  We study the set of solutions of the complex Ginzburg-Landau equation in
$\real^d, d<3$. We consider the global attracting set (i.e., the forward map of
the set of bounded initial data), and restrict it to a cube $Q_L$ of side $L$.
We cover this set by a (minimal) number $N_{Q_L}(\epsilon)$ of balls of radius
$\epsilon$ in $\Linfty(Q_L)$. We show that the Kolmogorov $\epsilon$-entropy
per unit length, $H_\epsilon =\lim_{L\to\infty} L^{-d} \log N_{Q_L}(\epsilon)$
exists. In particular, we bound $H_\epsilon$ by $\OO(\log(1/\epsilon)$, which
shows that the attracting set is smaller than the set of bounded analytic
functions in a strip. We finally give a positive lower bound:
$H_\epsilon>\OO(\log(1/\epsilon))$
