  Despite their apparent simplicity, random Boolean networks display a rich
variety of dynamical behaviors. Much work has been focused on the properties
and abundance of attractors. We here derive an expression for the number of
attractors in the special case of one input per node. Approximating some other
non-chaotic networks to be of this class, we apply the analytic results to
them. For this approximation, we observe a strikingly good agreement on the
numbers of attractors of various lengths. Furthermore, we find that for long
cycle lengths, there are some properties that seem strange in comparison to
real dynamical systems. However, those properties can be interesting from the
viewpoint of constraint satisfaction problems.
