  This paper is another attempt to measure the difference between the family
$A[0,1]$ of attractors for iterated function systems acting on $[0,1]$ and a
broader family, the set $A_w[0,1]$ of attractors for weak iterated function
systems acting on $[0,1]$.
  It is known that both $A[0,1]$ and $A_w[0,1]$ are meager subsets of the
hyperspace $K([0,1])$ (of all compact subsets of $[0,1]$ equipped in the
Hausdorff metric). Actually, $A[0,1]$ is even $\sigma$-lower porous while the
question about $\sigma$-lower porosity of $A_w[0,1]$ is still open.
  We prove that $A[0,1]$ is not $\sigma$-strongly porous in $K([0,1])$.
Moreover, we show that $A_w[0,1]\setminus A[0,1]$ is dense in $K([0,1])$.
