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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.
RACK STORAGE COMPONENT DESIGN BY PARAMETRIC CURVES AND SURFACES Puji Astuti; Kusno Kusno
Jurnal ILMU DASAR Vol 13 No 1 (2012)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (682.084 KB) | DOI: 10.19184/jid.v13i1.885

Abstract

The purpose of study is to obtain procedures of designing several models of rack support and pole component, so that the shape are varies, symmetrical, graded, and balance. The results show that the procedure of designing rack support component can be done by taking some data of a space frame construction of the cube, triangular prism, or cone, then we set a few points on the frame to build piece of parametric curve. Finally we interpolate the curves to find a rack support surfaces. As for the rack pole component, the procedures are: we extract data of straight line segments, oblique or helical shape, then we enumerate the lines into several sub-segments, and then breaks it down to build the trending, chain, and graded curve to get a balance rack pole .
Co-Authors Kosala Dwidja Purnomo Puji Astuti Rere Figurani Armana