Modification of Chaos Game with Rotation Variation on a Square
| Main Authors: | Purnomo, Kosala Dwidja, Larasati, Indry, Agustin, Ika Hesti, Ubaidillah, Firdaus |
|---|---|
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang
, 2019
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| Subjects: | |
| Online Access: |
http://ejournal.uin-malang.ac.id/index.php/Math/article/view/6936 http://ejournal.uin-malang.ac.id/index.php/Math/article/view/6936/pdf http://ejournal.uin-malang.ac.id/index.php/Math/article/downloadSuppFile/6936/668 |
Daftar Isi:
- Chaos game is a game of drawing a number of points in a geometric shape using certain rules that are repeated iteratively. Using those rules, a number of points generated and form some pattern. The original chaos game that apply to three vertices yields Sierpinski triangle pattern. Chaos game can be modified by varying a number of rules, such as compression ratio, vertices location, rotation, and many others. In previous studies, modification of chaos games rules have been made on triangles, pentagons, and -facets. Modifications also made in the rule of random or non-random, vertex choosing, and so forth. In this paper we will discuss the chaos game of quadrilateral that are rotated by using an affine transformation with a predetermined compression ratio. Affine transformation is a transformation that uses a matrix to calculate the position of a new object. The compression ratio r used here is 2. It means that the distance of the formation point is of the fulcrum, that is = 1/2. Variations of rotation on a square or a quadrilateral in chaos game are done by using several modifications to random and non-random rules with positive and negative angle variations. Finally, results of the formation points in chaos game will be analyzed whether they form a fractal object or not.