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

Table 3

Spectral exponent, fractal dimension, and related parameter values based on the standard exponential distributions (partial results).

Characteristic radius (𝑟0)	Sample path length (L)	Spectral exponent (β)	Fractal dimension (𝐷^∗𝑠)	Goodness of fit (𝑅^2)
4 = 2^2	64 = 2^6 = 64	1.3672	1.8164	0.9830
8 = 2^3	128 = 2^7 = 128	1.5387	1.7307	0.9867
16 = 2^4	256 = 2^8 = 256	1.6787	1.6607	0.9902
32 = 2^5	512 = 2^9 = 512	1.7116	1.6442	0.9900
64 = 2^6	1024 = 2^10 = 1024	1.7507	1.6247	0.9905
128 = 2^7	2048 = 2^11 = 2048	1.7738	1.6131	0.9905
256 = 2^8	4096 = 2^12 = 4096	1.7873	1.6064	0.9905