论文标题
阿巴拉契亚小径的分形维度
The fractal dimension of the Appalachian Trail
论文作者
论文摘要
阿巴拉契亚步道（AT）是美国东部的2193英里长的远足小径。该步道在不同的长度尺度上有许多弯曲和转弯，这使其具有非平凡的分形维度。在这里，我使用来自阿巴拉契亚步道保护区的GPS数据来估计AT的分形维度。我发现，在$ \ sim 20 $ m和$ \ sim 100 $ km之间的长度尺度上，该步道的定义明确的“分隔尺寸”约为1.08 $。考虑到从具有有限空间分辨率的地图（例如，Google Maps）估算的距离，该维度可用于估计两个点之间的真实远足距离。
The Appalachian Trail (AT) is a 2193-mile-long hiking trail in the eastern United States. The trail has many bends and turns at different length scales, which gives it a nontrivial fractal dimension. Here I use GPS data from the Appalachian Trail Conservancy to estimate the fractal dimension of the AT. I find that, at length scales between $\sim 20$ m and $\sim 100$ km, the trail has a well-defined "divider dimension" of $\approx 1.08$. This dimension can be used to estimate the true hiking distance between two points, given the distance as estimated from a map with finite spatial resolution (e.g., Google Maps).
