The research discussed in this paper focuses on the development of interactive methods to image and analyze the surface designs of cultural artifacts and the generation of new designs. The project is interdisciplinary and uses methodologies from aesthetic and cultural inquiry, mathematics and computer science. The results of the research are obtained by using a combination of tools, such as neural networks, pattern recognition techniques including edge detection, and pattern generating techniques such as shape grammars.The first phase of this research focuses on the analysis of Congolese Kuba cloth and Moroccan Zillij mosaics because each has a complete and complex surface pattern with very different characteristics. Our work has three main facets: the description of the geometric content of ethno-mathematical artifacts; the classification of this content; and the generation of grammatical rules for the creation of new designs based on the studied artifacts.