Two examples

[Akos Valentinyi]

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Hi, 

if anybody is interested how to use simple ps codes within the
\pscustom environment to compute points repeatedly using some
algorithm, and then connect, here are two examples

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*- Mode: Latex -*-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Dynamic1.tex --- Dynamical systems: a stable scalar system
x_{t+1}=f(x_t)
%% 
%% Author          : Akos Valentinyi (University of Southampton -- UK)
%%                                <av2 at soton.ac.uk>
%% Created the     : 20.11. 1997
%% Last mod. by    : 
%% Last mod. the   : 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\documentclass[12pt,a4paper]{article}
\usepackage{pstricks,pst-plot} 
\begin{document}


\psset{xunit=0.3in,yunit=0.3in,runit=0.3in,plotpoints=200,
       dash=4pt 4pt,linewidth=1.5pt,dotsep=4pt}  
\begin{pspicture}(0,0)(15,15)  
\psaxes[linewidth=1pt,labels=none,ticks=none]{-}(0,0)(0,0)(15,15) 
\uput{1ex}[180](0,14){$x_{t+1}$} 
\uput{1ex}[270](14,0){$x_t$} 
\SpecialCoor
\psplot{0}{15}{4 x 1 add ln mul} 
  \uput{1.75ex}[240](!15 4 15 1 add ln mul){$\psi(x_t)$} 
\psline(0,0)(15,15) 
  \uput{1ex}[180](15,15){$x_{t+1}=x_t$} 
\def\x{9.34665} 
  \qdisk(\x,\x){3pt} 
  \psline[linestyle=dashed](\x,0)(\x,\x) 
  \uput{1ex}[270](\x,0){$x$} 
  \uput{1ex}[135](!\x\space 4 \x\space 1 add ln mul){$\psi'(x)<1$}
\pscustom[linewidth=1.2pt,arrowscale=1.5]{
   \code{/x 1 def 
         /y 4 x 1 add ln mul def} 
      \multido{\i=1+1}{4}{
          \moveto(!x y) 
          \psline{->}(!x x)(!x y) \closepath 
          \psline{->}(!x y)(!y y) \closepath 
          \code{/x y def 
                /y 4 x 1 add ln mul def} 
      } 
   \code{/x 15 def 
         /y 4 x 1 add ln mul def} 
      \multido{\i=1+1}{2}{
          \moveto(!x y) 
          \psline{->}(!x x)(!x y) \closepath 
          \psline{->}(!x y)(!y y) \closepath 
          \code{/x y def 
                /y 4 x 1 add ln mul def} 
      } 
}
\end{pspicture} 

\end{document} 



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*- Mode: Latex -*-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Dynamic2.tex --- Dynamical system: an unstable scalar system
x_{t+1}=f(x_t)
%% 
%% Author          : Akos Valentinyi (University of Southampton -- UK)
%%                                <av2 at soton.ac.uk>
%% Created the     : 20.11. 1997
%% Last mod. by    : 
%% Last mod. the   : 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\documentclass[12pt,a4paper]{article}
\usepackage{pstricks,pst-plot} 
\begin{document}


\psset{xunit=0.3in,yunit=0.3in,runit=0.3in,plotpoints=200,
       dash=4pt 4pt,linewidth=1.5pt,dotsep=4pt}  
\begin{pspicture}(0,0)(15,15)  
\psaxes[linewidth=1pt,labels=none,ticks=none]{-}(0,0)(0,0)(15,15) 
\uput{1ex}[180](0,14){$x_{t+1}$} 
\uput{1ex}[270](14,0){$x_t$} 
\SpecialCoor
\psplot{0}{11}{2.71828 x 4 div exp 1 sub} 
  \uput{1.75ex}[180](!11 2.71828 11 4 div exp 1 sub){$\psi(x_t)$}
\psline(0,0)(15,15) 
  \uput{1ex}[180](15,15){$x_{t+1}=x_t$} 
\def\x{9.34665} 
  \qdisk(\x,\x){3pt} 
  \psline[linestyle=dashed](\x,0)(\x,\x) 
  \uput{1ex}[270](\x,0){$x$} 
  \uput{1ex}[135](!\x\space 2.71828 \x\space 4 div exp 1
sub){$\psi'(x)>1$} 
\pscustom[linewidth=1.2pt,arrowscale=1.5]{
   \code{/x 8.5 def 
         /y 2.71828 x 4 div exp 1 sub def} 
      \multido{\i=1+1}{4}{
          \moveto(!x y) 
          \psline{->}(!x x)(!x y) \closepath 
          \psline{->}(!x y)(!y y) \closepath 
          \code{/x y def 
                /y 2.71828 x 4 div exp 1 sub def} 
      } 
   \code{/x 9.9 def 
         /y 2.71828 x 4 div exp 1 sub def} 
      \multido{\i=1+1}{2}{
          \moveto(!x y) 
          \psline{->}(!x x)(!x y) \closepath 
          \psline{->}(!x y)(!y y) \closepath 
          \code{/x y def 
                /y 2.71828 x 4 div exp 1 sub def} 
      } 
}
\end{pspicture} 

\end{document} 




 
******************************************************************
Akos Valentinyi
Department of Economics
University of Southampton
Higfield
Southampton SO16 1BJ                      Phone: +44 1703 592536
United Kingdom                              Fax: +44 1703 593858
******************************************************************

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