A large part of biological collective behaviors involves motional formation patterns like migration, vortex, aggregation, etc., in three-dimensional space, but the phase transition principles among these patterns still remain a dilemma. In this letter, by tweaking the vision range of the particles in a minimal collective motion model, phase transitions are observed among gas-like, crystal-like, and liquid-sphere–like patterns. Significantly, the increase of noise magnitudes will destroy the moving direction synchronization of gas-like and crystal-like phases, but not the liquid-sphere–like phase. By contrast, three sub-phases of migration liquid-sphere, vortex liquid-sphere and aggregation liquid-sphere emerge by slightly increasing noise magnitudes. This study sheds some light onto the forming mechanisms of 3D motional patterns of abundant biological groups. These insights could be expected to enable tuning the collective motional formations of multi-unmanned systems or robots by simply tweaking a few dynamical parameters as well.

生物集体行为的很大一部分涉及三维空间中的迁移、涡旋、聚集等运动形成模式，但这些模式之间的相变原理仍然是一个两难的问题。在这封信中，通过在最小集体运动模型中调整粒子的视觉范围，观察到气体状、晶体状和液体球状图案之间的相变。值得注意的是，噪声幅度的增加会破坏类气体和类晶体相的运动方向同步，但不会破坏类液体球相。相比之下，迁移液球、涡旋液球和聚集液球三个子阶段随着噪声幅度的略微增加而出现。这项研究揭示了丰富的生物群体的 3D 运动模式的形成机制。这些见解有望通过简单地调整一些动态参数来调整多无人系统或机器人的集体运动形态。