Figure 1.

(a) Illustration of how a particle at position P_t calculates the ${\hat{C}}_t$ and ${\hat{D}}_t$ vectors in the heading update formula (equation (2.1)) on each time step. Black dots represent the neighbours of the particle and the blue square represents the LCM of the neighbours. (b) The groups present in the simplest version of the LAM model; (b(i)) Polarized group, (b(ii)) Mill and (b(iii)) Swarm. Dots represent position and rods the current heading (${\hat{D}}_t$). Note that the mills are undirected, i.e. particles traverse a mill in both the clockwise and counterclockwise directions.