Generative design is concerned with the definition and exploration of design spaces, and it has been suggested that emergence plays a key role in this process. In this paper, the impact of emergence on a design space is explored via consideration of different methods used to generate designs in a particular style. Three distinct methods of generating Islamic geometric patterns have been investigated and the extent to which emergence is employed in these methods has been explored. This research supports a discussion on the role of emergence in generative design, and an investigation into how design spaces are affected by the type of emergence employed in a generative process.