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

机译:中国大陆海岸线的随机分形特征和长度不确定性

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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.
机译:海岸线是地理系统中长度不确定的随机分形对象。为了确定一个国家或地区的海岸线长度,首先计算海岸线的缩放区域和分形维数,然后使用缩放范围下限或下限附近的比例尺来测量海岸线的长度。对于本研究,确定了中国大陆海岸线的缩放区域。使用ArcGIS软件使用33比例尺和1:500,000的地图比例尺计算盒计数尺寸,并使用C语言程序计算分隔线尺寸。此外,本文还讨论了目前广泛使用的中国海岸线长度值的可靠性。结果表明,中国大陆海岸线的尺度范围为0.1至400 km。在缩放区域中,海岸线的计盒维数和分隔线维数分别为1.2004和1.0929。根据分形理论,分隔线的尺寸更准确地表示海岸线的不规则性。当测量规模为0.1 km时,中国大陆海岸线的长度约为21,900 km;但是,当比例尺为0.25 km时,其长度为18,214 km,该值接近当今广泛使用的中国大陆长度(18,400 km)。尽管海岸线长度短于21,900 km,但由于测量比例尺(0.25 km)接近标尺区域的下限,因此该长度可以接受。

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