Atrial fibrillation (AF) is conventionally distinguished from atrial flutter by the irregularity of the ECG waveforms it produces. Yet, repetitive behaviour has been observed in endocardial activation maps, and cardiologists report that AF has a "limited repertoire" of patterns. We set out to investigate if a similar behaviour emerges from a sufficiently complex computational model of AF. For this purpose we were running many simulations with a high-resolution and structurally complex model of the human atria on a large-scale parallel system when we found that simulations with identical parameters could result in completely different activation orders after several seconds of AF. We investigated this non-reproducibility problem and found that it was due to a cascade of causes. Firstly, numerical "noise" at the nanovolt level occurred in the transmembrane potential at computational domain boundaries due to the variable order in which inter-process messages were received and treated. Second, these differences were amplified by several orders of magnitude due to small discontinuities in the functions representing state transition probabilities in the ionic model that was used (Courtemanche 1998). Finally, there were time instants in the simulations where the activation sequence was particularly sensitive to small perturbations. These instants were characterized by a sudden transition in activation pattern that occurred in one simulation, but not, or later, in another. Using a modified code that avoids the numerical noise and the discontinuities in the ionic model, we now aim to investigate the model's sensitivity to small perturbations in a more controlled manner.