Fig. 2: Non-monotonic size dependence of group formation on environmental crowding.

Groups (here defined as all clusters formed by at least 3 individuals) formed after 25 min as a function of the initial densities of active (ρ_a) and passive (ρ_p) particles. a Example images of the largest clusters of active colloids formed at different ρ_a and ρ_p. Independent of ρ_a, these images show how the largest sizes are obtained at intermediate values of ρ_p. Scale bar: 20 μm. b This visual trend is confirmed by the non-monotonic dependence of the average size \({C}_{\max }\) of the largest clusters (measured as number of active particles) as a function of ρ_p for different values of ρ_a. c Differently from \({C}_{\max }\), the total number of groups N_g tends to monotonically increase with ρ_p. The error bars in b and c represent one standard error around the average values obtained from triplicates. d Average number of active colloids in a group after 25 min calculated as the ratio between the number of particles in a group n_pg and the number of groups N_g. The error bars in d are obtained by propagating the standard errors on n_pg and N_g. Source data are provided as a Source Data file.