Close packings of uniform disks with perfect orientational order

Computer-generated close packings of uniform disks around rhomboidal seeds are studied. We explain why these packings have perfect long-range orientational order without long-range translational order. A variety of structures are formed that are either deterministic or nondeterministic. Simple geometrical considerations enable us to predict the nature of these structures from the characteristics of the seeds. Certain deterministic structures grow by propagating a branching network of defect arms that is fractal. The fractal dimension D is a universal function of the acute angle of the rhomboidal seed. All of our structures are free of topological defects; i.e., they can be continuously deformed into perfect triangular lattices without long-range reconstruction. We discuss the implications of our work for the general theory of packings, for fractal, branching structures, and for close-packed models of glasses. © 1987 The American Physical Society.