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In this paper we describe a novel local algorithm for large statisticalswarms using "harmonic attractor dynamics", by means of which a swarm canconstruct harmonics of the environment. This in turn allows the swarm toapproximately reconstruct desired structures in the environment. The robotsnavigate in a discrete environment, completely free of localization, being ableto communicate with other robots in its own discrete cell only, and being ableto sense or take reliable action within a disk of radius $r$ around itself. Wepresent the mathematics that underlie such dynamics and present initial resultsdemonstrating the proposed algorithm.

Approximate Structure Construction Using Large Statistical Swarms