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The paper presents an experiment in knowledge management, called Dreaming Knowledge Base, that is built upon the analogy between the self-organizing functions of knowledge performed by dreams, and the structuring of an organizational KB. The requirements in terms of knowledge, imposed by the context on a complex social organization, are analyzed, concluding that the structure of knowledge is a complex fractal-like system in itself. Then the analogy of genetics and memetics is considered, introducing the concept of the holomeme, that is the holonic representation of memes and of their groupings in our minds, and their role in the structuring of knowledge. A person's knowledge evolves partly during daytime under the control of conscience, and even more during sleep, in the dreaming process: the extended connections between holomemes are created mostly unconsciously, with self-organizing processes. The experiment consists in exploring the use of automatic processes that create and reinforce extended connections between documents and holomemes (structured in an ontology), during the "dream time" of a Knowledge Base that follows a circadian cycle. The issue that is being addressed is that of introducing chaotic behaviors in the dream-like phase. The KB users are involved in validating the results of the self-organization.