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Global properties of the resulting structures are observed to scale with the ratio of conductivity in the dendrite material to conductivity in the lattice material. Beyond a critical conductivity ratio, the resulting structures are naturally self\u2010avoiding and possess scale\u2010independent branching ratios. Our findings suggest that the conductivity ratio determines the geometric properties of naturally arising dendritic structures. We discuss empirical verification in the context of a system of self\u2010organizing agglomerates of metal particles in castor oil. \u00a9 2004 Wiley Periodicals, Inc. 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