The fractal dimension of the Appalachian Trail

TL;DR

This paper estimates the fractal dimension of the Appalachian Trail using GPS data, revealing a consistent dimension that can improve distance estimations over traditional map-based methods.

Contribution

It introduces a novel application of fractal geometry to quantify the trail's complexity and improve distance measurements between points on the trail.

Findings

Fractal dimension of approximately 1.08 at scales between 20 m and 100 km.

The fractal dimension can refine hiking distance estimates from map data.

Provides a method to quantify trail complexity using GPS data.

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).