The Construction of the Koch Curve (n,c) Using L-system

Abstract

The Koch curve is a fractal that has self-similarity. It is built from a straight line segment divided into three equal parts; then, the middle part is removed and transformed into a bottomless equilateral triangle. Fractal objects can be constructed by several methods, one of which is the L-system (Lindenmayer system). L-system is a form of notation of the system of repeating a symbol by building a simple part of the object using recursive rewriting rules. This paper aims to build the Koch (, ) curve generated by varying the middle segment, which is converted into a regular n-number, where n positive integers greater than or equal to 3. The value of c defines the length of the removed segment, where c is a real number (0 < < 1) so that the Koch (, ) curves do not overlap each other. From this rule, we obtained various Koch (, ) curves using the L-system by varying the value c, which approaches the lower and upper boundary of value c.