Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis

Figure 3

A log-log plot of a wave-spectrum relation based on negative exponential function. (Note that taking 𝜌₀=50000 and 𝑟₀=32 in (2.1) yields a sample path of 𝑁=512. A wave-spectrum analysis of this sample gives 𝛽=1.7116, which suggests that the fractal dimension of the self-affine record is around 𝐷_𝑠=1.6442.)