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

Table 5

The similarities and differences between inverse power law and negative exponential distributions.

Distribution	Level	Fractal property	Fractal dimension	Physical base
Power-law distribution	Macro level	Self-similarity	Radial dimension	Dual entropy maximization
	Micro level	Self-affinity	Profile dimension	fBm
Exponential distribution	Macro level	Non-fractality	Euclidean dimension	Entropy maximization
	Micro level	Self-affinity	Profile dimension	Brownian motion

Notes. The physical bases of the inverse power law and the negative exponential law can be found in the work of Chen [12, 37].