than longer ones. This is interesting, since many studies on dynamical systems, especially analytic, are made assuming infinite systems. However, most real systems are better mod- eled as finite, and here we can see that the length of a string—not only the scale—can play a relevant role on determining the emergence and complexity of systems. One implication of this finite size effect is that higher scales require less information to be described. Ex- trapolating, the “highest scale” ( b → ∞ ) implies no information ( I → 0): if everything is contained, then there is no information necessary to describe it (Gershenson, 2007b). 

## 6 Future Work 

There are several lines of future research that we would like to pursue: 

1. We are applying the proposed measures to ultra-large scale systems (Northrop et al., 2006) with interesting preliminary results (Amoretti and Gershenson, 2012). 

2. We intend to apply the proposed measures to time series from real systems, as well as considering a non-random I$_{in}$ . This will enable us to contrast the usefulness of the measures. 

3. We studied measures for RBNs with computer simulations. It would be relevant to develop analytical solutions and contrast these to our simulation results. 

4. There are some similarities between C and Fisher information (Prokopenko et al., 2011; Wang et al., 2011). It would be useful to study their potential relationship. 

5. Bennet’s logical depth (Bennett, 1995) has been recently used as a measure of im- age complexity (Zenil et al., 2012). The relationships between logical depth and the proposed measure of complexity are worth studying. 

6. We would like to evaluate our proposed measures on Turing machines (Delahaye and Zenil, 2007, In Press) and on ϵ -machines (Shalizi and Crutchfield, 2001; G¨ ornerup and 

