Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi Affine
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 tra...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitas Udayana
2016-12-01
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| Series: | Jurnal Matematika |
| Subjects: | |
| Online Access: | https://ojs.unud.ac.id/index.php/jmat/article/view/29277 |
| _version_ | 1828463175448657920 |
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| author | Kosala Dwidja Purnomo Rere Figurani Armana , Kusno |
| author_facet | Kosala Dwidja Purnomo Rere Figurani Armana , Kusno |
| author_sort | Kosala Dwidja Purnomo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T02:49:36Z |
| format | Article |
| id | doaj.art-26c9ff6e8f9a4c6f8319a77a7d1ced7c |
| institution | Directory Open Access Journal |
| issn | 1693-1394 |
| language | English |
| last_indexed | 2024-12-11T02:49:36Z |
| publishDate | 2016-12-01 |
| publisher | Universitas Udayana |
| record_format | Article |
| series | Jurnal Matematika |
| spelling | doaj.art-26c9ff6e8f9a4c6f8319a77a7d1ced7c2022-12-22T01:23:20ZengUniversitas UdayanaJurnal Matematika1693-13942016-12-0162869210.24843/JMAT.2016.v06.i02.p7129277Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi AffineKosala Dwidja Purnomo0Rere Figurani Armana1, Kusno2Jurusan Matematika FMIPA Universitas JemberJurusan Matematika FMIPA Universitas JemberJurusan Matematika FMIPA Universitas JemberThe 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.https://ojs.unud.ac.id/index.php/jmat/article/view/29277chaos gamedilationmidpointsSierpinski triangle |
| spellingShingle | Kosala Dwidja Purnomo Rere Figurani Armana , Kusno Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi Affine Jurnal Matematika chaos game dilation midpoints Sierpinski triangle |
| title | Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi Affine |
| title_full | Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi Affine |
| title_fullStr | Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi Affine |
| title_full_unstemmed | Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi Affine |
| title_short | Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi Affine |
| title_sort | kajian pembentukan segitiga sierpinski pada masalah chaos game dengan memanfaatkan transformasi affine |
| topic | chaos game dilation midpoints Sierpinski triangle |
| url | https://ojs.unud.ac.id/index.php/jmat/article/view/29277 |
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