It can be seen that this probability will increase with K , as more outputs from a node will increase the chances of damage propagation. Focussing on a node j from the outputs of i , then there will be a probability p that j = 1. Thus, there will be a probability 1 − p that a damage in i will propagate to j . Complementarily, there will be a probability 1 − p that j = 0, with a probability p that a damage in i will propagate to j . If there are on average 〈 K 〉 nodes that i can affect, then we can expect damage to spread if 〈 K 〉 2 p (1 − p ) ≥ 1 [32], which implies chaotic dynamics. This leads to the critical connectivity of Derrida and Pomeau [12], shown in equation 1. We briefly mention particular studies of coupled RBNs, which share similarities with the model of modular RBNs presented in the next section. A more detailed comparison can be found elsewhere [35]. Bastolla and Parisi [6] studied modularity within classical RBNs, i.e. functionally independent clusters, but not topological modularity. There have been different studies where only two coupled RBNs are considered [22, 4, 24]. There are studies where RBNs are generated in cells of a 2D lattice, similar to a cellular au- tomaton, where each RBN is weakly coupled with its von Neumann neighbors [45, 39, 11]. The goal is to model intercellular signaling in a tissue. Our model is more general than previous models, since there is an arbitrary number of coupled networks, and this is not restricted to spatial neighbors. Moreover, it is a natural extension of the classic RBN model. We propose a general model of modular random Boolean networks (MRBNs) that extend naturally the classic RBN model. A MRBN consists of M modules, each of which is a RBN with N nodes and on average 〈 K 〉 (intramodular) inputs per node. Each module has additional 〈 L 〉 (intermodular) inputs on average that link random nodes from different modules. These L intermodular connections 3 Modular Random Boolean Networks 7 2.2 Related Work