Fraktal I-Fibonacci Word dengan Modifikasi pada Pembentukan Barisan Menggunakan Aturan Penggambaran Ganjil-Genap

Abstract

Fractals are geometric objects characterized by complex patterns and self-similarity, one example of which is the i-Fibonacci Word fractal. This study examines modifications of the i-Fibonacci Word fractal through changes in the formation of its sequence. The purpose of this research is to analyze the characteristics of the i-Fibonacci Word fractal when the initial values and the recurrence rule of the sequence are modified, and to determine whether its fractal properties are preserved. Visualization is carried out using the even–odd drawing rule, where a single line segment is drawn for the digit “0”, followed by a right turn if the digit “0” is in an odd position and a left turn if it is in an even position, while the digit “1” is represented by a single straight line segment without any turn. The visualization is performed for both even and odd generalizations, specifically for i = 2, 3, 4, and 5. The results show that modifying the initial values produces different effects depending on the parameter i, fractal patterns remain formed for even values of i, but fail to form for odd values of i because the turning pattern becomes locked into an alternating right–left-right-left sequence, causing the curve to resemble a stair-like path. Meanwhile, modifying the recurrence rule still produces fractals for all values of i, but only affects the interval of repeating patterns.