Variation of Rotation in Chaos Game by Modifying the Rules

Abstract

The core concept of fractals is the process of rearranging identical components that have a large amount of self-similarity. One example of fractals is the Sierpinski trianglecan be generated using the chaos game method. This method is a form of play in drawing points on triangles that have certain rules and are repeated iteratively. This research will modify the rules of chaos game triangle with the addition of various rotationswith the center of rotation at one, two, three, four, and five reference points. The visual results obtained are in the form of fractals because they have self-similarity properties and a collection of new points formed experiences rotation with the center of rotation based on the selected reference point with the direction of rotation based on the rules. The visual results of the rotation θ angle are visually symmetrical about the axis-y with the visual results of the rotation 360⁰-θ angle at one, three, four, and five reference points as the center of rotation. At two reference points as the center of rotation it is obtained that there are two parts that are visually symmetrical about a certain line. Visual results of rotation 360⁰ angles at one, two, three reference points as the center of rotation have a shape similar to the Sierpinski triangle. Whereas at four and five points of reference as the center of rotation has a shape similar to the Sierpinski triangle.