Design research has generated many computational tools to aid the designer over the years. Most of these tools are focused on either the preliminary steps of customer need gathering or the concluding steps of embodiment or detail design. The conceptual design phase has seen fewer computational tools even though well known methods are available such as brainstorming, intrinsic and extrinsic searches and morphological analysis. In this paper a generalized computational conceptual design tool is presented to aid designers at the conceptual design stage. It relies on storing and reusing existing design knowledge to create new concept variants. Concept variants are computed using matrix manipulations, essentially creating a mathematical morphological matrix. The concept generator produces quick concepts that can be used for concept selection or as a basis for generating additional concept variants through non-computational, creative techniques.