Construct the nested squares as thus:

> restart;

> m:=[[1, 1],[-1, 1],[-1, -1],[1, -1], [1, 1]]:

> w:=[]:

> t:=0.1:

> for k to 20 do w:=[op(w),m]:sm:=[m[2],m[3],m[4],m[1],m[2]]:m:=(1-t)*m+t*sm:od:

> plot(w,axes=none,scaling=constrained,color=cyan);

>