Fig. 4.

Simulations of a dynamical model (see SI Text, section VIII for details). (A) Correlation function of the speed fluctuations at different values of g in a flock of $N=16\text{,}384$ birds. (Inset) Correlation length, measured from the exponential decay of the correlation functions at small r, as a function of $g/\left(J{n}_c\right)$. (B) For smaller g, correlation lengths are measured from the zero crossing of the correlation function. For $g/\left(J{n}_c\right)\ll 1$, ξ approaches a maximum value that depends on the size of the system. (Inset) Low g maximum of ξ, as a function of the system size; the linear dependence of ξ on L is typical of scale-free behavior.