Human languages include vast numbers of learned, arbitrary signal-meaning mappings but also many complex signal-meaning mappings that are systematically related to each other (i.e. not arbitrary). Although arbitrariness and systematicity are clearly related, the development of the two in communication systems has been explored independently. We present an experiment in which participants invent signs from scratch to refer to a set of real concepts that share semantic features. Through interaction, the systematic re-use of arbitrary elements emerges.