Figure 5
From: Speckle statistics as a tool to distinguish collective behaviors of Zebrafish shoals
Statistical quantifiers for P and \(P^2\) from experimental data: statistical quantifiers (average over time and the five trails, the standard deviation SD, and their ratio) for P (a) and \(P ^2\) (b) extracted from the experimental data. SD measures the variability of the polarization time series, acting as a noise estimator. Error bars concerning the variability of the average polarization measures among trials are of the order of the symbols’ size. Two shoal regimes can be identified. For \(N >N_c \simeq 10\) the finite-size scaling laws have the same exponents predicted for uncorrelated shoals but with larger coefficients. A new shoaling regime emerges for \(N <N_c \simeq 10\) with slower power-laws for the averages and roughly size-independent SDs.
