Java™ How To Program (Early Objects), Tenth Edition

18.9.1 Koch Curve Fractal

As an example, let’s look at the strictly self-similar Koch Curve fractal (Fig. 18.12). It’s formed by removing the middle third of each line in the drawing and replacing it with two lines that form a point, such that if the middle third of the original line remained, an equilateral triangle would be formed. Formulas for creating fractals often involve removing all or part of the previous fractal image. This pattern has already been determined for this fractal—we focus here on how to use those formulas in a recursive solution.

We start with a straight line (Fig. 18.12(a)) and apply the pattern, creating a triangle from the middle third (Fig. 18.12(b)). We then apply the pattern again to each straight line, resulting ...