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All Journal BERKALA SAINSTEK UNEJ e-Proceeding Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Majalah Ilmiah Matematika dan Statistika (MIMS) Jurnal Eurekamatika CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Juliyanto, Bagus
Jurusan Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Universitas Jember
Agriculture, Biological Sciences & Forestry Arts Humanities Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Education Industrial & Manufacturing Engineering Mathematics Physics Other

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Generation of Fractal Objects with Iterated Function System on the Developments of Trellis Ornament Designs Purnomo, Kosala Dwidja; Fatimah, Siti; Juliyanto, Bagus
BERKALA SAINSTEK Vol. 13 No. 1 (2025)
Publisher : Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/bst.v13i1.25656

Abstract

Fractals are one of a mathematical concept that provides artistic value and is therefore widely used to design various kinds of objects. The purpose of this study is to obtain various trellis ornament designs generated from fractal objects. Some fractal objects that will be used are Koch Snowflake (m,n,c), Koch Anti-Snowflake (m,n,c) and dragon curve. The basic trellis pattern is built from basic geometry, namely line segments, rhombuses and elliptical curved lines with certain sizes. In this study, the generation of fractal objects was carried out using the Iterated Function Systems (IFS) method. In this case, IFS is carried out by utilizing Affine transformations, namely dilation, rotation and reflection. Related to the generation of the Koch Snowflake curve (m,n,c), an m-sided polygon with 3≤m≤5 is used and the side looping form uses an n-sided polygon with 3≤n≤5. The c value or the middle segment divisor used is 0.3; 0.2; and 0.19. The dilation scale on the dragon curve is 0.6≤k≤9.8 and the angle θ=90°. The iteration used to generate the Koch curve is 2 iterations while the dragon curve is 15 iterations. By taking several parameters, a trellis ornament design consisting of 5 patterns is obtained and each pattern has 3 variations of trellis motifs.  
Co-Authors Ahmad Kamsyakawuni Alkhori, Ellenda Alkhori Dewi ANGGRAENI Dian Safitri Fatmasari, Christine Firdaus Ubaidillah Firdaus Ubaidillah, Firdaus Henik, Elsha Hikmah Ardiantika Sari Istiqomah, Rokhmatul Juniar, Vina Alpiani Kosala Dwidja Purnomo Kusbudiono Kusbudiono, Kusbudiono Kusno Kusno Maris, Ingka Miatullabibah Miatullabibah Mohamad Febri Setiawan Nadzira, Annisa Ayu Nur Kholifah Ramadhani Putri, Nurika Heidianti Rusli Hidayat Sakinah, Zulfatus Siti Fatimah Triadi, Muhammad Bagus Firman Wahana, Nadhilah Putri Wakik Faisahro