The concept of shape grammars has often been proposed to improve or support creative design processes. Shape grammar implementations have the potential to both automate parts of the design process and allow exploration of design alternatives. In many of the existing implementations, the main focus is either on capturing the rationale of a particular existing grammar or on allowing designers to develop a new grammar. However, little attention is typically given to the actual representation of the design space that can be explored in the interface of the implementation. With such representation, a shape grammar implementation could properly support designers who are still in the process of designing and may not yet have a clear shape grammar in mind. In this article, an approach and a proof-of-concept software system is proposed for a shape grammar implementation that provides a visual and interactive way to support design space exploration in a creative design process. We describe the method by which this software system can be used and focus on how designers can interact with the exploration process. In particular, we point out how the proposed approach realizes several important amplification strategies to support design space exploration.