We explore the relationship between physical distance and genetic correlation. We focus on the one-dimensional stepping-stone model of population structure, which describes the evolution of a neutral allele in a population that has been subdivided into a number of discrete islands. The generational processes of migration and reproduction are simulated for this population, and we investigate how these forces impact rk, the correlation between islands at a distance k. We consider different geographic structures-- linear and circular arrangements of islands-- as well as different migration patterns. We compare our results with asymptotic results derived by Kimura and Weiss under the assumption of infinitely many islands. We find substantial deviation from these asymptotic results especially with regard to long-distance migration.