Duality of Patterning, one of Hockett's (1960) proposed design features unique to human language, refers in part to the arrangements of a relatively small stock of distinguishable meaningless sounds which are combined to create a potentially infinite set of morphemes. Literature regarding the emergence of this design feature is less abundant than that exploring other levels of structure as focus is more often given to the emergence of syntax. In an effort to explore where combinatorial structure of meaningless elements arises the results of two pilot experiments are presented within which we observe human participants modifying a small lexicon of visual symbols through a process of iterated learning. As this lexicon evolves there is evidence that it becomes simpler and more learnable, more easily transmitted. I argue that these features are a consequence of spontaneous emergence of combinatorial, sub-lexical structure in the lexicon, that the pattern of emergence is more complex than the most widely espoused explanation suggests, and I propose ways in which future work can build on what we learn from these pilot experiments to confirm this hypothesis.