Following code must be changed into an animation. In the code where the "foreach" is, will be corresponding to one frame for each number, given 20 frames in total. Hence, when the animation is running the line is been drawn in real time.
\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\path[use as bounding box] (0,0) rectangle (11.5,12);
\gdef\oldy{-2}
\foreach \x in {-2.9,-2.85,-2.8,...,-1.9}
{
\pgfmathsetmacro{\y}{0.2*rand-1.6}
\pgfmathsetmacro{\oldx}{\x-0.05}
\draw (\oldx+8.5,\oldy+11) -- (\x+8.5,\y+11);
\xdef\oldy{\y}
}
\end{tikzpicture}
\end{document}
The code so far. However, the line change for each iteration.
\documentclass{beamer}
\usepackage{tikz,animate}
\newcounter{upperbound}
\begin{document}
\begin{frame}
\frametitle{ABC}
\begin{animateinline}[%
controls,
begin={\begin{tikzpicture}
\foreach [count=\i] \j in {a,...,u}
\node [scale=0.02] (\j) at (\i*0.30,0+rand*0.2) {};},
end={\end{tikzpicture}}
]{5}
\multiframe{20}{iCount=2+1}{%
\setcounter{upperbound}{\iCount}
\foreach [remember=\j as \k (initially a)] \j in {b,...,\alph{upperbound}} {
\draw (\k) -- (\j);
}
}
\end{animateinline}
\end{frame}
\end{document}