The multi-turmite system is composed of concurrent Turing machines acting on a two-dimensional grid. The machines obey simple local rules, namely Langton's ant rules, their updating is considered under various simulation conditions: synchronous or asynchronous updating methods and different conflict resolution policies. We present three emergent phenomena : clocks, gliders and deadlocks. We study to which extent these phenomena are robust to changes in the updating and in the conflict resolution policy. Regularities of behaviour are observed from simulation results. We describe these regularities within the mathematical framework of discrete dynamical systems and show how their robustness can be analysed from a local ``microscopic'' view.