Fig 5. Causal emergence in the flocking boids model.

As the avoidance parameter is increased, the flock transitions from an attractive regime (in which all boids orbit regularly around a stable center of mass), to a repulsive one (in which boids spread across space and no flocking is visible). a) Our criterion Ψ detects causal emergence in an intermediate range of the avoidance parameter (error bars represent the standard deviation estimated over surrogate data). b) Sample trajectories of boids (grey) and their center of mass ($\text{red}$).