As the field of complexity studies has developed, it has split into two subfields that examine two different kinds of emergence: the study of complex physical systems (CPS) and the study of complex adaptive systems (CAS):

Performance designates an agent’s behavioural repertoire at a point in time, typically specified by a set of conditional IF/THEN rules.

His famous example examines the effect on a conical sandpile of a narrow stream of sand grains falling on its apex: at a critical stage, cascades of sand avalanche to the bottom of the pile, completely changing its conical shape. Bak named this phenomenon self-organized criticality.

This marketing approach, called a bucket brigade algorithm in the literature, has the great advantage that each rule need only be ‘aware’ of the strengths of its immediate predecessors and successors (Figure 7).

analysis depends upon methods for discovering and exploiting recurring patterns in generated systems.

‘fat-tailed’ behaviour, where rare events (e.g. mass extinctions and market crashes) occur much more often than would be predicted by a normal (bell-curve) distribution

All CAS agents, whatever their particularities, have three levels of activity: 1. Performance (moment-by-moment capabilities) 2. Credit-assignment (rating the usefulness of available capabilities) 3. Rule-discovery (generating new capabilities).

CAS studies, in contrast to CPS studies, concern themselves with elements that are not fixed.

usually called agents, learn or adapt in response to interactions with other agents.