Modern engineered materials are composed of space-filling grains or domains separated by a network of interfaces or boundaries. Such polycrystalline microstructures have the capacity to coarsen through boundary migration. Grain growth theories account for the topology of grains and the connectivity of the boundary network in terms of the familiar Euclidian dimension and Euler's polyhedral formula, both of which are based on integer numbers. However, we recently discovered an unusual growth mode in a nanocrystalline Pd-Au alloy, in which grains develop complex, highly convoluted surface morphologies that are best described by a fractional dimension of ∼1.2 (extracted from the perimeters of grain cross sections). This fractal value is characteristic of a variety of domain growth scenariosincluding explosive percolation, watersheds of random landscapes, and the migration of domain walls in a random field of pinning centers-which suggests that fractal grain boundary migration could be a manifestation of the same universal behavior.The coarsening of typical polycrystalline materials results in compact, faceted grain shapes that resemble soap bubbles. The geometric form of these grains-characterized topologically by the number of faces, edges and vertices-imparts complexity to the network of boundaries: usually, three 2D grain faces meet along each 1D edge (triple line), and four edges begin or end at each zero-dimensional vertex (quadruple point) 1 . When provided with sufficient kinetics, the network evolves in such a manner that the overall area of boundaries decreases, as this reduces the excess energy stored therein 2 . This process entails larger grains growing at the expense of their smaller neighbors, which results in the successive elimination of shrinking grains and a concomitant increase in average grain size.Tuning the latter quantity to optimize specific properties is the task of materials processing, which exploits the response of polycrystalline microstructures to applied stresses and temperatures (thermomechanical treatment) 3 . The key challenge hereby is to promote or suppress coarsening via control of the migration of grain boundaries. Understanding boundary migration is, in turn, the basis for developing predictive models for microstructure evolution-one of the paramount goals of materials science and statistical physics 4 . In this regard much attention has been devoted to the idealized case of isotropic grain growth in two and three dimensions. Quite generally, models for the coarsening of polycrystalline microstructures presume that the excess energy of grain boundaries manifests itself in the form of a surface tension 2 , which imparts a driving force for boundary migration through the boundary's mean curvature. When the surface tension is equal or similar in magnitude for all grain boundaries in a specimen, then the average grain size 〈 〉 R grows parabolically with time (i.e., 〈 〉 ∝ R t 2 ), and the grain size distribution evolves self-similarly, as verified by both theory 2,5 and computer sim...