Extended Data Fig. 8: Effect of boundary conditions on the percolation threshold.

Three geometries are considered: (1) organisms in bulk, without confining surfaces (blue). This situation is presented in the main text. (2) Organisms at z = 0 near a liquid–air interface at z = 50 μm (green). Here, one reflecting image system is used. (3) Organisms in a liquid film, between liquid–air interfaces at z = ±50 μm, for which a series of reflecting image systems is used (magenta). In all three cases, the cells are located at z = 0 and oriented parallel to the x–y plane, for comparison. a, Contours of the critical strain rate \({\dot{\gamma }}_{{\rm{c}}}\) = 100 s⁻¹ for each of the three geometries (compare with Fig. 4c). This region of influence is largest in a film. b, Simulated percolation probability versus organism density for each geometry (compare with Fig. 4b). The percolation threshold is lowest in the film. Centre values show the mean of an ensemble of n = 100 independent simulations, each with about 10³ cells, and the error bars indicate two s.e.m.