Modeling Urban Growth and Form with Spatial Entropy

Complexity 2020:1-14 (2020)
  Copy   BIBTEX


Entropy is one of the physical bases for the fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. Using the fractal dimension, we can describe urban growth and form and characterize spatial complexity. A number of fractal models and measurements have been proposed for urban studies. However, the precondition for fractal dimension application is to find scaling relations in cities. In the absence of the scaling property, we can make use of the entropy function and measurements. This paper is devoted to researching how to describe urban growth by using spatial entropy. By analogy with fractal dimension growth models of cities, a pair of entropy increase models can be derived, and a set of entropy-based measurements can be constructed to describe urban growing process and patterns. First, logistic function and Boltzmann equation are utilized to model the entropy increase curves of urban growth. Second, a series of indexes based on spatial entropy are used to characterize urban form. Furthermore, multifractal dimension spectra are generalized to spatial entropy spectra. Conclusions are drawn as follows. Entropy and fractal dimension have both intersection and different spheres of application to urban research. Thus, for a given spatial measurement scale, fractal dimension can often be replaced by spatial entropy for simplicity. The models and measurements presented in this work are significant for integrating entropy and fractal dimension into the same framework of urban spatial analysis and understanding spatial complexity of cities.



    Upload a copy of this work     Papers currently archived: 77,697

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Entropy - A Guide for the Perplexed.Roman Frigg & Charlotte Werndl - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press. pp. 115-142.
Effective fractal dimensions.Jack H. Lutz - 2005 - Mathematical Logic Quarterly 51 (1):62-72.
Choosing a Definition of Entropy that Works.Robert H. Swendsen - 2012 - Foundations of Physics 42 (4):582-593.
Entropia a modelovanie.Ján Paulov - 2002 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 9 (2):157-175.
Time Evolution in Macroscopic Systems. II. The Entropy.W. T. Grandy - 2004 - Foundations of Physics 34 (1):21-57.
How does the Entropy/information Bound Work?Jacob D. Bekenstein - 2005 - Foundations of Physics 35 (11):1805-1823.
Maxwell's demon and the entropy cost of information.Paul N. Fahn - 1996 - Foundations of Physics 26 (1):71-93.


Added to PP

2 (#1,412,599)

6 months
1 (#481,005)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Add more references