Abstract
We introduce a simple dynamical rule in which each particle locates a particle that is farthest from it and moves towards it. Repeated application of this algorithm results in the formation of unusual dynamical patterns: during the process of assembly the system self-organizes into slices of low particle density separated by lines of increasingly high particle density along which most particles move. As the process proceeds, pairs of lines meet and merge with each other until a single line remains and particles move along it towards the zone of assembly. We show that this pattern is governed by particles (attractors) situated on the instantaneous outer boundary of the system and that both in two and in three dimensions the lines are formed by zigzag motion of a particle towards a pair of nearly equidistant attractors. This novel line-dominated assembly is very different from the local assembly in which particles that move towards their nearest neighbors produce point-like clusters that coalesce into new point-like clusters, etc.
Highlights
We introduce a simple dynamical rule in which each particle locates a particle that is farthest from it and moves towards it
We simulated an ensemble of particles randomly distributed in a circular region in two dimensions that follow a simple dynamical rule: every particle moves towards the farthest particle from it
As a follower moves towards its attractor, it approaches the perpendicular bisector of the imaginary line joining this attractor to its neighbouring attractor, and from this point on it executes a zigzag motion about this bisector as it switches between the two attractors; since deviations from the line are small, it appears that the particle moves along the line
Summary
We introduce a simple dynamical rule in which each particle locates a particle that is farthest from it and moves towards it. Since the amplitude of the zigzag motion is of the order of step size which we have chosen to be very small (Δx = 0.02) compared to the average interparticle distance, particle 1 appears to move along a straight line which is the perpendicular bisector of the side joining the two nearly equidistant attractors, particles 2 and 3.
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