This paper presents a computational system for enriching design discovery in the external 2D representation of architectural plans. Enriching discovery is achieved through an interpretative search process that involves emergent findings. The developed computational system employs a twofold discovery process, generative phase and an interpretative or explorative phase. In the generation phase the system allows designers to depict an initial building design in the form of 2D plans as a set of lines. The system recognizes possible components of the initial design by generating different forms of bounded shapes that are both explicit and implicit using the Hamiltonian circuit approach. In the interpretation phase the discovery process using the quest mechanism is invoked by selecting a geometrical semantic identified in the recognized shapes to generate possible alternative interpretations of the complete representation of initial design. This plays an important role in enriching discovery in the architectural design of buildings and provides a set of new moves and directions for the designer to pursue.