compared by calculating their symmetric difference, i.e. the subset of lattice cells that were built either in one or the other but not in both: $\Delta = \{(i,j);\;\delta_\mathrm{seq}(i,j,T) \neq \delta_\mathrm{par}(i,j,T)\}$. Then, these difference patterns $\Delta$ were projected on the same classification map $(D,I)$ used previously (Fig. \[fig\_imprint\]). The results showed that for many combinations of parameters, the model’s behavior could be noticeably influenced by the update scheme, as many difference patterns exhibited a nontrivial structure with high density or high Moran’s index or both. On the other hand, it exhibited a stronger invariance for the corner quadruplets of $\alpha_k$’s: in these cases the $\Delta$’s clustered near the origin and $D=0.5$. Based on this study, we decided to adopt a parallel update scheme with $n=15$ built cells per time step in the remainder of the experiments.

#### Exploration of parameter space

The above two preliminary studies validated the robustness of the model with respect to the initialization and update scheme, and helped us choose a reasonable number of runs (about 5) for each parameter combination, and a adequate degree of parallelism in the simulations ($n=15$). Next, we revisited the $\alpha_k$ hypercube (same 1295 points in the partition of step 0.2), this 