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Construction of Three Branches Fractal Trees Using Iterated Function System Kosala Dwidja Purnomo; Dita Wahyuningtyas; Firdaus Ubaidillah
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

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 Eka Yuni Wulandari; Kosala Dwidja Purnomo; Ahmad Kamsyakawuni
Jurnal ILMU DASAR Vol 18 No 2 (2017)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

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

Estimation of Plankton Population Using Ensemble Kalman Filter Kosala Dwidja Purnomo
Jurnal ILMU DASAR Vol 9 No 1 (2008)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (209.994 KB)

The objective of this paper is to simulate how the Ensemble Kalman Filter (EnKF) works to estimate plankton in the one-dimensional three components ecosystem model. The analysis has been done separately between nutrition component and plankton component. The simulation demonstrated that the EnKF with 100 ensembles has as good estimation as with 1000 ensembles. It will also be ilustrated that the increasing of ensemble size in EnKF can decrease the norm of error covariance of plankton component.

PENERAPAN METODE EXTENDED KALMAN FILTER PADA KASUS PERTUMBUHAN PENDUDUK KABUPATEN JEMBER Rory Ronella Agustin; Kosala Dwidja Purnomo; Alfian Futuhul Hadi
MathVisioN Vol 1 No 02 (2019): September 2019
Publisher : Prodi Matematika FMIPA Unirow Tuban

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (182.416 KB)

This study discusses the estimated number of people using the methods of Jember Regency Extended Kalman Filter (EKF) and determine the appropriate logistic growth model for predicting the next populations in Jember. There are two assumptions logistic growth model will be compared, first is logistic growth model assuming a linear populations function and the second is logistic growth model assuming parabolic populatins function. To determine efficiency of Extended Kalman Filter conducted trial process, using 6, 14, 28 measurements data. Each data taken from Central Statistic Agency of East Java Province during 1990-2017. Finally, this study indicate that the logistic growth model assuming parabolic populations function is an appropiate better than logistic growth model assuming a linear populations for populations in Jember during 1990-2017. The Extended Kalman Filter method is able to increase the confidence level of the estimation results indicated by getting smaller of average norm covariance error. More data used, the estimation results using Extended Kalman Filter method are getting better and closer to the real data.

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

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

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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

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.

On The Modification of Chaos Game Rules on A Square Kosala Dwidja Purnomo; Anindita Setya Mawarni; Firdaus Ubaidillah
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

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.

ANALISIS PENENTUAN LOKASI ATM MENGGUNAKAN DIAGRAM VORONOI PADA BANK SYARIAH Kosala Dwidja Purnomo; Fitria Iga Pramesti
Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) 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

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.

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