L´ opez-Ruiz et al. (1995) which we used in this paper, these two profiles could be combined to develop a new complexity profile. This would illustrate general properties of complexity at different scales. In the ECA experiments, it could be seen that rules mainly fall in two categories: ei- ther they compute something ( E > 0) or they don’t ( E = 0). This is related to Wolfram’s principle of computational equivalence (Wolfram, 2002; Zenil, 2010), which conjectures that dynamical systems are either capable of universal computation (complex) or they are not (simple). From ECA, only rule 110 has been proven to be capable of universal computa- tion (Cook, 2004), but other rules possibly are also capable. Not only from class IV, but also from class III, although the variability makes it difficult to store information. Still, there are techniques to achieve complex dynamics of chaotic systems, e.g. with memory (Mart´ınez et al., In Press) or with regular external signals (Luque and Sol´ e, 1997, 1998) (chaos control). Class II might be considered too regular for universal computation, but adding noise 2 or a complex signal might enable them also to perform universal computation. Class I is too static, it would require most of the computation to come from the outside of the system. In general, one can employ different techniques to drive a dynamical system towards a high complexity (Gershenson, In Pressa). In most cases, homeostasis is related to self-organization, since a high S indicates low variability, which is also a characteristic of a high H , while low S in most cases is accom- panied by an uncorrelated H ≈ 1 2 $_{b}$. This is also a signature of chaotic dynamics (high E ). Nevertheless, some CA with a low S have a correlated H > 1 2 b or anticorrelated H < 1 2 $_{b}$, which is a characteristic of complex structures interacting on a regular background (ether). In this respect, different ECA rules can have high C at a particular scale because S ≈ 0 . 5. However, rules with a H deviating from 1 2 b show a signature of complex structures on an ether. The ether eases the computation, so universality can be explored more easily. This deviation of H ≈ 1 2 b could also be used to explore the immense space of possible dynamical $^{2}$Gabriel Barello, personal communication. 25