  In this paper we describe a novel local algorithm for large statistical
swarms using "harmonic attractor dynamics", by means of which a swarm can
construct harmonics of the environment. This in turn allows the swarm to
approximately reconstruct desired structures in the environment. The robots
navigate in a discrete environment, completely free of localization, being able
to communicate with other robots in its own discrete cell only, and being able
to sense or take reliable action within a disk of radius $r$ around itself. We
present the mathematics that underlie such dynamics and present initial results
demonstrating the proposed algorithm.
