Self-organized criticality and emergent oscillations in models of termite architecture with crowding

The termite architecture model of O'Toole et'al. (1999) is extended to incorporate arbitrary halting time-scales. It is shown that this also means that the assumption of synchronous building must be relaxed. Numerical simulations show that ordered nest architecture emerges under a wide range of time-scales but also that there is an optimal region of halting times. This optimal region is explained by the emergence of synchronized periods of termite activity. The correlation length of the building distribution is shown to diverge providing strong evidence that the model is self-organized critical.