On the emergence of intelligent global behaviours from simple local actions

Artificial intelligence focuses on the question of how to design systems to exhibit intelligent behaviour in complex environments. Complex global behaviours can emerge from simple systems acting in a complex environment; however, this emergence requires that the systems' internal structure reflects essential structures in the environment This paper examines the algebraic structure of a system's actions. We find that these actions often possess a self-similar local neighbourhood structure that permits analysis and synthesis to be performed locally and yet produces global intelligent behaviours. A procedure for finding this local structure is presented and illustrated with examples.