Complexity-seeking Ants

Deneubourg et al. 1] introduced a model of sorting behavior in ants. They found that simple model ants were able to sort into piles objects initially strewn randomly across the plane. The model is in qualitative agreement with the behavior of real ants. The model ants operate according to local strategic rules and possess only local perceptual capacities. Nonetheless, they are able to impose global order. What is the mechanism underlying this phenomenon? We hypothesize that it is the combination of two processes, one which decreases small-scale complexity, and another which couples small-scale decreases in complexity to larger scales. To test this hypothesis, we introduce variant ants which have a complexity-seeking strategy. These ants can "see" local complexity, and tend to perform actions (picking up and putting down objects) in regions of highest local complexity. Using this strategy, they are able to accomplish their task more eeciently than the basic ants. For both basic and complexity-seeking ants, we nd that complexity-reduction begins at the nest scale and propagates out to ever-increasing scales. We quantify the eeciency of various ant sorting strategies in terms of the amount of energy (in the form of random strategic choices) the ants require in order to eeect the reduction of global spatial entropy.