An Analysis of Applying Fractal Dimension to Stream Networks

Fractal dimensions have been frequently applied to generalize the complexity and drainage of particular stream networks. Certain techniques to calculate dimension have become particularly popular, specifically the Divider method, functional-box counting, and as a function between bifurcation and length ratios. The frequency and variability with which these techniques are applied creates discrepancies as each technique applies different presumptions and display different fractal dimension values, skewing conclusions drawn on stream complexity. In addition, stream networks are assumed to be fractal without further validation. Analysis was conducted comparing the fractal dimensions at different sub-networks within a drainage basin to contrast the differing values between calculation techniques as well as to verify the fractality of the basin. Results indicated that the basin was fractal, but fractal dimensions between calculation techniques vary wildly and imply different relative complexities among sub-networks.