Construction of Three Branches Fractal Trees Using Iterated Function System

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.