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An efficient, economical, as well as reliable energy distribution system plays important roles in distributing energy resources from energy suppliers to energy consumers in different regions. In this paper, we present a decentralized self-organized mechanism that draws on the methodology of autonomy-oriented computing (AOC) to study the formation of an energy distribution network from a bottom-up viewpoint. We utilize ideas from the animals' foraging behaviors (i.e., the Lévy flight) for energy consumers to search for energy suppliers. Simulation-based experimental results based on the real-world data of crude oil production and consumption in U.S. and Canada show that distribution hubs, which are essential to enhance supply opportunities and flexibilities in the real world, can also be observed from the AOC-based mechanism. This work provides a possible way for understanding the fundamental principles behind the formation of an efficient and reliable distribution system.