IMPLEMENTASI TEOREMA COLLAGE UNTUK MENDESAIN SISTEM FUNGSI ITERASI (SFI): STUDI AWAL MENDESAIN SFI MOTIF SONGKET LOMBOK
DOI:
10.29303/jpm.v10i2.21Published:
2015-09-01Downloads
Abstract
Abstrak: Geometri fraktal merupakan cabang matematika yang memfokuskan kajiannya pada objek-objek fraktal. SFI yaitu teknik yang dapat digunakan untuk memodelkan objek fraktal. Tulisan ini memaparkan bagaimana mengaplikasikan teorema Collage untuk mendesain SFI suatu himpunan K ÃÂ yang memilikiÃÂ sifat self-similarity. Mendesain SFI suatu himpunan K ÃÂ berarti mencari sejumlah berhingga pemetaan kontraktif berupa transformasi affine:
ÃÂ
dengan àsedemikian sehingga àuntuk n=1,2,ââ¬Â¦,N. Keenam parameter pada persamaan di atas disebut sebagai kode SFI. Penelitian ini bertujuan untuk merancang suatu algoritma berdasarkan ide dari teorema Collage dalam menentukan kode SFI yang akan digunakan untuk memvisualisasikan atraktor dari objek fraktal menggunakan bahasa pemrograman. Algoritma yang telah disusun selanjutnya diterapkan untuk memperoleh SFI motif songket Lombok dan diperoleh hasil sebagai berikut:
dengan faktor kontraktivitas s = 0.70434.
Kata Kunci: Teorema Collage; Sifat Self-Similarity; Transformasi Affine; Algoritma; SFI; Atraktor.
ÃÂ
Abstract: Fractal geometry is the branch of mathematics that focus its studies on fractals. Iterated Function Systems (IFS) acts as a technique to generate fractal models. This article presents how to implement the Collage Theorem to design IFS ofÃÂ K ÃÂ which hold self-similarity property. Designing IFS of K ÃÂ means that finding the finite contractive mapping i.e. affine transformation:
ÃÂ
where ààsuch that àfor n=1,2,ââ¬Â¦,N. The six parameters on the equation above are called IFS codes. The aim of the study is constructing the algorithm based on the Collage theorem to determine the IFS codes which are used to visualize the attractor of the fractal objects through programming language. The Algorithm is implemented to obtain the IFS of Songketââ¬â¢s texture of Lombok and the result is given below:
with a contractivity factor s = 0.70434.
Keywords: Collage Theorem; Self-Similarity; Affine Transformation; Algorithm; IFS; Attractor.License
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