Emergent Behaviour in Complex Software Systems

Complex software systems often exhibit emergent behaviours that are not explicitly programmed into individual components. These behaviours arise from interactions among modules, processes, and constraint structures operating within a shared computational environment. This paper interprets emergent behaviour through the admissibility framework of the Paton System. Within this interpretation, emergent phenomena arise when interacting components collectively explore admissible regions of system state space defined by governing constraints. The resulting behaviours appear novel at the system level despite being generated through locally valid operations. The framework clarifies why large-scale software systems display unexpected patterns, stability regimes, and cascading failure modes. Emergent behaviour is therefore interpreted not as uncontrolled complexity but as structured exploration of admissible computational state space. This work forms part of the Paton System Tier-7 Domain Instantiation (Computational Systems) series, which applies the admissibility framework to distributed computation, artificial intelligence, and algorithmic stability.