  A random boolean cellular automaton is a network of boolean gates where the
inputs, the boolean function, and the initial state of each gate are chosen
randomly. In this article, each gate has two inputs. Let $a$ (respectively $c$)
be the probability the the gate is assigned a constant function (respectively a
non-canalyzing function, i.e., {\sc equivalence} or {\sc exclusive or}).
Previous work has shown that when $a > c$, with probability asymptotic to 1,
the random automaton exhibits very stable behavior: almost all of the gates
stabilize, almost all of them are weak, i.e., they can be perturbed without
affecting the state cycle that is entered, and the state cycle is bounded in
size. This article gives evidence that the condition $a = c$ is a threshold of
chaotic behavior: with probability asymptotic to 1, almost all of the gates are
still stable and weak, but the state cycle size is unbounded. In fact, the
average state cycle size is superpolynomial in the number of gates.
