode)$),
    \n2 = {atan2(\y4,\x4)},
    \n{delta} = {-Mod(\n1-\n2,360)}
  in 
    {-- (\p1) arc[start angle=\n1, delta angle=\n{delta}, radius=#2] -- (\p2)}
}
-- cycle
}

\begin{document}
\thispagestyle{empty}

\begin{tikzpicture}
\node (f) {f}
    child { node (g) {g} 
      child { node (a) {a}
    }
      child { node (b) {b}
    }
  }
    child { node (h) {h}
      child { node (c) {c}
    }
  };
\begin{pgfonlayer}{background}
\fill[red,opacity=0.3] \convexpath{a,g,b}{8pt};
\fill[blue,opacity=0.3] \convexpath{g,f,h,c,h,f}{8pt};
\end{pgfonlayer}
\end{tikzpicture}

\end{document}

enter image description here

[Tex/LaTex] How to define the default vertical distance between nodes

I don't really get the question so I hope this is what you wanted. If you include a full document (such that we copy paste and see the problem on our systems) things are much more easier.

Here, you can change the default setting within a scope but your block style had a node distance which was resetting every time it is issued. I've made it 2mm such that we can see the difference easier.

\documentclass[tikz]{standalone}
\usetikzlibrary{arrows,shapes.geometric,positioning}

\begin{document}
\begin{tikzpicture}[decision/.style={diamond, draw, text width=4.5em, text badly centered, node distance=3.5cm, inner sep=0pt},
                    block/.style   ={rectangle, draw, text width=6em, text centered, rounded corners, minimum height=4em, minimum height=2em},
                    cloud/.style   ={draw, ellipse, minimum height=2em},
                    line/.style    ={draw,-latex'},
                    node distance = 1cm, 
                    auto]
    \node [block] (1st) {1st};
    \node [block, right= of 1st]  (2nd1) {2nd1};
\begin{scope}[node distance=2mm and 10mm]%Here we change it for everything inside this scope
    \node [block, above= of 2nd1] (2nd2) {2nd2};
    \node [block, below= of 2nd1] (2nd3) {2nd3};
    \node [block, right= of 2nd1] (3rd1) {3rd1};
    \node [block, above= of 3rd1] (3rd2) {3rd2};
    \node [block, above= of 3rd2] (3rd3) {3rd3};
\end{scope}
    \node [block, below= of 3rd1] (3rd4) {3rd4};
    \node [block, below= of 3rd4] (3rd5) {3rd5};

    \path [line] (1st) -- (2nd1);
    \path [line] (2nd1) -- (2nd2);
    \path [line] (2nd1) -- (2nd3);
    \path [line] (2nd2) -- (3rd3);
    \path [line] (2nd1) -- (3rd1);
    \path [line] (1st) -- (2nd1);
\end{tikzpicture}
\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] Highlight a group of nodes in a tikz tree

[Tex/LaTex] How to define the default vertical distance between nodes

Related Question