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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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ANALISIS PENENTUAN LOKASI ATM MENGGUNAKAN DIAGRAM VORONOI PADA BANK SYARIAH Kosala Dwidja Purnomo; Fitria Iga Pramesti
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 14 No 1 (2022): Jurnal Ilmiah Matematika dan Pendidikan Matematika
Publisher : Jurusan Matematika FMIPA Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2022.14.1.5646

Abstract

Determining the right location for distribution of ATM Bank Syariah in Jember Regency considers several parameters including public facilities, ease of access and population. The problem in determining of location is called Facility Location Problem (FLP). The problem solving of location determination can use Voronoi diagram, which is to divide each desired region into several parts. Each part of the region represents a single point of location. Each point of location will be mapped with each point of the nearest location. Determining the nearest location point using Euclid distance. Determination of location based on parameters by giving a score on each data and giving a weight value on each parameter. From the score value and weight values owned will be obtained the total weight value of each region. The region with the highest weight value is designated as the district center. Each subdistrict center will have several service areas based on the nearest Google Maps distance. Determinating location of ATM Bank Syariah will be carried out based on parameters potential analysis in each service area.
PENENTUAN LOKASI OUTLET BANK MENGGUNAKAN DIAGRAM VORONOI DENGAN JARAK EUCLID Nur Indah Aries Permatasri; Kosala Dwidja Purnomo
UNEJ e-Proceeding 2022: E-Prosiding Seminar Nasional Matematika, Geometri, Statistika, dan Komputasi (SeNa-MaGeStiK)
Publisher : UPT Penerbitan Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Banking is an essential element in developing a country that has a role in raising funds to improve the standard of living of many people. Customers who will visit or use products from a bank will consider several factors. One of them is the location factor or so-called FLP. The algorithm for finding the FLP solution is a Voronoi diagram. Determination of the location will be more emphasize the location of the branch because the location of the branch is a place where banking products are traded and bank control. Determination of the location of this branch by using the Euclidean distance method. Determination of this location will use relevant parameters according to the needs and conditions of the bank such as the number of residents in an area. The Voronoi diagram is used to find the closest location based on a set of points in a closed polygon using 31 locations. The places to be used are from 31 sub-districts from the City of Jember. The method used is the Euclidean distance method which is a method of finding the proximity of the distance of two variables that is used to analyze the problem by determining two adjacent location distances. The results of this study are eight sub-districts that have been weighted for each parameter. Keywords: Euclidean Distance, FLP, Voronoi Diagram
Pembangkitan Pohon Fraktal Bercabang Menggunakan Metode Iterated Function System Retno Wulandari; Kosala Dwidja Purnomo; Ahmad Kamsyakawuni
Jurnal EurekaMatika Vol 10, No 2 (2022): Jurnal Eurekamatika
Publisher : Universitas Pendidikan Indonesia (UPI)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.17509/jem.v10i2.51210

Abstract

The Pythagorean tree is a flat fractal composed of squares. A Pythagorean tree with two branches developed into three components is called a fractal tree. In this article, the author generates a fractal tree that has been expanded to have n branches using the Iterated Function Systems (IFS) method. The fractal tree will be caused by the IFS method using affine transformations, namely dilation, translation, and rotation on a square as the initial geometric object. The generation of a fractal tree begins with determining the basic shape of the branching. The choice of the primary form of branching will affect the body and characteristics of the resulting fractal tree. There are two primary forms of branching to produce a fractal tree that has several variations in the selection of angles: the same angle, a different angle, and a random angle.Keywords: Affine Transformation, Fractal, Fractal Tree, Iterated Function System Method.AbstrakPohon Pythagoras adalah sebuah fraktal datar yang tersusun dari bujur sangkar. Pohon Pythagoras yang memiliki dua percabangan dikembangkan menjadi tiga percabangan disebut dengan istilah pohon fraktal. Pada artikel ini, penulis membangkitkan pohon fraktal yang dikembangkan jumlah cabangnya sampai sebanyak  menggunakan metode Iterated Function Systems (IFS). Pohon fraktal dibangkitkan dengan metode IFS menggunakan transformasi affine yaitu dilatasi, translasi, dan rotasi pada persegi sebagai objek geometri awal. Pembangkitan pohon fraktal dimulai dengan menentukan bentuk dasar percabangan. Pemilihan bentuk dasar percabangan akan berpengaruh pada bentuk dan karakteristik dari pohon fraktal yang dihasilkan. Ada dua macam bentuk dasar percabangan sehingga dapat menghasilkan pohon fraktal yang memiliki beberapa variasi pemilihan sudut yakni sudut sama, sudut berbeda, dan sudut random.
ANALISIS PENENTUAN LOKASI ATM MENGGUNAKAN DIAGRAM VORONOI PADA BANK SYARIAH Purnomo, Kosala Dwidja; Pramesti, Fitria Iga
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 14 No 1 (2022): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2022.14.1.5646

Abstract

ABSTRACT. Determining the right location for distribution of ATM Bank Syariah in Jember Regency considers several parameters including public facilities, ease of access and population. The problem in determining of location is called Facility Location Problem (FLP). The problem solving of location determination can use Voronoi diagram, which is to divide each desired region into several parts. Each part of the region represents a single point of location. Each point of location will be mapped with each point of the nearest location. Determining the nearest location point using Euclid distance. Determination of location based on parameters by giving a score on each data and giving a weight value on each parameter. From the score value and weight values owned will be obtained the total weight value of each region. The region with the highest weight value is designated as the district center. Each subdistrict center will have several service areas based on the nearest Google Maps distance. Determinating location of ATM Bank Syariah will be carried out based on parameters potential analysis in each service area.Keywords: Voronoi diagram, Euclidean distance, location ATM ABSTRAK. Penentuan lokasi pemerataan ATM Bank Syariah di Kabupaten Jember mempertimbangkan beberapa parameter antara lain fasilitas publik, kemudahan akses dan jumlah penduduk. Permasalahan dalam penentuan lokasi disebut dengan Facility Location Problem (FLP). Penyelesaian permasalahan penentuan lokasi dapat menggunakan diagram Voronoi, yaitu dengan membagi setiap wilayah yang diinginkan menjadi beberapa bagian. Setiap bagian dari wilayah tersebut mewakili satu titik lokasi. Setiap satu titik lokasi akan dipetakan dengan setiap titik lokasi yang terdekat. Penentuan titik lokasi yang terdekat menggunakan perhitungan jarak Euclid. Penentuan lokasi berdasarkan parameter dilakukan dengan pemberian nilai skor pada setiap data yang digunakan dan pemberian nilai bobot pada setiap parameter. Dari nilai skor dan nilai bobot yang dimiliki akan diperoleh nilai bobot total dari setiap wilayah. Wilayah dengan nilai bobot paling tinggi ditetapkan sebagai pusat kecamatan. Setiap pusat kecamatan terebut akan memiliki beberapa service area berdasarkan dari jarak Google Maps terdekat. Penentuan lokasi ATM Bank Syariah akan dilakukan berdasarkan analisis potensi parameter pada setiap service area. Kata Kunci: Diagram Voronoi, jarak Euclid, lokasi ATM
Construction of Three Branches Fractal Trees Using Iterated Function System Purnomo, Kosala Dwidja; Wahyuningtyas, Dita; Ubaidillah, Firdaus
Jurnal ILMU DASAR Vol 23 No 1 (2022)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/jid.v23i1.17447

Abstract

There are two types of fractal: natural fractals and fractals set. The examples of natural fractals are trees, leaves, ferns, mountain, and coastlines. One of the examples of fractals set is Pythagorean tree. In the earlier study, the Pythagorean tree has two branches generated through several affine transformations, i.e dilation and rotation. Here, we developed the Pythagorean tree (or fractal tree) with three branches through dilation, translation, and rotation transformation using Iterated Function System (IFS) method. Some values of height and length parameters were selected to ensure the formation of a fractal tree. These parameters affected the branching angle that can result in different fractal tree shape. Some random values of height and length parameters produced several variations of fractal tree. These values influenced the shape of fractal whether it tended to the left, to the right, or symmetrical shape.
Development Design Labako Batik with Combine Fractal Geometry Dragon Curve and Tobacco Leaf Motif Wulandari, Eka Yuni; Purnomo, Kosala Dwidja; Kamsyakawuni, Ahmad
Jurnal ILMU DASAR Vol 18 No 2 (2017)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1410.076 KB) | DOI: 10.19184/jid.v18i2.5650

Abstract

Labako Batik is a typical batik Jember, derived from the term "La Bako" is the language of Madura that describes the activities of farmers to plant and process the leaves of tobacco. The resulting motives are inspired by the potential of natural resources in Jember such as tobacco, cocoa, dragon fruit, coffee, bamboo, birds and butterflies. The selection of tobacco leaf pattern because Jember Regency as one of the best tobacco producing cities in Indonesia, so that the form of tobacco leaf becomes the most dominant characteristic in making Batako Labako. In recent years the application of fractal forms in batik began to be popularly known as fractal batik. Fractal batik is batik whose design is made with mathematical formulas done with computer technology. Development of Labako batik motif by generating the pattern of tobacco leaves using L-System and then combining with the fractal geometry of dragon curve that has been modeled, using techniques of geometry transformation in Matlab software. Keywords: labako batik, tobacco leaf, fractal, dragon curve, l-system
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.  
Variation Of Rotation In Chaos Game By Modifying The Rules Afifah, Rana Arij; Purnomo, Kosala Dwidja; Ubaidillah, Firdaus
ZERO: Jurnal Sains, Matematika dan Terapan Vol 4, No 1 (2020): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v4i1.7931

Abstract

The core concept of fractals is the process of rearranging identical components that have a large amount of self-similarity. One example of fractals is the Sierpinski trianglecan be generated using the chaos game method. This method is a form of play in drawing points on triangles that have certain rules and are repeated iteratively. This research will modify the rules of chaos game triangle with the addition of various rotationswith the center of rotation at one, two, three, four, and five reference points. The visual results obtained are in the form of fractals because they have self-similarity properties and a collection of new points formed experiences rotation with the center of rotation based on the selected reference point with the direction of rotation based on the rules. The visual results of the rotation θ angle are visually symmetrical about the axis-y with the visual results of the rotation 360⁰-θ  angle at one, three, four, and five reference points as the center of rotation. At two reference points as the center of rotation it is obtained that there are two parts that are visually symmetrical about a certain line. Visual results of rotation 360⁰ angles at one, two, three reference points as the center of rotation have a shape similar to the Sierpinski triangle. Whereas at four and five points of reference as the center of rotation has a shape similar to the Sierpinski triangle.
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