In his article Army Ants: A Collective Intelligence
, Nigel Franks wrote "[I]f 100 army ants are placed on a flat surface, they will walk around and around. . .until they die of exhaustion. In extremely high numbers, however, it is a different story.
If you could add ants, one at a time, how many would you need to add before the "different story" emerged?
The main result of this paper is that HAT exhibits a remarkable phase transition, wherein the addition of a single particle or dimension changes the limiting behavior from one of stationarity to one of transience.
Furthermore, transience occurs in only one "way": The group of particles splits into clusters of two or three particles, but no other number, which become increasingly separated.
In this analogy: army ants = particles; flat surface = low dimension; walking around and around = stationarity; different story = clustering and transience.