systems. Using principal component analysis, we also found that for RBNs the standard deviation of H is correlated with C : RBNs in the ordered regime have consistently high H , RBNs in the chaotic regime have consistently uncorrelated H , while RBNs in the critical regime have a variable H . This is also related to Wuensche’s Z parameter, which measures the variance of input entropy over time (Wuensche, 1999). Multiscale profiles of the measures give more insight than using them at particular scales, as shown in Figure 11. This was seen clearly with certain class II rules, where at one scale they have a high E , but a minimal at higher scales. The change of the measures across scales provides a useful tool to study dynamical systems (Wolpert and Macready, 1999; Polani, 2004; Weeks, 2010), as it has been formalized by Krohn-Rhodes theory (Rhodes, 2009; Egri- Nagy and Nehaniv, 2008). For example, a system with a high (but not maximum) E across scales can be said to be more emergent than one with E close to maximum at one scal e but close to minimal at other scales. Combinations of the measures can be used to better understand and classify systems. Looking only at C or H , it is not possible to distinguish complex from chaotic rules, but their combination reveals the ether required for the interaction of complex structures. There is also the question of how to consider and measure the information used by the measures. For example, in ECA different results are obtained if bit strings are considered vertically (as we did), horizontally, or diagonally. The results of RBNs change little with scale. This is precisely because RBNs are randomly generated. ECA are much more regular (in structure and function). Still, there are ECA which do not change much with scale, either they are too ordered (class I) or too chaotic (some of class III). In between, there are several rules with characteristic patterns which make scale matter. Most phenomena do have characteristic patterns, so their scale should also be relevant. For RBNs and ECA with chaotic dynamics, emergence is reduced slightly with increasing scale. This is a finite size effect, because shorter strings have their emergence reduced more 26