Implementasi Natural Drawing Rule pada Variasi Fraktal i Fibonacci Word telah diuji dandisetujui pada

Abstract

Fractals are geometric structures with self-similarity properties that can be generated through recursive processes. One example is the Fibonacci Word, which later developed into the i-Fibonacci Word, still retaining repeating patterns and self-similarity. This study discusses the implementation of the Natural Drawing Rule on variations of the i-Fibonacci Word fractal by varying the placement of the number 1 in the initial sequence and applying modifications to the morphism rule. The resulting i-Fibonacci Word sequence is converted into a Dense Fibonacci Word, then visualized using the Natural Drawing Rule for the generalization of even and odd values, specifically values and . The purpose of this analysis is to analyze the visualization of i-Fibonacci Word fractal based on the variations made. The Natural Drawing Rule uses three digits {0,1,2}, namely: ‘0’ for straight line segments, ‘1’ for straight line segments and right turns, and ‘2’ for straight line segments and left turns. The results show that variations in i-Fibonacci Word still produce fractal patterns that have selfsimilarity properties. Placing the number 1 on even digits tends to form similar patterns, while on odd digits the fractal patterns are still similar but can experience position shifts and orientation changes due to variations in the morphism rule. In addition, the greater the generalization parameter value, the more complex the fractal pattern formed. Thus, the implementation of the Natural Drawing Rule in the i-Fibonacci Word fractal variation is able to show the relationship between sequence modification, morphism rules, and the visual characteristics of fractal structures.