Complexity theory is a relatively new branch of research that investigates how simplicity builds complexity.
Networks of agents engage in simple interaction with each other, such that the output of each one is fed back into the inputs of others, to form dynamical systems1.
In a system where each agent is connected to and interacting with all other agents, the behaviour of the system is chaotic and random. In a system in which each agent is connected to only one other, behaviour is static. However, somewhere inbetween order and chaos, the agents self-organise around cyclic attractors into circuits or programmes2. This behaviour is known as emergent behaviour or the emergent property of the system.
A number of artificial cellular automata have been devised to demonstrate emergent, complex behaviour in networks of simple agents. John Conway's 'Life' and Stuart Kauffman's 'NK Boolean Networks' are two notable examples.
Many natural systems form this kind of system and display emergent behaviour, eg the way genes interact to control the way they are expressed, colonies of ants and the fuzzy networks of neurones in the brain.