Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi Affine

  • Kosala Dwidja Purnomo Jurusan Matematika FMIPA Universitas Jember
  • Rere Figurani Armana Jurusan Matematika FMIPA Universitas Jember
  • , Kusno Jurusan Matematika FMIPA Universitas Jember

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.

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Author Biographies

Kosala Dwidja Purnomo, Jurusan Matematika FMIPA Universitas Jember

Jurusan Matematika FMIPA Universitas Jember

Rere Figurani Armana, Jurusan Matematika FMIPA Universitas Jember

Jurusan Matematika FMIPA Universitas Jember

, Kusno, Jurusan Matematika FMIPA Universitas Jember

Jurusan Matematika FMIPA Universitas Jember

Published
2016-12-30
How to Cite
PURNOMO, Kosala Dwidja; ARMANA, Rere Figurani; KUSNO, ,. Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi Affine. Jurnal Matematika, [S.l.], v. 6, n. 2, p. 86-92, dec. 2016. ISSN 2655-0016. Available at: <https://ojs.unud.ac.id/index.php/jmat/article/view/29277>. Date accessed: 22 nov. 2024. doi: https://doi.org/10.24843/JMAT.2016.v06.i02.p71.
Section
Articles

Keywords

chaos game; dilation; midpoints; Sierpinski triangle