Self-Organising Systems: Admissibility and Emergent Structure in Complex Systems

Many complex systems exhibit the capacity to organise structure without centralised control. Such systems arise through local interactions between components that collectively produce coherent global behaviour. Examples include biological pattern formation, flocking behaviour in animal groups, distributed computation networks, and large-scale social organisation. This paper interprets self-organising systems within the Paton System framework as processes in which admissible structural relationships emerge through local constraint compatibility. System organisation arises when interactions between components remain compatible with structural and environmental constraints. When these interactions exceed admissible limits, system organisation may destabilise or collapse. Understanding self-organisation through admissibility provides a structural interpretation of emergent order in complex systems.