The fractal dimension of the Appalachian Trail

Abstract

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).