Starting with a quadrilateral $q_0=(A_1,A_2,A_3,A_4)$ of
$\m R^2$,
one constructs
a sequence of quadrilaterals $q_n=(A_{4n+1},\ldots ,A_{4n+4})$ by
iteration of foldings~: $q_n=
\ph_4\circ\ph_3\circ\ph_2\circ\ph_1(q_{n-1})$
where the folding $\ph_j$ replaces the vertex
number $j$ by its symmetric with respect to the opposite diagonal.
We have studied [1]
the dynamical behavior of this sequence.
In particular, we have seen that
the drift ${\D v(q_0):= \lim_{n\ra\infty}}\frac1n q_n$ exists
and, for Lebesgue almost all $q_0$, the sequence
$( q_n -nv(q_0))_{n\geq 1}$ is dense on a bounded
analytic curve.
Here, we prove that,
for Baire generic $q_0$, the closure of the same sequence
$( q_n -nv(q_0))_{n\geq 1}$ contains all the translates of $q_0$.