My thesis, "Shape Analysis for Digital Representation of East Asian Silk Patterns," focuses on the geometric analysis and digital representation of East Asian silk patterns, primarily found in traditional Korean and Chinese architecture. These patterns, despite being deeply rooted in cultural and historical contexts, have not been formally studied in a computational sense, and I sought to address this gap.

Korean dancheong patterns, including geummun, have always fascinated me with their beautiful geometric art, which is widely used in traditional Korean wooden buildings. Geummun, a specific type of pattern used in dancheong, is built on a geometric configuration. Unlike other patterns that are more representational and descriptive, geummun is abstract and repetitive, defined by hexagonal symmetry and interwoven laces. Through my research, I sought to investigate these geometric designs, which have yet to be systematically archived or analyzed, and explore their shared heritage between Korea and China.

While there has been significant research on computational representations of Islamic geometric patterns, I noticed that no such systematic study has been conducted on Korean geummun patterns. Additionally, tracing their historical and geographical evolution is difficult due to the lack of accessible sources, as the patterns are often repainted every decade. Since Spring 2015, I conducted a series of design analyses based on parametric shape grammar to understand the geometric construction of existing geummun patterns. Using this analysis, I experimented with non-traditional arrangement styles to create new variations of geummun based on existing motifs.

Through my work, I realized the importance of taking a more holistic approach to understanding the relationship between these patterns and geometric designs from other cultures. By comparing silk patterns from Korea and China, I identified that they share a common heritage. I propose using symmetry analysis—often used in archaeology—to highlight the material cultural relevance between these two adjacent cultural groups. This comparative analysis allowed me to uncover deeper connections between the geometric patterns of the region.

One of my key contributions is the creation of a web-based platform that allows users to either archive existing geummun patterns or create their own, based on the design principles I uncovered. To verify the platform's effectiveness, I introduced a machine learning model to crosscheck between computer-generated and existing patterns. This, along with an automated pattern generator I developed, allows for batch creation of silk patterns with specific symmetries, which can then be used to train machine learning models.

I also introduced a symbolic notation system to identify different stacking orders between designs. This system can be used to analyze many traditional examples of silk patterns and generate new ones. I incorporated this system into my machine learning model, which classifies the symmetries of these patterns using convolutional neural networks (CNNs). By generating images of silk patterns, I was able to take a significant step toward creating a symmetry classifier capable of analyzing and categorizing patterns more efficiently than manual archiving allows.

In conclusion, my work contributes by providing an accessible archive of silk patterns, introducing new tools for pattern creation and classification, and promoting greater awareness of the shared cultural heritage of East Asia. In the future, I plan to extend the platform’s capabilities to include functionalities for converting these digital designs into physical objects—potentially using origami tessellation or 3D-printed auxetic structures—to bring these stunning geometric designs into new and innovative forms.

The interactive web app for creating geometric patterns.