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it implies that differences between A and B also increase. 

Since there is only one bit difference between S$_{i}$ and S ′ i and each state has N$_{T}$ bits: 

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Now, to measure the sensitivity to initial conditions, the difference between the final and initial Hamming distances Δ H is used: 

where 

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A large number of random initial states for a large number of MRBNs are used to calculate an average Δ H for an ensemble. 

If Δ H < 0, then different initial states converge to the same final state. This is a characteristic of the ordered regime, where trajectories in state space tend to converge. If Δ H > 0, then small differences in initial states tend to increase, a characteristic of the chaotic regime, where trajec- tories in state space tend to diverge. If Δ H = 0, them small initial differences are maintained, a characteristic of the critical regime, where trajectories in state space neither converge nor diverge (in practice, Δ H ≈ 0). Thus, the average Δ H can indicate the regime of a MRBN. 

Boxplots of the results for cases 1, 2 and 3 are shown in Figure 11. Notice that boxplots show medians. Means can be compared in Tables A.6, A.7, and A.8; found in Appendix A. 

For K$_{T}$ = 1, the dynamics are in the ordered regime for all cases, since small differences in initial states tend to be reduced, indicated by a negative Δ H = − 1 N$_{T}$ . For K$_{T}$ = 2, Tables A.6, A.7, and A.8 in Appendix A show that the average Δ H is close to zero for all cases, suggesting a critical regime. The difference caused by modularity is clearly seen for K$_{T}$ > 2, i.e. in the chaotic regime. The sensitivity to initial conditions is inversely correlated with κ . This can be explained as follows: the higher the κ , the more “isolated” modules are. Thus, it is more difficult for damage to spread 

