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This paper presents computational models of creative designing. It commences with describing notions of creative designing within individuals, groups and then societies. In doing so it moves from absolute to situated cognition approaches. The paper then describes various computational approaches that simulate individual create designing processes with exemplars. It then moves on to describe situated cognition as the basis for group creative designing, which is described through a multi-agent example. Finally, the notion of creativity as a social behaviour is explored through simulations.