verbatimtex
%&latex
  \documentclass{article}
  \begin{document}
  etex
  
beginfig(1)
  numeric rmin, rmax, r, dr, n, ux, uy;
  rmin := 2.9; rmax := 3.9;
  r := rmin; n := 175;
  dr := (rmax - rmin)/n;
  ux := 8cm; uy := 8cm;
  for i = 1 upto n:
    x := 0.5; % our starting point
    for j=1 upto 75: % initial iterations
      x := r*x*(1-x);
    endfor
    for j=1 upto 150: % the next 100 iterations
      x := r*x*(1-x);
      draw (r*ux,x*uy) withpen pencircle scaled .5pt;
    endfor
    r := r+dr;
  endfor;
  draw (rmin*ux,0) -- (rmax*ux,0);
  draw (rmin*ux,0) -- (rmin*ux,uy);
  labeloffset := 0.25cm;
  label.bot(decimal(rmin), (rmin*ux,0));
  label.bot(decimal((rmin+rmax)/2), ((rmin+rmax)/2*ux,0));
  label.bot(decimal(rmax), (rmax*ux,0));
  label.lft(decimal(0), (rmin*ux,0));
  label.lft(decimal(0.5), (rmin*ux,0.5*uy));
  label.lft(decimal(1), (rmin*ux,uy));
  label.bot(btex $r$ etex, ((rmax-0.2)*ux,0));
  label.lft(btex orbit etex rotated 90, (rmin*ux,0.75*uy));
endfig;
end;