  We deal with the finite family $\mathcal{F}$ of continuous maps on the
Hausdorff space. A nonempty compact subset $A$ of such space is called a strict
attractor if it has an open neighborhood $U$ such that
$A=\lim_{n\to\infty}\mathcal{F}^n(S)$ for every nonempty compact $S\subset U$.
Every strict attractor is a pointwise attractor, which means that the set
$\{x\in X ; \lim_{n\to\infty}\mathcal{F}^n(x)=A\}$ contains $A$ in its
interior. We present a class of examples of pointwise attractors - from the
finite set to the Sierpi\'nski carpet - which are not strict when we add to the
system one nonexpansive map.
