A Mathematical Inquiry into the Structure Complexity of Miao Batik Patterns: A Frieze Group Analysis

Celebrated for its intricate patterns, Miao batik has been the subject of previous research and primarily focused on key pattern studies. However, there is a lack of systematic analysis within the Miao batik border pattern. This research endeavors to conduct a meticulous investigation and analysis of the structural intricacies inherent in Miao Batik border patterns. This qualitative research examines a case study of typical border patterns in Bailing Miao batik, deconstructing and analysing the visual characteristics embedded in these patterns through a visual analytical approach. Grounded in the mathematical framework of Frieze groups, the study seeks to elucidate the nuanced relationship between mathematical abstractions and the cultural richness manifested in these traditional textile designs. The research aims to provide a profound and comprehensive understanding of the sophisticated mathematical underpinnings governing the formation and organization of Miao Batik patterns. The study results showed that the design of Miao batik patterns unconsciously incorporates rich mathematical graphics and concepts, and also proves the feasibility of classifying and generating batik patterns through a frieze group. By delving into the intricate interplay between mathematical concepts and cultural expressions, this study contributes to the scholarly discourse on the intersection of mathematics and art, offering a novel perspective on the inherent complexity and cultural significance of Miao Batik patterns. Further, the findings of this study also serve as a valuable resource for those who are also committed to preserving, documenting, and further exploring the unique traditional Miao batik culture.