The Application of Frieze Groups and Crystallographic Groups in Generating Batak Toba Ornament Motifs Using a Matlab Graphical User Interface
DOI:
https://doi.org/10.31764/jtam.v8i1.17130Keywords:
Ornament, Isometric, Frieze group, Crystallographic group, Graphical User Interface (GUI) Matlab.Abstract
Gorga is a carving or sculpture typically found on the exterior of a Toba Batak traditional house. The Batak people use fractal (geometric) dimensions in Batak gorga carvings. In mathematics, repetitive and symmetrical patterns in planes that result from transformations are included in the plane symmetry groups. Ethnomathematics is a cultural approach to the concept of mathematics. A frieze group can be defined as a symmetrical group which arises from a unidirectional translation and subsequently generates a linear pattern that recurs exclusively in a single direction. There are seven different pattern types in the frieze groups. Meanwhile, crystallographic patterns are flat two-dimensional patterns that form a lattice. There are 17 crystallographic types of patterns with five different types of unit lattices. The purpose of this study is to generate motifs for Batak ornaments based on frieze groups and crystallographic groups using a Matlab Graphical User Interface (GUI). A total of 119 new motifs were generated based on seven types of patterns in the frieze groups, namely, F1,F2,F3,F4,F5,F6, and F7. Meanwhile, in the crystallographic groups, 153 new motifs were generated based on nine types of patterns, namely, p1,p2,pm,pg,cm,pmg,pmm,cmm, and pgg. To keep with trends, the new motifs generated can be used in everyday life as decorations or business symbols that are characteristic of the Toba Batak region.References
Andriani, L., & Muchyidin, A. (2020). Pola Frieze Group pada Gerakan Tari Buyung Kuningan. Jurnal Edukasi Dan Sains Matematika (JES-MAT), 6(2), 81–100. https://doi.org/10.25134/jes-mat.v6i2.2997
Andriyanti, S. (2016). Kontinuitas Gorga Batak Toba. In Pantun: Jurnal Ilmiah Seni Budaya 1 (2), 132–144. https://doi.org/10.26742/pantun.v1i2.765
Astriandini, M. G., & Kristanto, Y. D. (2021). Kajian Etnomatematika Pola Batik Keraton Surakarta Melalui Analisis Simetri. Mosharafa: Jurnal Pendidikan Matematika, 10(1), 13–24. https://doi.org/10.31980/mosharafa.v10i1.831
Cooper, C. D. H. (2013). Techniques of Algebra. Macquarie University. https://coopersnotes.net/docs/techniques%20of%20algebra/CONTENTS.pdf
Ditasona, C. (2018). Ethnomathematics Exploration of the Toba Community: Elements of Geometry Transformation Contained in Gorga (Ornament on Bataks House). IOP Conference Series: Materials Science and Engineering, 335(1). https://doi.org/10.1088/1757-899X/335/1/012042
Gallian, J. A. (2021). Contemporary Abstract Algebra. Chapman and Hall/CRC. https://doi.org/10.1201/9781003142331
Hermita, R., & Sianturi, N. E. (2020). Penerapan Ornamen Motif Gorga Pada Hiasan Dinding. PROPORSI : Jurnal Desain, Multimedia Dan Industri Kreatif, 6(1), 44–55. https://doi.org/10.22303/proporsi.6.1.2020.44-55
Kartika, D., & Rahmawati Suwanto, F. (2022). Generating of North Sumatran Songket Fabric Motifs Based on Crystallographic Groups Using Matlab GUI. https://doi.org/10.4108/eai.11-10-2022.2325312
Mingka, R. A., Kartika, D., & Suwanto, F. R. (2023). Development of Malay Deli Songket Motifs Based on Symmetry Groups. JTAM (Jurnal Teori Dan Aplikasi Matematika), 7(1), 82. https://doi.org/10.31764/jtam.v7i1.10279
Pane, R. N., & Sihotang, M. A. I. (2022). Etnomatematika Pada Rumah Bolon Batak Toba. PRISMA, Prosiding Seminar Nasional Matematika, 5, 384–390. http://repositori.unsil.ac.id/9831/12/DAFTAR%20PUSTAKA.pdf
Panjaitan, M. C., Kartika, D., Suwanto, F. R., & Niska, D. Y. (2022). Kajian Etnomatematika Motif Songket Melayu Deli Berdasarkan Pola Frieze dan Pola Kristalografi. PRISMA, Prosiding Seminar Nasional Matematika 5, 5, 675–684. https://journal.unnes.ac.id/sju/index.php/prisma/article/view/54708%0Ahttps://journal.unnes.ac.id/sju/index.php/prisma/article/download/54708/21112
Purba, R. (2016). Tipografi Kreasi Motif Gorga Batak. PROPORSI : Jurnal Desain, Multimedia Dan Industri Kreatif, 1(2), 190–201. https://doi.org/10.22303/proporsi.1.2.2016.190-201
Puspasari, R., Hartanto, S., Gufron, M., Wijayanti, P., & Budiarto, M. T. (2022). Frieze Pattern on Shibori Fabric. Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, 6(1), 67. https://doi.org/10.31331/medivesveteran.v6i1.1904
Rahmawati, A., Helmi, & Fran, F. (2018). Frieze Group Pada Seni Dekoratif Masjid. Buletin Ilmiah Math, Stat, Dan Terapannyaan Terapannya, 7(1), 23–32. https://doi.org/10.26418/bbimst.v7i1.23583
Rajagukguk, H. V. (2020). Perancangan Kasula dan Stola dengan Ide Penggambaran Gorga Batak Toba Melalui Teknik Batik Tulis. Corak, 9(1), 37–52. https://doi.org/10.24821/corak.v9i1.4101
Ray, Steven Nataliani, Y. (2022). Pengolahan Citra Digital pada Pembuatan Motif Keramik Menggunakan Grup Simetri. Buana Informatika, 13 (1), 11–20. https://doi.org/10.4108/eai.11-10-2022.2325312
Saragih, D. A., Yulianto, & Pakpahan, R. (2019). Kajian Ornamen Gorga di Rumah Adat Batak Toba (Studi Kasus: di Kawasan Desa Wisata Tomok , Huta Siallagan dan Huta Bolon di Kabupaten Samosir). Alur Jurnal Arsitektur, 2(1), 1–14. https://doi.org/10.54367/alur.v2i1.368
Schattschneider, D. (2018). The Plane Symmetry Groups: Their Recognition and Notation. The American Mathematical Monthly, 85(6), 439–450. https://doi.org/10.1080/00029890.1978.11994612
Siahaan, U. (2019). Rumah Adat Batak Toba Dan Ornamennya Desa Jangga Dolok, Kabupaten Toba – Samosir. Jurnal SCALE, 6(2), 24. https://doi.org/10.33541/scale.v6i2.45
Siburian, T. P. (2022). Bentuk Visual Dan Makna Simbolik Gorga Batak Toba. Journal of Contemporary Indonesian Art, 8(1), 49–57. https://doi.org/10.24821/jocia.v8i1.7047
Sihombing, S., & Tambunan, H. (2021). Etnomatematika: Eksplorasi Ornamen Rumah Bolon Batak Toba Terhadap Konsep Geometri. JPMI (Jurnal Pendidikan Matematika Indonesia), 6(2), 100–104. https://journal.stkipsingkawang.ac.id/index.php/JPMI/article/view/2552
Silalahi, R., Kartika, D., Suwanto, F. R., & Niska, D. Y. (2022). Pola Frieze dalam Kain Batik Sumatera Utara. PRISMA, Prosiding Seminar Nasional Matematika, 5, 667–674. https://journal.unnes.ac.id/sju/index.php/prisma/
Sopamena, Patma, Kaliky, Syafrudin & Assagaf, G. (2018). Etnomatematika Suku Nuaulu Maluku. In LP2M IAIN Ambon. http://repository.iainambon.ac.id/id/eprint/1490%0A
Suwanto, F. R., Kartika, D., & Niska, D. Y. (2022). Ethnomathematics: An Analysis of Frieze and Crystallographic Patterns on Ulos. AIP Conference Proceedings, 2659. https://doi.org/10.1063/5.0113269
Tampubolon, Y. S., & Tampake, T. (2023). Manifestasi Gender dalam Masyarakat Batak Toba pada Gorga ( Ukiran Simbol ) dalam Rumah Adat. Jurnal Basataka (JBT), 6(1), 208–220. https://doi.org/10.36277/basataka.v6i1.218
Umble, R. N., & Han, Z. (2008). Plane geometry. Fabric Architecture, 20(1), 56. https://doi.org/10.5948/9781614444077.009
Yuhandri. (2019). Perbandingan Metode Cropping pada Sebuah Citra untuk Pengambilan Motif Tertentu pada Kain Songket Sumatera Barat. Jurnal KomtekInfo, 6(1), 97–107. https://doi.org/10.35134/komtekinfo.v6i1.45
Downloads
Published
Issue
Section
License
Authors who publish articles in JTAM (Jurnal Teori dan Aplikasi Matematika) agree to the following terms:
- Authors retain copyright of the article and grant the journal right of first publication with the work simultaneously licensed under a CC-BY-SA or The Creative Commons Attribution–ShareAlike License.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
