Kajian Pembentukan Segitiga Sierpinski Pada Masalah Chaos Game dengan Memanfaatkan Transformasi Affine
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.
Penulis: Kosala Dwidja
Purnomo, Rere Figurani Armana, Kusno
Koder Jurnal: jpmatematikadd160254
