\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
    path base; base = fullcircle scaled 300;
    path astroid; astroid = 
    for t=0 step 1/16 until 8:
      hide(pair a, b, p; 
        a = (xpart point t of base, 0);
        b = (0, ypart point t of base); 
        draw a -- b withpen pencircle scaled 1/4 withcolor 3/4;
        p = whatever[a, b]; p - point t of base = whatever * (a - b) rotated 90;
    ) p --
    endfor cycle;
    draw astroid withcolor 2/3 red;
endfig;
\end{mplibcode}
\end{document}