\documentclass{standalone}
\usepackage{luamplib}
\usepackage{dwmpcode}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
 path h[], snake;
 h0 = for i = 1 upto 6: 40 dir 60i -- endfor cycle;
 h0 := h0 rotated - angle (9, sqrt(3));
 for i = 1 upto 6:
   h[i] = h0 shifted (point 0 of h0 - point 2 of h0) rotated -(120+60i);
   draw h[i] withcolor 3/4;
 endfor
 snake = point 0 of h1 -- point 1 of h2 -- point 2 of h3
      -- point 1 of h4 -- point 2 of h5 -- point 3 of h6
      -- point 4 of h5 -- point 0 of h5;
 ahangle := 30;
 z0 = point 0 of snake; z1 = point 8 of snake; z23 = 2/3[z0, z1];
 drawoptions(withcolor 1/2);
   drawarrow z0 -- z23; draw z23 -- z1;
 drawoptions(withcolor \mpcolor{textred});
   draw snake;
   for t=1, 5, 6:    drawarrow subpath (t, t-2/3) of snake; endfor
   for t=1, 2, 3, 6: drawarrow subpath (t, t+2/3) of snake; endfor
 drawoptions();
 dotlabel.llft("$(0, 0)$", z0);
 dotlabel.lrt ("$(1, 0)$", z1);
endfig;
\end{mplibcode}
\end{document}