A Tessellation-Transformation Method for Categorizing and Generating Geometric Textile Design Patterns

By Yang Liu and Godfried Toussaint.

Published by The Design Collection

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Article: Print $US10.00
Article: Electronic $US5.00

Ornamental patterns are a fundamental aspect of textiles in all cultures stretching into the distant past. Traditionally the scientific analysis of textiles has been carried out on several physical structural levels of the fabrics. However, apart from analysing their symmetry groups, a scientific analysis of the geometric structure of the textile patterns themselves has been largely ignored. Textile museums have traditionally classified textiles chronologically and geographically, ignoring the geometric structure. We propose a new approach to the scientific study of textiles that breaks with this tradition. It is shown that a large collection of geometric textile designs from a wide cross-section of world cultures and historical periods, can be generated from the regular square tiling pattern, with a few simple geometric global transformations and local operations. These operations may serve as new analytical tools for categorizing textile designs, with applications to education, research on the cultural and evolutionary aspects of textiles, writing software for computer-aided design of textiles, and cataloguing for retrieval purposes in museums and libraries. The operations also serve as features for determining the cultural salience of existing geometric patterns, for discovering universal patterns, and for generating new patterns. The distance (or disimilarity) between two textile patterns, is defined as the minimum number of mutations required to change one pattern into the other. The distance of a pattern from the square tessellation serves as a measure of the pattern’s complexity. The potential of these ideas is illustrated with examples of traditional textile patterns found in many countries. Finally, several connecting bridges are provided between textile design and geometric problems of interest to mathematicians.

Keywords: Geometric Textile Patterns, Measuring Textile Design Similarity, Measuring Textile Pattern Complexity, Transformations of Tessellations, Categorization of Textile Patterns, Textile Retrieval

Design Principles and Practices: An International Journal, Volume 2, Issue 4, pp.101-112. Article: Print (Spiral Bound). Article: Electronic (PDF File; 1.585MB).

Yang Liu

Student, International Fashion School, LaSalle College, Concordia University, Montreal, Canada

Yang Liu obtained a Bachelor of Arts Degree in Western Literature from the English Department at Harbin Normal University in Harbin, China in July 1994. In July 2001 she received a Master of Arts Degree in Eastern and Western Culture from the Institute of Tourism, Culture, and History at Liaoning Normal University, Dalian, China. Her thesis was on Pedagogical Aspects of Tourism, Culture, and History. From 2006 to 2008 she was a student at the International Fashion Institute, LaSalle College, Montreal, Canada, majoring in Fashion Design with emphasis on geometric textile design in a cultural context. From 1998 to 2003 she was a professor in the Institute of Tourism, Culture, and History, Liaoning Normal University, Dalian, China. From July 1994 to July 1998. she was an assistant Professor in the Department of English, Changchun Institute of Post and Telecommunications (now called Jilin University). She was also a Reporter (part-time) for the Changchun televisions Station in Changchun from July 1994 to July 1995. She has published one book titled: Reading and Translation Praxis, Chapters 19-24, Northeast Normal University Press, November 1995. In 2008 she became a graduate student in the Department of Art Education at Concordia University in Montreal.

Dr. Godfried Toussaint

Professor, School of Computer Science, and Centre for Interdisciplinary Research in Music Media and Technology, Schulich School of Music, McGill University, Montreal, Canada

Godfried T. Toussaint received a Ph.D. in Electrical Engineering in 1972 from the University of British Columbia in Vancouver, Canada. Since then he has been teaching and doing research in the School of Computer Science at McGill University in Montreal, in the areas of information theory, pattern recognition, textile-pattern analysis and design, computational geometry, instance-based learning, music information retrieval, and computational music theory. In February 2005 he also became a researcher in the Centre for Interdisciplinary Research in Music Media and Technology, in the Schulich School of Music at McGill University. In 1978 he was the recipient of the Pattern Recognition Society’s Best Paper of the Year Award and in 1985 he was awarded a Senior Killam Research Fellowship by the Canada Council. In May 2001 he was awarded the David Thomson Award for excellence in graduate supervision and teaching at McGill University. He is a founder of several conferences and workshops, an editor of several journals, has appeared on television programs to explain his research on the mathematical analysis of flamenco rhythms, and has published 350 papers. In 2007 he was promoted to the rank of Professor Emeritus.

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