Flock data.

We set the number of individuals to 100. The graphs in Figure3B and 3C show an average of 100 simulations, where each simulation consists of 4000 steps. The data were taken by waiting for each flock stabilized the motion. (A) The graph shows an example of a time series for changing directions. We take the absolute value of the rate of change and plot its evolution over time. The vertical line corresponds to a rate change (radian) compared with previous 10 steps. In this graph, the flock changes its direction up to 0.25 radians. (B) A graph showing the average distance between an individual and its neighbor with the topological rank. There is a roughly proportional relation between the average distance between individuals and its topological rank. (C) A graph showing the probability distribution for the nearest neighbor’s distance. The probability distribution shows an asymmetric relation around its center, 80 L. This asymmetry comes from the difference property between the repulsion of the metric interaction. The graph shows that a nearest neighbor is hard to exist within 80 L because of the repulsion zone.