[pstricks] Simulated random walks and Brownian motions

[Herbert Voss]

John Harris schrieb:
>  
> I am relatively new to PSTricks and would greatly appreciate some help 
> trying to draw simulated random walks and Brownian motions. Presumably 
> if I could do a random walk then scaling down the step size would 
> produce a passable Brownian motion but I have not been able to get 
> anything to work so far.
>  
> Any hints anyone has would be great thanks.

I need it some time ago to show a kind of chaotic
behaviour and I did it in this way. The point could
only move one pixel left/right/up/down

Herbert

\documentclass{article}
\usepackage{pst-plot}
\makeatletter
\def\pstRandomWalk{\@ifnextchar[{\pst at RandomWalk}{\pst at RandomWalk[]}}
% #1 options which are passed to pstricks
% #2,#3 the starting point
% #4 the number of points
\def\pst at RandomWalk[#1](#2,#3)#4{%
	\psset{#1}
	\doRandomWalk(#2,#3){#4}
}
\def\doRandomWalk{%
	\def\pst at par{}
	\pst at object{psRandomWalk}%
}
\def\psRandomWalk at i(#1,#2)#3{%
   \pst at killglue
   \begingroup
     \use at par
     \@nameuse{beginplot@\psplotstyle}%
     \addto at pscode{%
       \psplot at init
       /plotPoints #3 def
       /x #1 def
       /y #2 def
       /xyWalk {
		/xRandom rand 3 mod 1 sub def
		/yRandom rand 3 mod 1 sub def
		/x x xRandom add def
		/y y yRandom add def
		x y} def
       }%
     \gdef\psplot at init{}%
     \@nameuse{testqp@\psplotstyle}%
     \psRandomWalk at ii
   \endgroup
   \ignorespaces%
}
\def\psRandomWalk at ii{%
     \addto at pscode{%
       xyWalk \@nameuse{beginqp@\psplotstyle}
       xyWalk moveto
       plotPoints {
           xyWalk \@nameuse{doqp@\psplotstyle}
	 } repeat
       xyWalk \@nameuse{doqp@\psplotstyle}
	}
   \@nameuse{endqp@\psplotstyle}%
}
\makeatother
\begin{document}
\begin{pspicture}(-3,-3)(3,3)
	\psframe(-3,-3)(3,3)
	\pstRandomWalk[plotstyle=line, linewidth=0.5pt](0,0){5000}
\end{pspicture}
\end{document}