McCulloch-Pitts brains and pseudorandom functions

In a pioneering classic, Warren McCulloch and Walter Pitts proposed a model of the central nervous system. Motivated by EEG recordings of normal brain activity, Chv'atal and Goldsmith asked whether or not these dynamical systems can be engineered to produce trajectories which are irregular, disorderly, apparently unpredictable. We show that they cannot build weak pseudorandom functions.