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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 : jurnal matematika

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Kajian Morfisme Untuk Variasi Kurva Dense Fibonacci Word Anggi Enggar Sari; Kosala Dwidja Purnomo; Firdaus Ubaidillah
Jurnal Matematika Vol 11 No 1 (2021)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2021.v11.i01.p136

Abstract

The Fibonacci word is one example of a fractal object. The fractal Fibonacci word has the property of being similar to curves with curves. The curve Fibonacci word generated based on the Fibonacci word sequence. The Fibonacci word sequence can be defined by morphism so that a new sequence with the three-digit rule {0,1,2} is called Dense Fibonacci Word. In this research, the variation of the curve Dense Fibonacci Word generated by using the method L-Systems which applies several morphisms. This research method is divided into five stages, the first is the interpretation of the Dense Fibonacci Word and variations of morphism based on the Fibonacci word sequence. Second, the interpretation of fractals Dense Fibonacci Word using the method L-Systems mathematically. Third, the interpretation of fractals Dense Fibonacci Word using the method L-Systems graphically. Fourth, program making and fifth, analysis of results. The results obtained in this study are the visualization of the curve Dense Fibonacci Word with the method L-Systems, the shape of the curve Dense Fibonacci Word varies by applying several morphisms. The variation of the curve Dense Fibonacci Word is compared to each morphism which results in a different shape of the curve Dense Fibonacci Word in the small generation, but the larger the generation the fractal pattern is the same.
Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi Affine Kosala Dwidja Purnomo; Rere Figurani Armana; , Kusno
Jurnal Matematika Vol 6 No 2 (2016)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/JMAT.2016.v06.i02.p71

Abstract

The collection of midpoints in chaos game at early iteration looked like a shapeless or chaos. However, at the thousands of iterations the collection will converge to the Sierpinski triangle pattern. In this article Sierpinski triangle pattern will be discussed by the midpoint formula and affine transformation, that is dilation operation. The starting point taken is not bounded within the equilateral triangle, but also outside of it. This study shows that midpoints plotted always converge at one of vertices of the triangle. The sequence of collection midpoints is on the line segments that form Sierpinski triangle, will always lie on the line segments at any next iteration. Meanwhile, a midpoint that is not on the line segments, in particular iteration will be possible on the line segments that form Sierpinski triangle. In the next iteration these midpoints will always be on the line segment that form Sierpinski triangle. So, the collection of midpoints at thousands of iteration will form Sierpinski triangle pattern.
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