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In this paper, we present five types of constructive assemblies that emerge through a form-finding process resembling growth. The synthetic growth is obtained through the assembly of identical blocks performed by two competing users. Each block type gives rise to different morphologies during each assembly session depending on the user and the environment that is augmented through projection on the synthetic structure and around it. The digitally augmented tangible interface is evaluated by professionals and students in interaction design. We introduce the concept of Emergent Interfaces (EI), which proposes harnessing non-determinism, temporal design, and self-organization. This work could contribute to organic user interfaces and morphogenetic engineering.