Visualization of dynamic structure in flocking behavior

The flock structures produced by individuals, e.g., animals, self-organize and change their complexity over time. Although flock structures are often characterized by the spatial alignment of each element, this study focuses on their dynamic and hierarchical nature, temporal variations, and meta-structures. In hierarchical systems, sometimes, the upper structure is unchanged, whereas the lower components change constantly over time. Current clustering methods aim to capture the static and mono-layer features of complex patterning. To detect and track dynamic and hierarchical objects, a new clustering technique is required. Hence, in this study, we improve the generative topographic mapping (GTM) method to visualize such dynamic hierarchical structures as they continuously change over time. Using examples from our recent studies on the large-scale Boids model, we confirm that the newly developed method can capture the complex flocking objects as well as track the merging and collapsing events of objects.