From disorder to design: Entropy-driven self-organization in an agent based swarming model and pattern formation

This letter aims to elucidate the deep connection between complexity, self-organization, emergent behaviour, pattern formation, and entropy – concepts that illuminate self-organization in complex systems – to advance agent-based modelling of swarms. By exploring these ideas through the lenses of physics, information theory, and nonlinear dynamics, we uncover a compelling narrative. Beginning with a random cluster of particles, each possessing distinct internal properties, we initiate their interactions and observe the emergence of intricate patterns over time. This process illustrates a transition from less probable to more probable states. At extreme parameter values, the system exhibits striking patterns and turbulent motions remarkable emergent behaviours driven by entropy and the dynamic exchange of mutual information. Applying probability theory enables us to uncover the underlying structure of these interactions, highlighting not only their importance but also their potential to transform our understanding of complex systems.