Let $X_c$ be the attractor of the IFS generated by $z\mapsto cz\pm 1$ with $|c|<1$. Let $M$ be the set of $c$ for which $X_c$ is connected, and $M'\subset M$ the subset where $0\in X_c$. Bousch (1996, unpublished!!) proved that both are connected and locally connected, and related these sets to the set of zeroes of power series with coefficients in $ \{-1,1\}$, or in $\{-1,0,1\}$. In light of the several talks on this subject, I thought it would be useful to go over Bousch's proofs.