Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition

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Tentacles on soft corals exhibit intriguing spatiotemporal dynamics of motions, which may benefit their survival and fitness. Despite their significance, studies of their quantitative properties still remain challenging and unexplored. Such motions are characterized by coherent patterns across both space and time, yet computational methods that address spatiotemporal dynamics are rare. Here, we introduce a data-driven method called dynamic mode decomposition (DMD) to explore the spatiotemporal behavior of tentacles of Anthelia glauca, where the motions of eight tentacles are captured by stereovision and object tracking techniques. The DMD reveals the stochastic motions of the tentacles, which can be well modeled as $1/f$-type motion. Additionally, the pulsation behaviors of our soft corals are also captured by analyzing the DMD spectrum and the sliding-window DMD, where these behaviors emerge as spatial DMD modes with increased power. Finally, the impact of light conditions on the $1/f$-type motion and pulsation behaviors is explored, where certain light conditions can manipulate the $1/f$-type motion and emergence of pulsation behaviors. Our work, combining experimental observation and a data-driven method to characterize spatiotemporal motions of coral tentacles, paves the way to exploring the complex behaviors of individual organisms and colonies, and the effect from changing environmental variables.