It has been proposed that cultural evolution was made possible by a cognitive transition brought about by onset of the capacity for self-triggered recall and rehearsal. Here we develop a novel idea that models of collectively autocatalytic networks, developed for understanding the origin and organization of life, may also help explain the origin of the kind of cognitive structure that makes cultural evolution possible. In this setting, mental representations (for example, memories, concepts, ideas) play the role of 'molecules', and 'reactions' involve the evoking of one representation by another through remindings and associations. In the 'episodic mind', representations are so coarse-grained (encode too few properties) that such reactions must be 'catalyzed' by external stimuli. As cranial capacity increased, representations became more fine-grained (encoded more features), which facilitated recursive catalysis and culminated in free-association and streams of thought. At this point, the mind could combine representations and adapt them to specific needs and situations, and thereby contribute to cultural evolution. In this paper, we propose and study a simple and explicit cognitive model that gives rise naturally to autocatalytic networks, and thereby provides a possible mechanism for the transition from a pre-cultural episodic mind to a mimetic mind. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.