‘Classical’ compartmental modelling techniques involve numerical solution of large sets of ordinary differential equations (ODEs). The computational cost of neuronal network evaluation using these techniques forms a major bottleneck in the exploration of the effects of dendrite morphology on network functionality. To reduce computational load, we have developed a finite-state automaton model of membrane activity, which will potentially permit the evaluation and comparison of large numbers of simulated 3-dimensional networks. The automaton mimics the behaviour of 2-equation ODE models for wave propagation in excitable media, and was found to be capable of modelling the most important characteristics of neural membranes.