Visualization of dynamic structure in flocking behavior
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ORIGINAL ARTICLE
Visualization of dynamic structure in flocking behavior Daichi Saito1 · Norihiro Maruyama1 · Yasuhiro Hashimoto2 · Takashi Ikegami1 Received: 19 May 2020 / Accepted: 13 September 2020 © International Society of Artificial Life and Robotics (ISAROB) 2020
Abstract 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. Keywords Swarm visualization · Hierarchical structure · Generative topographic mapping · Boids model
1 Introduction Self-assembling and flocking behaviors have long been a popular subject of research [1, 2]. In the field of complex sciences, the Boids model and Vicsek model have been well studied for the simulation and analysis of complex flocking behaviors emerging from simple interactions among individuals [3, 4]. In the Vicsek model, a flock is defined as a macroscopic ordered state. In other words, each individual flock is not considered as a definite object, but is taken as a “flocking ordered state” only when its flock size scales up to a system size. Here, we consider different flocks with different spatial scales and behaviors. In our previous studies, it has been shown that different sized flocks have different statistical properties and often mutually interact with each other [5]. This work was presented in part at the 3rd International Symposium on Swarm Behavior and Bio-Inspired Robotics (Okinawa, Japan, November 20–22, 2019). * Daichi Saito [email protected]‑tokyo.ac.jp 1
The Graduate School of Arts and Sciences, The University of Tokyo, Tokyo, Japan
Division of Computer Science, The University of Aizu, Hukushima, Japan
2
These flocks exist in between the scale of individual components and the entire system. Such intermediate scale patterns are often observed in flocking behavior with general hierarchical structures, such as fish schools, chemical droplets, and web services. In general, animals that live in a flock may share roles among individuals or may benefit from interactions among individuals within the flock. Moreover, according to the “super-organism” concept, when a flock is considered to be one agent, it i
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