ANALISIS DIMENSI POLA RECURRENT DAN NON-RECURRENT DALAM PEMBANGUNAN POHON FRAKTAL DI DIMENSI 3 BERBASIS ITERATED FUNCTION SYSTEM (IFS)

ALLYZA YUSYKARINA SAFITRI, . (2025) ANALISIS DIMENSI POLA RECURRENT DAN NON-RECURRENT DALAM PEMBANGUNAN POHON FRAKTAL DI DIMENSI 3 BERBASIS ITERATED FUNCTION SYSTEM (IFS). Sarjana thesis, UNIVERSITAS NEGERI JAKARTA.

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Abstract

Fraktal merupakan objek geometri yang dibentuk melalui proses iteratif dan rekursif serta memiliki karakterisitik utama yaitu self-similarity dan detail yang tak hingga. Penelitian ini mengeksplorasi pembangkitan pohon fraktal tiga dimensi (3D) menggunakan metode Iterated Function System (IFS). Dua pola utama, yaitu recurrent (deterministik) dan non-recurrent (acak), dibangun melalui transformasi affine (skalasi, translasi, dan variasi rotasi), kemudian dimensi fraktalnya diestimasi menggunakan metode Box Counting. Visualisasi menunjukkan perbedaan signifikan: pola recurrent menghasilkan struktur simetris dengan sifat self-similarity akibat rotasi yang tetap, sementara pola non-recurrent menampilkan bentuk menyerupai pertumbuhan pohon alami yang acak dan sulit diprediksi. Perhitungan dimensi fraktal menunjukkan bahwa pola recurrent, yang dianalisis berdasarkan konsep self-similarity, memiliki nilai 2,5510. Perhitungan dimensi fraktal untuk kedua pola (recurrent dan non-recurrent) menunjukkan nilai yang tidak melebihi 3, selaras dengan teori dasar batasan dimensi fraktal dalam 3D. ***** Fractals are geometric objects formed through iterative and recursive processes and have the main characteristics of self-similarity and infinite detail. This research explores the generation of three-dimensional (3D) fractal trees using the Iterated Function System (IFS) method. Two main patterns, namely recurrent (deterministic) and non-recurrent (random), are constructed through affine transformations (scaling, translation, and rotation variations), then their fractal dimensions are estimated using the box counting method. Visualization reveals significant differences: the recurrent pattern yields a symmetrical structure with self-similarity due to fixed rotation, while the non-recurrent pattern exhibits a shape resembling the random and unpredictable growth of a natural tree. The fractal dimension calculation reveals that the recurrent pattern, which is analyzed based on the concept of self-similarity, has a value of 2.5510. The fractal dimension calculation for both patterns (recurrent and non-recurrent) shows a value that does not exceed 3, in line with the basic theory of fractal dimension limitation in 3D.

Item Type:	Thesis (Sarjana)
Additional Information:	1). Ibnu Hadi, M.Si. 2). Dr. Lukita Ambarwati, S.Pd., M.Si.
Subjects:	Sains > Matematika
Divisions:	FMIPA > S1 Matematika
Depositing User:	Allyza Yusykarina Safitri .
Date Deposited:	11 Aug 2025 04:12
Last Modified:	11 Aug 2025 04:12
URI:	http://repository.unj.ac.id/id/eprint/59195

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