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=== Orientation Models === Hoetzlein<ref>{{Cite journal |last=Hoetzlein, R. C. | year=2024 | title=Flock2: A model for orientation-based social flocking | journal=J. Theoretical Biology | volume=593 | pages=111880 | doi=10.1016/j.jtbi.2024.111880 | doi-access=free| arxiv=2404.17804 }}</ref> introduced the orientation-model in 2024 which separates the perceptual aspects of bird flight from the underlying aerodynamic model, linking these two control systems only by a heading target similar to real flight control. The perceptual model of each bird is orientation-based, mapped to a sphere, more closely match the biological vision system. The output of perception is a target heading angle (not a vector), which is used to control an aerodynamic model much like a flight simulator. Energy and frequency analysis in this work bridge the study of real bird kinetics with simulation models. This model demonstrates emergent, spontaneous orientation waves for the first time, a key feature in flocking murmurations.
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