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%
% markov.tex -- Illustration markov-Kette
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usepackage{pgfplots}
\usepackage{csvsimple}
\usetikzlibrary{arrows,intersections,math}
\begin{document}
\def\skala{1}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\def\punkt#1#2#3{
\fill[color=white] #1 circle[radius=0.10];
\fill[color=#2] #1 circle[radius=0.13];
\node[color=white] at #1 {$\scriptstyle #3$};
}
\def\xs{2.5}
\def\ys{1}
\foreach \x in {0,...,5}{
\draw[color=red,line width=0.5pt]
({\x*\xs},{-0.7*\ys}) -- ({\x*\xs},{-8.5*\ys});
}
\def\dotradius{0.04}
\def\dotrow#1#2{
\punkt{({#1*\xs},{-1*\ys})}{#2}{1}
\punkt{({#1*\xs},{-2*\ys})}{#2}{2}
\fill[color=#2] ({#1*\xs},{-3*\ys-0.3}) circle[radius=\dotradius];
\fill[color=#2] ({#1*\xs},{-3*\ys-0.15}) circle[radius=\dotradius];
\fill[color=#2] ({#1*\xs},{-3*\ys}) circle[radius=\dotradius];
\fill[color=#2] ({#1*\xs},{-3*\ys+0.15}) circle[radius=\dotradius];
\fill[color=#2] ({#1*\xs},{-3*\ys+0.3}) circle[radius=\dotradius];
\punkt{({#1*\xs},{-4*\ys})}{#2}{7}
\punkt{({#1*\xs},{-5*\ys})}{#2}{8}
\punkt{({#1*\xs},{-6*\ys})}{#2}{9}
\fill[color=#2] ({#1*\xs},{-7*\ys-0.3}) circle[radius=\dotradius];
\fill[color=#2] ({#1*\xs},{-7*\ys-0.15}) circle[radius=\dotradius];
\fill[color=#2] ({#1*\xs},{-7*\ys}) circle[radius=\dotradius];
\fill[color=#2] ({#1*\xs},{-7*\ys+0.15}) circle[radius=\dotradius];
\fill[color=#2] ({#1*\xs},{-7*\ys+0.3}) circle[radius=\dotradius];
\punkt{({#1*\xs},{-8*\ys})}{#2}{s}
}
\def\fan#1#2{
\foreach \x in {1,2,4}{
\foreach \y in {1,2,4}{
\draw[->,shorten >= 2mm,shorten <= 2mm,color=#2]
({#1*\xs},{-\x*\ys})
--
({(#1+1)*\xs},{-\y*\ys});
}
}
\foreach \x in {5,6,8}{
\foreach \y in {5,6,8}{
\draw[->,shorten >= 2mm,shorten <= 2mm,color=#2]
({#1*\xs},{-\x*\ys})
--
({(#1+1)*\xs},{-\y*\ys});
}
}
}
\begin{scope}
\clip (-0.5,{-8.5*\ys}) rectangle ({5*\xs+0.5},-0.5);
\fan{-1}{gray}
\fan{0}{gray}
\fan{1}{gray}
\fan{2}{black}
\fan{3}{gray}
\fan{4}{gray}
\fan{5}{gray}
\end{scope}
\dotrow{0}{gray}
\dotrow{1}{gray}
\dotrow{2}{black}
\dotrow{3}{black}
\dotrow{4}{gray}
\dotrow{5}{gray}
\def\ty{-0.5}
\node[color=gray] at ({0.5*\xs},{\ty*\ys}) {$T(n-1,n-2)$};
\node[color=gray] at ({1.5*\xs},{\ty*\ys}) {$T(n,n-1)$};
\node[color=black] at ({2.5*\xs},{\ty*\ys}) {$T(n+1,n)$};
\node[color=gray] at ({3.5*\xs},{\ty*\ys}) {$T(n+2,n+1)$};
\node[color=gray] at ({4.5*\xs},{\ty*\ys}) {$T(n+3,n+2)$};
\draw[->,color=red] (-0.7,{-8.5*\ys}) -- ({5*\xs+0.7},{-8.5*\ys}) coordinate[label={$t$}];
\foreach \x in {0,...,5}{
\draw[color=red]
({\x*\xs},{-8.5*\ys-0.05})
--
({\x*\xs},{-8.5*\ys+0.05});
}
\node[color=red] at ({0*\xs},{-8.5*\ys}) [below] {$n-2\mathstrut$};
\node[color=red] at ({1*\xs},{-8.5*\ys}) [below] {$n-1\mathstrut$};
\node[color=red] at ({2*\xs},{-8.5*\ys}) [below] {$n\mathstrut$};
\node[color=red] at ({3*\xs},{-8.5*\ys}) [below] {$n+1\mathstrut$};
\node[color=red] at ({4*\xs},{-8.5*\ys}) [below] {$n+2\mathstrut$};
\node[color=red] at ({5*\xs},{-8.5*\ys}) [below] {$n+3\mathstrut$};
\end{tikzpicture}
\end{document}
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