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+\documentclass{article}
+
+\usepackage{pstricks} % To use the standard "color" package with PSTricks
+\usepackage{multido}
+\input{random.tex} % From Donald Arseneau (on macros/generic on CTAN)
+
+\newdimen\dX
+\newdimen\dY
+\newdimen\Coor
+
+% Random walk in the unit square (#1 = number of steps)
+\def\RandomWalk#1{%
+\setrandim\dX{0pt}{1pt}
+\setrandim\dY{0pt}{1pt}
+\psdot[dotstyle=*,dotsize=6pt](\pointless\dX,\pointless\dY) % Initial point
+\pscustom{%
+ \moveto(\pointless\dX,\pointless\dY) % Move to initial point
+ \multido{\i=1+1}{#1}{%
+ \MoveCoordinate{\dX}
+ \MoveCoordinate{\dY}
+ \lineto(\pointless\dX,\pointless\dY)}}} % Line between old and new position
+
+% Computation of new horizontal or vertical position of point
+\def\MoveCoordinate#1{%
+\setrandim\Coor{-0.06pt}{0.06pt} % The move
+\advance #1 by \Coor % New position
+% To stay in the square...
+\ifdim#1>1pt
+ #1=1pt
+\fi
+\ifdim#1<0pt
+ #1=0pt
+\fi}
+
+\pagestyle{empty}
+\parindent=0pt
+
+\begin{document}
+
+\psset{unit=11,dimen=middle}
+\begin{pspicture}(1,1)
+ \psframe[linewidth=0.1pt](1,1)
+ \RandomWalk{300}
+ \psset{linecolor=red}
+ \RandomWalk{300}
+ \psset{linecolor=green}
+ \RandomWalk{300}
+\end{pspicture}
+
+\end{document}