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We propose a sub-symbolic connectionist model in which a functionally compositional system self-organizes by learning a provided set of goal-directed actions. This approach is compatible with an idea taken from usage-based accounts of the developmental learning of language, especially one theory of infants' acquisition process of symbols. The presented model potentially explains a possible continuous process underlying the transitions from rote knowledge to systematized knowledge by drawing an analogy to the formation process of a geometric regular arrangement of points. Based on the experimental results, the essential underlying process is discussed.