Stable dynamic patterns generated by retrograde model

A heterogeneous boid is a multi-agent system comprised of several types of agents that communicate locally. It forms diverse patterns of agent groups through various interactions. With appropriately tuned interactions, it forms stable patterns of a unified cluster with symmetrical structures that reflect local interactions. This ensures that these patterns remain stable, regardless of the number of agents (i.e., scalability). Prior research introduced the retrograde model, where two agent types exhibited reverse movement while a third type formed a unified cluster. By tuning the interaction, this model formed stable dynamic patterns. With a large number of agents, even under appropriate interactions, long-lasting metastable states emerge, making it difficult to distinguish them from stable patterns. In this study, by focusing on large-scale structures (cluster shape and agent flow), we reclassified three stable dynamic patterns formed by the retrograde model, removing the metastable states. We identify a new dynamic stable pattern, named as an irregular-oscillating pattern, by focusing on a cluster of specific shapes.