RBNs (Wuensche, 1998; Gershenson, 2002a), where all nodes have the same function (rule) and the structure is regular, i.e. each node has K = 3, inputs: themselves and their closest neighbors. There are 256 possible “rules” (the possible combinations of Boolean functions for 3 inputs are 2 2 3 = 2 8 = 256), although only 88 equivalence classes (Li and Packard, 1990; Wuensche and Lesser, 1992). There have been several classifications of ECA dynamics, the most popular being Wolfram’s (1984). Roughly, class I and II rules generate ordered dy- namics. Rules from class I tend to point attractors from all initial states, while class II rules tend to cycle attractors. Class III rules have chaotic dynamics. Rules from class IV generate critical dynamics, and some have been proven to be capable of universal computation (Cook, 2004). There are several methods to measure criticality in RBNs, including Derrida’s annealed approximation (Derrida and Pomeau, 1986), Lyapunov exponents (Luque and Sol´ e, 2000), and Hamming distances (Gershenson, 2004b). The study of complexity and related properties of discrete dynamical systems with in- formation theory is becoming a very active area. For example, Fisher information was used recently to measure criticality in RBNs (Wang et al., 2011). Zenil (2010) proposed a compression-based method to detect phase transitions (which are related to complexity). Novel measures of complexity of RBNs have been proposed by Gong and Socolar (2012). Mart´ınez et al. (In Press) study CA with memory, being able to extract critical dynamics from chaotic rules. 4.2 Experimental setup Several experiments were performed to explore the measures proposed in Section 3. To measure emergence E , self-organization S , and complexity C , the time series of single nodes were evaluated in equations 3, 5, and 7 and then averaged to obtain the results for the network. To measure homeostasis H , d was measured between the last two states. 1000 RBNs ran from a random initial state for 1000 steps and then 1000 “additional” steps were 14