Think globally, sense locally: From local information to global features

Shannon's information theory can be used to quantify morphological and topological features of a collective of agents in an arbitrary environment. In particular the ability of individual agents to extract information locally about global features of the collective can be quantified. Here, we considered chains of agents in a grid world. The agents are equipped with local sensors. We then quantified the amount of information the sensors contain about certain features global to the chain. Furthermore, we compared the amount of locally available information to the amount of information the whole collective could in principle acquire about a feature in different contexts.