Inspired by the swarming or flocking of animal systems we study groups of agents moving in unbounded 2D space. Individual trajectories derive from a ``bottom-up'' principle: individuals reorient to maximise their future path entropy over environmental states. This can be seen as a proxy for keeping options open, a principle that may confer evolutionary fitness in an uncertain world. We find an ordered (co-aligned) state naturally emerges, as well as disordered states or rotating clusters; similar phenotypes are observed in birds, insects and fish, respectively. The ordered state exhibits an order-disorder transition under two forms of noise: (i) standard additive orientational noise, applied to the post-decision orientations (ii) ``cognitive'' noise, overlaid onto each individual's model of the future paths of other agents. Unusually, the order increases at low noise, before later decreasing through the order-disorder transition as the noise increases further.

翻译：受动物系统集群或结群行为的启发，我们研究了在无界二维空间中运动的智能体群体。个体轨迹源于一种“自下而上”的原则：个体通过重新定向以最大化其在环境状态下的未来路径熵。这可以被视为保持选项开放的一种代理原则，该原则可能在不确性世界中赋予进化适应性。研究发现，有序（共定向）状态、无序状态或旋转集群会自然涌现；这些表型分别与鸟类、昆虫和鱼类的行为相似。有序状态在两种噪声形式下表现出有序-无序转变：（i）标准加性定向噪声，施加于决策后的定向；（ii）“认知”噪声，叠加于每个个体对其他智能体未来路径的模型之上。异常的是，在低噪声下有序度先增加，随后随着噪声进一步增大，通过有序-无序转变而下降。