Frieze Group in Generating Traditional Cloth Motifs of the East Nusa Tenggara Province

Abstract

Ethnomathematics studies the relationship between mathematics and culture. Indonesia has many traditional cultures. One of them is traditional cloth. The traditional cloth from East Nusa Tenggara (NTT) province is called tenun ikat. Since the motif of tenun ikat consists of symmetrical and repeated patterns, it can be generated using Frieze groups. The Frieze groups are the plane symmetry groups of patterns whose subgroups of translations are isomorphic to Z. There are seven groups in the Frieze groups, i.e., F_1, F_2, F_3, F_4, F_5, F_6, and F_7. Translation, reflection, rotation, and glide reflection are the transformation used in the Frieze groups. In this paper, Frieze groups are used to generate digital tenun ikat motifs from the basic pattern. Since one piece of original tenun ikat may consist of some basic patterns, the basic patterns are identified first, and then each of them is generated into the desired pattern, according to the suitable Frieze groups. Furthermore, a GUI Matlab program is developed to generate the Frieze groups. Three motifs of tenun ikat are presented to demonstrate the implementation of Frieze groups. With the Frieze group, users can generate other patterns from a basic pattern, so users can generate new motifs of tenun ikat without leaving the cultural characteristics of NTT province.