\documentclass[a4paper]{article}
\usepackage{multido}
\usepackage{pstricks}

\input{random.tex}% From Donald Arseneau (CTAN:macros/generic/random.tex)

\newcount\NumberDots
\newdimen\DotSize
\newdimen\Hue
\newdimen\XPos
\newdimen\YPos

% Circle with dots at random positions
\def\CircleWithDotsA#1#2{%
% #1=radius of the circle
% #2=number of dots (put on the (-#1,-#1)(#1,#1) square,
%    not on the circle itself!)
\pspicture(-#1,-#1)(#1,#1)
  \setrannum{\NumberDots}{0}{#2}%
  \psclip{\pscircle{#1}}
    \multido{\iDots=1+1}{\NumberDots}{%
      \setrandim{\XPos}{-#1 pt}{#1 pt}%
      \setrandim{\YPos}{-#1 pt}{#1 pt}%
      \psdot(\pointless\XPos,\pointless\YPos)}
  \endpsclip
\endpspicture}

% Circle with dots at random positions, with random dot sizes
\def\CircleWithDotsB#1#2{%
% #1=radius of the circle
% #2=number of dots (put on the (-#1,-#1)(#1,#1) square,
%    not on the circle itself!)
\pspicture(-#1,-#1)(#1,#1)
  \setrannum{\NumberDots}{0}{#2}%
  \psclip{\pscircle{#1}}
    \multido{\iDots=1+1}{\NumberDots}{%
      \setrandim{\XPos}{-#1 pt}{#1 pt}%
      \setrandim{\YPos}{-#1 pt}{#1 pt}%
      \setrandim{\DotSize}{2pt}{15pt}%
      \psdot[dotsize=\DotSize](\pointless\XPos,\pointless\YPos)}
  \endpsclip
\endpspicture}

% Circle with dots at random positions, with random dot sizes
% and random colors
\def\CircleWithDotsC#1#2{%
% #1=radius of the circle
% #2=number of dots (put on the (-#1,-#1)(#1,#1) square,
%    not on the circle itself!)
\pspicture(-#1,-#1)(#1,#1)
  \setrannum{\NumberDots}{0}{#2}%
  \psclip{\pscircle{#1}}
    \multido{\iDots=1+1}{\NumberDots}{%
      \setrandim{\XPos}{-#1 pt}{#1 pt}%
      \setrandim{\YPos}{-#1 pt}{#1 pt}%
      \setrandim{\DotSize}{2pt}{15pt}%
      \setrandim{\Hue}{0pt}{1pt}%
      \definecolor{MyColor}{hsb}{\pointless\Hue,0.8,1}
      \psdot[dotsize=\DotSize,linecolor=MyColor]
            (\pointless\XPos,\pointless\YPos)}
  \endpsclip
\endpspicture}

\pagestyle{empty}
\parindent=0pt

\begin{document}

% To fix the random seed (otherwise the clock is used)
\randomi=123456
\begin{center}
\CircleWithDotsA{1}{10}
\psset{dotstyle=o}
\CircleWithDotsA{1}{50}
\psset{dotstyle=*}
\CircleWithDotsA{1}{100}
\psset{dotstyle=square}
\CircleWithDotsA{1}{1000}
\psset{dotstyle=square*}
\CircleWithDotsA{1}{1500}

%{\psset{dotscale=3,dotstyle=x}\CircleWithDotsA{3}{500}} % Bigger fixed dots

%\psset{dotstyle=+}
%\CircleWithDotsB{2}{10}
%\psset{dotstyle=B+}
%\CircleWithDotsB{2}{100}
%\CircleWithDotsB{2}{200}

\psset{dotstyle=|}
\CircleWithDotsC{1.75}{50}
\psset{dotstyle=x}
\CircleWithDotsC{1.75}{100}
\psset{dotstyle=oplus}
\CircleWithDotsC{1.75}{500}
\end{center}

\end{document}
