Table 5.

The correspondence relationships between entropies and fractal dimensions for the spatial analysis of cities.

Parameter Level		Entropy	Fractal Dimension
Global parameter	General	Renyi entropy spectrum	Global multifractal dimension spectrum
	Special	Hartley entropy	Capacity dimension
		Shannon entropy	Information dimension
		The second-order Renyi entropy	Correlation dimension
Connection		Legendre Transform
Local parameter	General	Generalized Shannon entropy spectrum	Local multifractal dimension spectrum
		Mixed entropy	Singularity exponent spectrum
	Special	Hartley entropy	Capacity dimension
		Shannon entropy	Information dimension

Note: The Hartley entropy and Shannon entropy represent the intersection of the Renyi entropy and the generalized Shannon entropy; thus, the capacity dimension and information dimension form the intersection of the global multifractal dimensions and local multifractal dimensions.