\documentclass{standalone}

\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\mplibshowlog{enable}
\begin{mplibcode}
beginfig(1);
randomseed := 3612.11746;
numeric w, h, n; w = 377; h = 80; n = 500;
draw (origin--right) scaled w;
draw (origin--right) scaled w shifted (0,+h/2) withcolor 3/4;
draw (origin--right) scaled w shifted (0,-h/2) withcolor 3/4;
numeric y; y = 0;
path walk; walk = (0, y) for x=w/n step w/n until w:
hide(y := y + 4 normaldeviate)
-- (x, y)
endfor;
path bridge; bridge = point 0 of walk for i=1 upto n:
-- point i of walk + (0, i/n * -y) endfor;
draw walk withcolor 7/8; % so you can see how it works
undraw bridge withpen pencircle scaled 3/4;
draw bridge withcolor 3/4 blue;
endfig;
\end{mplibcode}
\end{document}