Construct the nested squares as thus:

>

> restart;

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

> w:=[]:

> t:=.1:

> for k to 25 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,color=green,scaling=constrained,axes=none);

>