Collective Motion and Path-Entropy

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Collective Motion is a captivating and highly contemporary area of study that spans applied mathematics, physics, zoology, robotics and machine learning. Research into the subject has only become possible with the advancement of computational capabilities, enabling scientists to explore phenomena exhibited by flocking birds, schooling fish, and swarming bees. The motivation and execution of these remarkable natural occurrences are not yet well understood. Beyond the visual allure, there are various potential applications of Collective Motion, in fields such as CGI graphics, robotics and swarm intelligence. Research has been undertaken on "top-down" models of Collective Motion since the mid-90s. This style of model enforces specific dynamics that broadly mimic observed behaviours, such as alignment, cohesion and collision avoidance. While these models yield some insights into theoretical possibilities, and have close analogies with spin models within physics, their limited ability toreplicate the full complexity of real-world scenarios hampers their practical applicability. More recent work has explored Collective Motion and flocking using "bottom-up" models, using the principals of "Future State Maximization" and "Path-Entropy Maximization" respectfully, motivated by Causal Entropic Forces. In these models, each bird utilizes projected visual states to formulate anydecision to reorientate. Both models can produce highly ordered cohesive flocks that demonstrate marginal opacity. However, both models have only been studied in 2D. This fundamentally limits their applicability to systems involving motion in full 3D (birds, fish etc) and thereby makes comparison with experiment difficult. In this PhD thesis, we are looking to expand previous work to simulate flockingbirds in 3D. Previous 3D models are "top-down", such as the Boids Model which is defined by three simple rules (separation, alignment, and cohesion). We aspire to provide a deeper understanding into flocking behaviour and the validity of the application of "bottom-up" models to 3D Collective Motion. Our core research questions are: How can we translate the 2D projection method to present visualstimulus in 3D? Can we create improved models for visual projection that are computationally efficient, e.g. using "ray tracing" techniques? Do the flocks demonstrate marginal opacity? Does the algorithm produce complex structures reminiscent of the manifolds seen in nature?