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All Journal Jurnal Matematika Jurnal Ilmu Dasar BERKALA SAINSTEK CAUCHY: Jurnal Matematika Murni dan Aplikasi Prosiding Seminar Matematika dan Pendidikan Matematik UNEJ e-Proceeding Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Zero : Jurnal Sains, Matematika, dan Terapan Mathvision : Jurnal Matematika Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Majalah Ilmiah Matematika dan Statistika (MIMS) Jurnal Eurekamatika
Kosala Dwidja Purnomo
Jurusan Matematika FMIPA Universitas Jember
Agriculture, Biological Sciences & Forestry Arts Humanities Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Control & Systems Engineering Education Industrial & Manufacturing Engineering Mathematics Physics

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Journal : BERKALA SAINSTEK

 1 
Kajian Fraktal k-Fibonacci Word Menggunakan Natural Drawing Rule Prastiwi, Ulfi Mega; Purnomo, Kosala Dwidja; Ubaidillah, Firdaus
BERKALA SAINSTEK Vol 6 No 2 (2018)
Publisher : Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/bst.v6i2.9225

Abstract

Fraktal k-Fibonacci Word dapat dibentuk dari suatu barisan khusus dari bilangan biner {0,1}. Barisan ini didefinisikan k secara rekursif sebagai, f =0 , f =0k−1 1 , f untuk n≥2 d a n k≥1 . Pembangkitan k ,0 k ,1 k ,n = f k ,n−1 f k , n−2 fraktal k-Fibonacci word dapat dilakukan dengan cara memodifikasi barisan baru yaitu menggunakan barisan Dense Fibonacci Word untuk menghasilkan kurva fraktal dengan menggunakan tiga digit {0,1,2}, kemudian untuk membangkitkan kurva fraktalnya menggunakan aturan garis sederhana yang disebut natural drawing rule. Tujuan dari penelitian ini adalah bagaimana cara menerapkan natural drawing rule untuk membangkitkan kurva fraktal k-Fibonacci Word dan mengetahui perubahan bentuk kurva generalisasi k genap dan k ganjil. Karakteristik yang diperoleh untuk barisan Dense Fibonacci word generalisasi k ganjil dan k genap berbeda untuk generalisasi k ganjil mempunyai kesamaan kurva F sedangkan untuk k−2 , n generalisasi k genap mempunyai kesamaan kurva yaitu F . k−4 , n Kata Kunci: fraktal k-Fibonacci Word, barisan Dense Fibonacci Word, natural drawing rule
On The Modification of Chaos Game Rules on A Square Purnomo, Kosala Dwidja; Mawarni, Anindita Setya; Ubaidillah, Firdaus
BERKALA SAINSTEK Vol 10 No 3 (2022)
Publisher : Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/bst.v10i3.24183

Abstract

Fractal is a collection of geometric patterns found in nature and can also be a mathematical model visualization in which the pattern is repeated on a different scale. The formation of a fractal object can be done with a rule called chaos games. Chaos games explain a dot that moves erratically. On this research there will be random and non-random modification of the chaos game rules on a square. The purpose of this research is to make modifications and get visual results from modifications of the rules random and non-random chaos game. Depictions of random and non-random chaos game are carried out using MATLAB programs. Visualization of the random chaos game rule modification is a new fractal object that has self-similarity. Whereas modifications of the non-random rules by giving a particular sequence in selection a square point result in convergent points at specific coordinates. This is demonstrated by showing the value of the limit from the distance between points that produced by non-random chaos game is zero.
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 , Kusno Afifah, Rana Arij Ahmad Kamsyakawuni Alfian Futuhul Hadi Alkhori, Ellenda Alkhori Anggi Enggar Sari Arum Andary Ratri, Arum Andary Firdaus Ubaidillah Firdaus Ubaidillah, Firdaus Fitria Iga Pramesti Hadi Siswanto Ika Hesti Agustin, Ika Hesti Jafna Kamalia Sundusia Juliyanto, Bagus Juwitarty, Novita Anggraini Kamil, Abdul Kiswara Agung Santoso Kusbudiono Kusbudiono, Kusbudiono Larasati, Indry Maris, Ingka Mawarni, Anindita Setya Nur Indah Aries Permatasri NURIL AFANDI, NURIL Pramesti, Fitria Iga Prastiwi, Ulfi Mega Rafi’ulfath R Riwansia, Rafi’ulfath R Rere Figurani Armana Retno Wulandari Riwansia, Rafi’ulfath R Rory Ronella Agustin Rusli Hidayat Siti Fatimah Suny, Vian Hafid Ubaidillah, Firdaus Vianda Nuning Fitriani Wahyuningtyas, Dita Wulandari, Eka Yuni