\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
input colorbrewer-rgb
beginfig(1);
path s; s = unitsquare shifted -(1/2, 1/2) scaled 21;
path t; t = s rotated 45;
vardef show_corners(expr p) =
save s; numeric s; s = abs(point 1 of p - point 0 of p) / (2 + sqrt(2));
image( for i=0 upto 3:
fill unitsquare scaled s shifted point 0 of p rotated 90i withcolor Oranges[8][1+2i];
draw unitsquare scaled s shifted point 0 of p rotated 90i;
endfor)
enddef;
pair u, v;
u = point 1 of s - point 0 of s;
v = u rotated 90;
numeric n; n = 8;
for i = -n upto n:
for j = -n upto n:
draw show_corners(s) shifted (i * u + j * v);
draw show_corners(s) rotated -45 shifted (i * u + j * v);
endfor
endfor
