For a sequence of complex parameters $(c_n)$ we consider the composition of functions $f_{c_n} (z) = z^2 + c_n$ , the non-autonomous version of the classical quadratic dynamical system. The definitions of Julia and Fatou sets are naturally generalized to this setting. We answer a question posed by Brück, Büger and Reitz, whether the Julia set for such a sequence is almost always totally disconnected, if the values $c_n$ are chosen randomly from a large disc. Our proof is easily generalized to answer a lot of other related questions regarding typical connectivity of the random Julia set. In fact we prove the statement for a much larger family of sets than just discs; in particular if one picks $c_n$ randomly from the main cardioid of the Mandelbrot set, then the Julia set is still almost always totally disconnected.

对于一系列复杂参数 $(c_n)$ ，​​我们考虑函数 $f_{c_n} (z) = z^2 + c_n$ 的组合，这是经典二次动力系统的非自治版本。Julia 和 Fatou 集的定义自然地推广到这个设置。我们回答了 Brück、Büger 和 Reitz 提出的一个问题，如果 $c_n$ 的值是从一个大圆盘中随机选择的，那么这种序列的 Julia 集是否几乎总是完全断开的。我们的证明很容易推广，以回答有关随机 Julia 集的典型连通性的许多其他相关问题。事实上，我们证明了一个更大的集合族的陈述，而不仅仅是圆盘；特别是如果有人选择 $c_n$ 随机从 Mandelbrot 集的主心形指向，然后 Julia 集仍然几乎总是完全断开连接。