Innovative Textile Pattern Creation Through Mathematical Computation: Applying Fibonacci Techniques to Enhance Aesthetic Dimensions in Fabric Design

Abstract

This research aims to 1) study the principles and techniques of the Fibonacci sequence as applied to textile pattern design; 2) develop textile patterns using the Fibonacci-based techniques to enhance aesthetic dimensions and uniqueness; and 3) inspire and provide guidelines for integrating mathematics into design and handicrafts for designers, researchers, and entrepreneurs in the textile industry. This is a research and development study. Data were collected through purposive interviews with five experts to gain in-depth insights into artistic values, design concepts, and the application of the Fibonacci sequence in the creation of textile patterns. The data were analyzed using content analysis to summarize key issues in three main areas: design process, design trends, and functional benefits of textile patterns. These designs were based on the Fibonacci sequence and the golden ratio and were created using Adobe Illustrator CS5. These designs were presented to experts for evaluation, and the most suitable pattern was selected for further development into a prototype. The selected pattern was refined based on expert scoring and feedback to ensure it reflects mathematical concepts effectively and is suitable for use in contemporary textile products.
The findings revealed that the principles and techniques of the 
Fibonacci sequence can be effectively applied to textile pattern design, enhancing balance, harmony, and natural beauty. The resulting patterns are unique and reflect deep aesthetic qualities, representing a successful integration of mathematics and traditional craft. The design of the pattern, which uses the Fibonacci technique to create dimensions of beauty and uniqueness in the fabric—particularly the contemporary spiral pattern that experts 
endorse—received an average score of 9.0 (S.D. = 0.63) and was noted for its continuity, symmetry, and outstanding aesthetic qualities. The application of the Fibonacci sequence in textile pattern design opens new perspectives that connect mathematics and art. The resulting patterns are not only beautiful but also conceptually meaningful, offering potential for further development across various fields of handicrafts.