Since the self-organizing properties of the swarm are instability driven, the structures that form have some very interesting properties with respect to large perturbations. We performed the following experiment: the system was tuned to a region of the phase plane where lines form, and a stable network of traffic in a straight line was set up. Then the noise level was increased so that system is tuned below the transition line (
). One observes that the ants fall away from their orderly patterns and immediately start executing random walks on the lattice. As a result the pheromone distribution starts to fluctuate and become more and more random. If 
is then tuned back to its original value at some time later the line will eventually reform with little or no change. This occurs even if the randomization is allowed to proceed to the point that the pheromonal field is almost totally randomized.
Fig. 3 is shows a measure of how much of the original pattern in the pheromonal field is left over time as the ants execute a random walk for a certain time and then go back to nonlinear scent response. We define 
as the number of lattice sites where the concentration of pheromone is above the average for the grid in both the original pattern and the current field, as a percentage of the number of current sites with above average pheromone. Thus 
is a measure of the overlap of the current pattern with the original pattern. The figure plots 
for different durations of the random walk, and shows the stable patterns that re-form after the nonlinear scent response is turned back on. For times up to about twice the decay time 
even small, virtually undetectable memory effects of the field can be amplified causing the patterns to reform without significant changes. As shown in Fig. 3, as much as 90% of the pattern can be erased, and entirely reconstituted later.
To further show the adaptability of the swarm in certain regions of the parameter space, the following experiment was performed. The system was tuned to a region of 
-
parameter space where trails never form, and the motion of the ants remains random. A weak ``bootstrapping" trail was then added to the grid, the pheromone density of which was on the order of some of the larger random fluctuations in the field. In a region slightly below the phase transition, this causes the swarm to organize and amplify the trail, in spite of the fact that a network would not have formed spontaneously. Fig. 4 plots a measure of pheromone concentration 
, which is the ratio of lattice sites with below-average pheromone concentration to those with above-average concentration. Three runs are shown; one where no bootstrapping trail is added; another in which a bootstrapping trail causes the swarm to shift into the trail, and lastly, an attempt at bootstrapping which failed because the swarm was too far from the phase transition line. We emphasize that this behavior appears below, but near enough to the phase transition line.
Memory reconsolidation and bootstrapping are two seemingly conflicting functional abilities which appear in the vicinity to the phase transition line. Firstly, these organized patterns of behavior are really quite stable with respect to large perturbation,s which might have an obvious usefulness to operation in a changing and unpredictable environment. Secondly, because the patterns are due to the formation of an initially weak stable cooperative structure, the swarm can act as an information amplifier, and even a weak external perturbation (such as the location of a food source by a single ant) might lead to a significant response. Thus swarms posses both a long memory and the ability to learn.
Erik Rauch