Generation of Fractal Objects with Iterated Function System on the Developments of Trellis Ornament Designs

Abstract

Fractals are one of a mathematical concept that provides artistic value and is therefore widely used to design various kinds of objects. The purpose of this study is to obtain various trellis ornament designs generated from fractal objects. Some fractal objects that will be used are Koch Snowflake (m,n,c), Koch Anti-Snowflake (m,n,c) and dragon curve. The basic trellis pattern is built from basic geometry, namely line segments, rhombuses and elliptical curved lines with certain sizes. In this study, the generation of fractal objects was carried out using the Iterated Function Systems (IFS) method. In this case, IFS is carried out by utilizing Affine transformations, namely dilation, rotation and reflection. Related to the generation of the Koch Snowflake curve (m,n,c), an m-sided polygon with 3≤m≤5 is used and the side looping form uses an n-sided polygon with 3≤n≤5. The c value or the middle segment divisor used is 0.3; 0.2; and 0.19. The dilation scale on the dragon curve is 0.6≤k≤9.8 and the angle θ=90°. The iteration used to generate the Koch curve is 2 iterations while the dragon curve is 15 iterations. By taking several parameters, a trellis ornament design consisting of 5 patterns is obtained and each pattern has 3 variations of trellis motifs.