  Consider two objects associated to the Iterated Function System (IFS)
$\{1+\lambda z,-1+\lambda z\}$: the locus $\mathcal{M}$ of parameters
$\lambda\in\mathbb{D}\setminus\{0\}$ for which the corresponding attractor is
connected; and the locus $\mathcal{M}_0$ of parameters for which the related
attractor contains $0$. The set $\mathcal{M}$ can also be characterized as the
locus of parameters for which the attractor of the IFS $\{1+\lambda z, \lambda
z, -1+\lambda z\}$ contains $\lambda^{-1}$. Exploiting the asymptotic
similarity of $\mathcal{M}$ and $\mathcal{M}_0$ with the respective associated
attractors, we give sufficient conditions on $\lambda\in\partial\mathcal{M}$ or
$\partial\mathcal{M}_0$ to guarantee it is path accessible from the complement
$\mathbb{D}\setminus\mathcal{M}$.
