For a sequence (cn) of complex numbers, the quadratic polynomials $f_{c_n}:=z^2+c_n$ and the sequence (Fn) of iterates $F_n:=f_{c_n}\circ\dotsb \circ f_{c_1}$ are considered. The Fatou set $\mathcal{F}(c_n)$ is defined as the set of all $z\in \hat{\mathbb{C}}: =\mathbb{C}\cup \{\infty\}$ such that (Fn) is normal in some neighbourhood of z, while the complement $\mathcal{J}(c_n)$ of $\mathcal{F}(c_n)$ (in $\hat{\mathbb{C}}$) is called the Julia set. In this paper we discuss the conditions for $\mathcal{J}(c_n)$ to be totally disconnected. A problem posed by Brück is solved.