On the Fractal Dimension of the Coastline of Negros Island, Philippines

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ABSTRACT

Coastlines have irregular shapes, are known to have fractal properties, and are formed and changed by various activities in nature. Fractals are geometric shapes with detailed structures found at any scale, and they appear very similar in different magnifications. Such a property of fractals is called self-similarity. Fractal dimension is a mathematical term that measures the complexity of a pattern, an image, or a signal by quantifying the dimensionality of fractals. Since coastlines have fractal properties, the fractal dimension can be calculated to measure the degree of irregularity in coastlines. In this study, NetLogo and a high-resolution image of the coastline of Negros Island in the Philippines were used. A box-counting dimension approach and algorithm were implemented and utilized on NetLogo to measure its fractal dimension. Results showed that the fractal dimension of the Negros Island is 1.018, which is similar to the fractal dimensions of other coastlines in the literature, although it has a relatively lower value than the rest, indicating that tectonic fault systems in this island exert strong structural control; in effect, it has less geometric complexity and a relatively smoother coastline. These results confirm the accuracy of the algorithm and the model applied, which is not far from the existing box-counting dimensions as computed by many researchers. With this, the fractal dimension of the coastlines of other islands in the Philippines, especially those challenging coastlines, can be computed using this algorithm.

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