%% 
%%  Ein Beispiel der DANTE-Edition
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%%  7. Auflage
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%%  Beispiel 32-02-46 auf Seite 723.
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%%  Copyright (C) 2016 Herbert Voss
%% 
%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%% 
%%  See http://www.latex-project.org/lppl.txt for details.
%% 
%% 
%% ==== 
% Show page(s) 1
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\documentclass[]{exaarticle}
\pagestyle{empty}
\setlength\textwidth{352.81416pt}
\setlength\parindent{0pt}
%StartShownPreambleCommands
\usepackage{pst-ode,pst-3dplot}
%StopShownPreambleCommands
\begin{document}
\pstVerb{/alpha 10 def  /beta 28 def  /gamma 8 3 div def }%
\pstODEsolve[algebraic,saveData]{lorenzXYZ}{0 1 2}{0}{25}{2501}{10 10 30}{%
  alpha*(x[1]-x[0]) | x[0]*(beta-x[2]) - x[1] | x[0]*x[1] - gamma*x[2] }
\begin{pspicture}(-6,-2)(6,10)
\psset{unit=0.17cm,Alpha=160,Beta=15} \listplotThreeD[linecolor=blue]{lorenzXYZ}
\psset{unit=0.425cm,linestyle=dashed}
\pstThreeDNode(0,0,0){O} \pstThreeDNode(0,0,5){Z} \pstThreeDNode(5,0,0){X}
\pstThreeDNode(0,5,0){Y} \pstThreeDNode(-10,-10,0){A}
\pstThreeDNode(-10,-10,20){B}\pstThreeDNode(-10,10,20){C}
\pstThreeDNode(-10,10,0){D}  \pstThreeDNode(10,-10,0){E}
\pstThreeDNode(10,-10,20){F} \pstThreeDNode(10,10,20){G}
\pstThreeDNode(10,10,0){H}   \pspolygon(A)(B)(C)(D) \pspolygon(E)(F)(G)(H)
\psline(A)(E) \psline(B)(F) \psline(D)(H) \psline(C)(G)
\psset{linestyle=solid,linecolor=red}
\psline{->}(O)(X) \psline{->}(O)(Y) \psline{->}(O)(Z)
\end{pspicture}
\end{document}
