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It has been said that there is something deeply touching about creating something and then having a chat with it. Machines in general, and more specifically computers, are not the exception to that tendency. In fact, since the Turing dissertation "Computing Machinery and Intelligence", machines' ability to perform a human-like conversational behavior has been regarded as the basis to consider the machines as "intelligent entities". In this paper, we propose the idea of the discovery of critically self-organized interaction, using its inherent structure as the basis to modeling computer chat.