dilation in euclid, how to call the same function in asymptote

Question

I would like to draw the image of euclid dilation of square in asymptote. One square, and the other one with the corners on the middle points of the previous one.

settings.outformat="pdf"; 
    
include graph;
include math;
import geometry;
    
size(11cm,0);
    
pen dBlack=rgb(16/255, 15/255, 13/255);
pen pp=1.1bp+dBlack;    // 
  
pair A=(-1,-1), B=(1,-1), C=(1,1), D=(-1,1);

void drawsquare(pair A, pair B, pair C, pair D, int n)
{
 if (n == 0) {draw(A--B);} 
 else{   
    draw(A--B--C--D--cycle,pp);
pair A1= midpoint(A--B);
pair B1= midpoint(B--C);
pair C1= midpoint(C--D);
pair D1= midpoint(D--A);
drawsquare(A1,B1,C1,D1,n-1);}}

drawsquare(A,B,C,D,10);
    
shipout(bbox(2mm,invisible));

Black Mild · Answer

Your figure is quite simple, so there are many ways to draw. This is a TikZ solotion

documentclass[tikz,border=5mm]{standalone}
begin{document}
begin{tikzpicture}[scale=2.5]
defn{10}
defmybox{(1,1) rectangle (-1,-1)}
foreach i in {0,...,n}
draw[scale=1/sqrt(2^i),rotate=i*45] mybox;
end{tikzpicture}
end{document}

and here is Asymptote one

// http://asymptote.ualberta.ca/
unitsize(2cm);
int n=12;
path mybox=box((-1,-1),(1,1));
for (int i=0; i<n; ++i)
draw (scale(1/sqrt(2^i))*rotate(45*i)*mybox,blue);
shipout(bbox(2mm,invisible));

dilation in euclid, how to call the same function in asymptote

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