  We examine a simple biologically-motivated neural network, the three-layer
version of the Chialvo-Bak `minibrain' [Neurosci. 90 (1999) 1137], and present
numerical results which indicate that a non-equilibrium phase transition
between ordered and disordered phases occurs subject to the tuning of a control
parameter. Scale-free behaviour is observed at the critical point. Notably, the
transition here is due solely to network geometry and not any noise factor. The
phase of the network is thus a design parameter which can be tuned. The phases
are determined by differing levels of interference between active paths in the
network and the consequent accidental destruction of good paths.
