\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
numeric r, theta; r = sqrt 1/2; theta = 45;
vardef dragon(expr level, a, b) = 
  if level > 0:
    save p; pair p;
    p = r[a, b] rotatedabout(a, theta); 
    dragon(level - 1, a, p) & reverse dragon(level - 1, b, p)
  else:
    a .. b
  fi
enddef;

vardef rounded_corners expr p = 
  save r, n; numeric r, n; r = 1/3; n = length p;
  subpath (0, 1-r) of p 
  for t=1 upto n-1:
    .. subpath (t+r, t+1-r) of p
  endfor .. subpath (n-r, n) of p
enddef;

beginfig(1);

  path d; d = dragon(15, origin, 240 right);
  draw d withpen pencircle scaled 1/4 withcolor (.2, .2, .7);
  label.top("The dragon curve at level 15", point 1/3 of bbox currentpicture);

  draw rounded_corners dragon(10, origin, 240 right)
    shifted 280 down
    withcolor .54 red;

  label.top("\dots\ and at level 10 with rounded corners", point 1/3 of bbox currentpicture);

endfig;
\end{mplibcode}
\end{document}