Schematic diagram of the model and the behavior of a model simulation.

<p>(A) Illustration of a transition of a swarm in lattice space. Each individual is represented by a blue cell and their potential transition is represented by a red arrow. The principal vector is represented by a thick red arrow. First, velocity matching is applied to the principal vectors (upper left). Next, the mutual anticipation is estimated. The amount of overlap between targets of potential transitions is calculated and sites with an overlap larger than 1 (threshold) are obtained (pink site). For example, the popularity of the highest pink site is 2 (upper center). An individual whose potential transitions reach some popular sites moves to the most popular site (black arrow in the upper right). After that, followers (lower left) and free wanderers (lower center) move, which results in the final distribution (lower right). (B) How changing <i>P</i> and <i>α</i> affects the patterns of a swarm composed of 100 individuals in a 50×50 lattice. Each individual is represented by a square and a trajectory tail, where <i>L</i> = 4, <i>R_f</i> = 2, and <i>R_M</i> = 3.