IMPLEMENTASI TEOREMA COLLAGE UNTUK MENDESAIN SISTEM FUNGSI ITERASI (SFI): STUDI AWAL MENDESAIN SFI MOTIF SONGKET LOMBOK

Authors

Afifurrahman Afifurrahman

DOI:

10.29303/jpm.v10i2.21

Published:

2015-09-01

Issue:

Vol. 10 No. 2 (2015): September

Articles

Downloads

How to Cite

Afifurrahman, A. (2015). IMPLEMENTASI TEOREMA COLLAGE UNTUK MENDESAIN SISTEM FUNGSI ITERASI (SFI): STUDI AWAL MENDESAIN SFI MOTIF SONGKET LOMBOK. Jurnal Pijar Mipa, 10(2). https://doi.org/10.29303/jpm.v10i2.21
Crossref
Scopus
Google Scholar
Europe PMC

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

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 àyang memilikià sifat self-similarity. Mendesain SFI suatu himpunan K àberarti mencari sejumlah berhingga pemetaan kontraktif berupa transformasi affine:

à

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.

à


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 ofà K àwhich hold self-similarity property. Designing IFS of K àmeans that finding the finite contractive mapping i.e. affine transformation:

à

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

The following terms apply to authors who publish in this journal:
1. Authors retain copyright and grant the journal first publication rights, with the work simultaneously licensed under a Creative Commons Attribution License 4.0 International License (CC-BY License) that allows others to share the work with an acknowledgment of the work's authorship and first publication in this journal.

2. Authors may enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., posting it to an institutional repository or publishing it in a book), acknowledging its initial publication in this journal.
3. Before and during the submission process, authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website), as this can lead to productive exchanges as well as earlier and greater citation of published work (See The Effect of Open Access).