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

Table 4

Fractal dimensions, spectral exponents, and related statistics of land use and population distribution in Beijing.

Type	Dimensions evaluated from				Dimensions from direct calculation
	wave spectrum relation				or theoretical derivation
	𝛽	𝐷^∗𝑓	𝐷^∗𝑠	𝑅^2	𝐷𝑓	𝐷𝑠	𝑅^2
Land use (2005)	1.7030	1.8515	1.6485	0.9905	1.7827a	1.7173a	0.9850
Population (2000)	2.0549	2.0275	1.4726	0.9537	2.0000b	1.5000b	(1.0000)

Notes. ^aThe calculated value from the number-radius scaling; ^bThe expected values from the theoretical derivation. For the power-law distribution, the results can be corrected with (3.2); while the results for the xponential distribution need no correction.