Majalah Ilmiah Matematika dan Statistika Volume 21 Nomor 2 2021, 77 – 92 http://jurnal.ac.is/index.php/MIMS/index ISSN 1441-6669 77 VARIASI POHON FRAKTAL MENGGUNAKAN L-SYSTEMS (Fractal Tree Variations Using L-Systems) Pradifta G. Ramadhan, Kosala D. Purnomo, Firdaus Ubaidillah Jurusan Matematika, Fakultas MIPA, Universitas Jember Jl. Kalimantan 37 Jember 68121, Indonesia e-mail: pradiftagilangramadhan@gmail.com, kosala.fmipa@unej.ac.id Abstract. Fractal tree is simply a trunk and a number of branches, each of which looks like the tree itself. The fractal tree can be generated using the IFS and L- Systems methods. In this article, the author develops fractal tree generation using L- Systems with additional variations. The variations given are in thickness, length, and branch angle. This development is expected to produce more diverse fractal tree patterns. In generating a fractal tree using L-Systems, it begins by determining the letters and symbols to be used. Then determine which axioms should be used. Then the production rules are made together with the determination of the parametric L- Systems. And the last is to determine the probability value for the stochastic L- Systems. In the deterministic L-Systems, thickness variations, length variations, and branch angle variations are carried out. In the variation of branch thickness, if the ratio of the thickness of the left branch is greater than that of the right branch, the fractal tree is skewed to the left. Then in the variation of branch length if the ratio of the length of the left branch is smaller than the ratio of the length of the right branch, the length of the left branch is longer than the length of the right branch. Then at the angle of the branching the smaller the  that is included causes the branches to be closer together. The use of stochastic L-Systems can produce more diverse fractal tree patterns, even though they use the same production rules and parameter values. Keywords: Fractal, Fractal Tree, L-Systems MSC2020: 03D78 1. Pendahuluan Fraktal berasal dari bahasa Latin fractus yang artinya "patah", "rusak" atau "tidak teratur [13]. Fraktal merupakan benda geometris yang kasar pada segala skala dan terlihat dapat dibagi bagi dengan cara yang radikal [5, 10]. Inti dari konsep fraktal adalah adanya proses pembangkitan bagian-bagian yang identik melalui aturan atau rumusan tertentu dan memiliki “kesamaan diri” (self-similarity) dalam jumlah besar. Prinsip yang paling sederhana dari pembangkitan tersebut adalah keteraturan (regularity) dan keteracakan (randomness). Berdasarkan prinsip keteraturan, bagian-bagian terkecil dari suatu struktur dapat menyusun diri sendiri dalam sebuah mode periodik atau kuasiperiodik menghasilkan bentuk seperti segitiga sierpinski, kurva Koch-snowflake dan himpunan Cantor. Sementara dari prinsip keteracakan, contohnya yaitu chaos game dan