Estimation of Citarum Watershed Boundary’s Length Based on Fractal’s Power Law by the Modified Box-Counting Dimension Algorithm

Michael Lim, Alit Kartiwa and Herlina Napitupulu ()
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Michael Lim: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Jawa Barat, Indonesia
Alit Kartiwa: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Jawa Barat, Indonesia
Herlina Napitupulu: Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Jawa Barat, Indonesia

Mathematics, 2023, vol. 11, issue 2, 1-12

Abstract: This research aimed to estimate the length of the Citarum watershed boundary because the data are still unknown. We used the concept of fractal’s power law and its relation to the length of an object, which is still not described in other research. The method that we used in this research is the Box-Counting dimension. The data were obtained from the geographic information system. We found an equation that described the relationship between the length and fractal dimension of an object by substituting equations. Following that, we modified the algorithm of Box-Counting dimension by consideration of requiring a high-resolution image, using the Canny edge detection so that the edges look sharper and the dimension values are more accurate. A Box-Counting program was created with Python based on the modified algorithm and used to execute the Citarum watershed boundary’s image. The values of ε and N were used to calculate the fractal dimension and the length for each scale by using the value of C = 1 , assuming the ε as the ratio between the length of box and the length of plane. Finally, we found that the dimension of Citarum watershed boundary is approximately 1.1109 and its length is 770.49 km.

Keywords: fractal dimension; Citarum watershed boundary; box-counting dimension; fractal’s power law (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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