Random fractal characters and length uncertainty of the continental coastline of China

Abstract

A coastline is a random fractal object in a geographical system whose length is uncertain. To determine the coastline length of a country or a region, the scaling region and fractal dimension of the coastline is first calculated, and then, the length of the coastline is measured using the scale at the lower limit or near the limit of the scaling region. For this study, the scaling region of the continental coastline of China is determined. The box-counting dimension was calculated with ArcGIS software using 33 scales and a map scale of 1:500,000, and the divider dimension calculated by a C language program. Moreover, the reliability of the Chinese coastline length value, which is widely used currently, is discussed in this paper. The results show that the scaling region of the continental coastline of China is from 0.1 to 400 km. In the scaling region, the box-counting dimension and the divider dimension of the coastline are 1.2004 and 1.0929, respectively. According to fractal theory, the divider dimension more accurately represents the irregularity of a coastline. The length of the continental coastline of China is approximately 21,900 km when the measurement scale is 0.1 km; however, the length is 18,214 km when the scale is 0.25 km, and this value approaches the continental length of China (18,400 km) in popular use today. Although the coastline length is shorter than 21,900 km, the length is acceptable because the measurement scale (0.25 km) is close to the lower limit of the scaling region.