PEMBANGKITAN POLA SIMETRI P3 DARI SIMULASI SISTEM DINAMIK
DOI:
https://doi.org/10.25077/jmua.12.4.318-328.2023Keywords:
Sistem dinamik, pola simetri p3, kriteria konvergensi.Abstract
Pola simetri p3 memiliki simetri translasi pada sumbu-x dan sumbu-y, serta simetri rotasi sebesar 120. Dalam makalah ini akan dibahas pembangkitan pola simetri p3 menggunakan aplikasi MatLab melalui simulasi sistem dinamik. Pertama-tama, dilakukan analisis untuk menentukan fungsi dinamik yang memenuhi sifat-sifat pola simetri p3. Kemudian, pada proses pembangkitannya di MatLab, setiap titik pada bidang digunakan sebagai titik awal iterasi sistem dinamik, dan warna pada titik tersebut ditentukan berdasarkan jumlah iterasi yang dihasilkan melalui tiga kriteria konvergensi, yaitu Tes Euclidean, Tes Jarak Fraksional, dan Tes Jarak Maksimum. Dengan mensimulasikan beberapa kombinasi nilai-nilai parameter pada fungsi-fungsi dinamik dan menggunakan ketiga kriteria konvergensi, diperoleh berbagai pola simetri p3 yang lebih bervariasi.
References
Durbin, J.R. 2009. Modern Algebra: An Introduction Sixth Edition. John Wiley and Sons, Austin.
Gdawiec, K. 2017. Procedural Generation of Aesthetic Patterns from Dynamics and Iteration Processes. International Journal of Application Mathematics and Computers. 27(4): 827-837.
Schattschneider, D. 1978. The Plane Symmetry Groups: Their Recognition and Notation. American Mathematical Monthly. 85(6): 430-450.
Chung, K.W. dan H.S.Y. Chan. 1993. Symmetrical Patterns from Dynamics. Computer Graphics Forum, Vol 12. No. 1, 33-40.
Gdawiec, K. 2017. Procedural Generation of Aesthetic Patterns from Dynamics and Iteration processes. International Journal of Applied Mathematics and Computer Science, Vol. 27, No. 4, 827-837.
Jhonson, D. L. 2001. Symmetries. Springer Undergraduate Mathematics Series, London.
Putri, R.M. 2020. Pembangkitan Pola Simetri Refeksi dan Rotasi 60^o dari Simulasi Sistem Dinamik. Skripsi. Fakultas Matematika dan Ilmu Pengetahuan Alam. Padang : Universitas Andalas.
Viera, W.O. 2020. Pembangkitan Pola Simetri p2mm dari Simulasi Sistem Dinamik. Journal of Mathematics and Its Applications, Vol. 19, No. 2, 241-251.
Cania, K.F. 2021. Pembangkitan Pola Simetri Rotasi 90^o dari Simulasi Sistem Dinamik. Jurnal Matematika UNAND, Vol. 10, No. 1, 20-28.
Prabowo, R. 2022. Pembangkitan Pola Simetri p2 dari Simulasi Sistem Dinamik. Jurnal Matematika UNAND, Vol. 11, No. 4, 210-219.
Putra, A.R. 2022. Pembangkitan Pola Simetri p3m1 dari Simulasi Sistem Dinamik. Skripsi. Fakultas Matematika dan Ilmu Pengetahuan Alam. Padang : Universitas Andalas.
Downloads
Additional Files
Published
Issue
Section
License
All articles published in Jurnal Matematika UNAND (JMUA) are open access and licensed under the Creative Commons Attribution-ShareAlike (CC BY-SA) license. This ensures that the content is freely available to all users and can be shared and adapted, provided appropriate credit is given and any adaptations are distributed under the same license.
Copyright Holder
The copyright of all articles published in Jurnal Matematika UNAND is held by the Departemen Matematika dan Sains Data, Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA), Universitas Andalas (UNAND). This applies to all published versions, including the HTML and PDF formats of the articles.
Author Rights
While the Departemen Matematika dan Sains Data FMIPA UNAND holds the copyright for all published content, authors retain important rights under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA). This license grants authors and users the following rights:
- Reuse: Authors can reuse and distribute their work for any lawful purpose, including sharing on personal websites, institutional repositories, or in subsequent publications.
- Attribution and Adaptation: Authors and others may remix, adapt, and build upon the published work for any purpose, even commercially, as long as proper credit is given to the original authors, and any derivative works are distributed under the same CC BY-SA license.
Creative Commons License (CC BY-SA)
Under the terms of the CC BY-SA license, users are free to:
- Share: Copy and redistribute the material in any medium or format.
- Adapt: Remix, transform, and build upon the material for any purpose, even commercially.
However, the following conditions apply:
- Attribution: Users must give appropriate credit to the original author(s) and Departemen Matematika dan Sains Data FMIPA UNAND, provide a link to the license, and indicate if changes were made. Attribution must not imply endorsement by the author or the journal.
- ShareAlike: If users remix, transform, or build upon the material, they must distribute their contributions under the same license as the original.
For more information about the CC BY-SA license, please visit the Creative Commons website.
Third-Party Content
If authors include third-party material (such as figures, tables, or images) that is not covered by a Creative Commons license, they must obtain the necessary permissions for reuse and provide proper attribution. Authors are required to ensure that any third-party content complies with open-access licensing requirements or includes permissions for redistribution under similar terms.
Copyright and Licensing Information Display
The copyright and licensing terms will be clearly displayed on each article's landing page, as well as within the full-text versions (HTML and PDF) of all published articles.
No "All Rights Reserved"
As an open-access journal, JMUA does not use "All Rights Reserved" policies. Instead, the CC BY-SA license ensures that the works remain accessible and reusable for a wide audience while still protecting both the authors' and the copyright holder's rights.
Â









