Kosala Dwidja Purnomo

Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Jember, Indonesia

Dita Wahyuningtyas

Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Jember, Indonesia

Firdaus Ubaidillah

Jurusan Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Jember, Indonesia

DOI: https://doi.org/10.19184/jid.v23i1.17447

ABSTRACT 

There are two types of fractal: natural fractals and fractals set. The examples of natural fractals are trees, leaves, ferns, mountain, and coastlines. One of the examples of fractals set is Pythagorean tree. In the earlier study, the Pythagorean tree has two branches generated through several affine transformations, i.e dilation and rotation. Here, we developed the Pythagorean tree (or fractal tree) with three branches through dilation, translation, and rotation transformation using Iterated Function System (IFS) method. Some values of height and length parameters were selected to ensure the formation of a fractal tree. These parameters affected the branching angle that can result in different fractal tree shape. Some random values of height and length parameters produced several variations of fractal tree. These values influenced the shape of fractal whether it tended to the left, to the right, or symmetrical shape.

Keywords: fractals, fractal tree with three branches, Iterated Function System, affine transformation.