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We present a novel distributed localization algorithm, called Swarm-Intelligent Localization (SIL), for computing the physical locations of nodes in wireless sensor networks. The algorithm assumes that only a small fraction of the nodes have a priori knowledge of their positions, and that noisy distance measurements are available between all neighboring nodes. The algorithm has no explicit global state and it can handle nodes that are both mobile and that can arrive in the network at any time. SIL works in two different phases, a coarse phase where nodes compute rough positions for themselves based on information about remote anchors, and a fine phase where nodes iteratively refine their positions from the coarse phase by collaborating with their neighbors. The average computational complexity per node running SIL is very low, namely constant in the network size and linear in the connectivity of the network. We evaluate the algorithm through extensive simulations. The results indicate that SIL is able to compute accurate positions for the majority of nodes in a wide range of network topologies and settings, and that it can handle difficulties such as large distance measurement errors and low network connectivity.