Next Article in Journal
A Simple Method to Estimate Entropy and Free Energy of Atmospheric Gases from Their Action
Next Article in Special Issue
Classification of Heart Sounds Based on the Wavelet Fractal and Twin Support Vector Machine
Previous Article in Journal
Symmetry and Shannon Measure of Ordering: Paradoxes of Voronoi Tessellation
Previous Article in Special Issue
Local Complexity Estimation Based Filtering Method in Wavelet Domain for Magnetic Resonance Imaging Denoising
Article Menu
Issue 5 (May) cover image

Export Article

Open AccessArticle

The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation

Department of Geography, College of Urban and Environmental Sciences, Peking University, Beijing 100871, China
Entropy 2019, 21(5), 453; https://doi.org/10.3390/e21050453
Received: 28 February 2019 / Revised: 15 April 2019 / Accepted: 29 April 2019 / Published: 30 April 2019
(This article belongs to the Collection Wavelets, Fractals and Information Theory)
  |  
PDF [753 KB, uploaded 15 May 2019]
  |  

Abstract

Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of the study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal dimension estimation and the potential solutions to it. Using regular fractals as archetypes, we can reveal the causes and effects of the diversity of fractal dimension estimation results by analogy. The main factors influencing fractal dimension values of cities include prefractal structure, multi-scaling fractal patterns, and self-affine fractal growth. The solution to the problem is to substitute the real fractal dimension values with comparable fractal dimensions. The main measures are as follows. First, select a proper method for a special fractal study. Second, define a proper study area for a city according to a study aim, or define comparable study areas for different cities. These suggestions may be helpful for the students who take interest in or have already participated in the studies of fractal cities. View Full-Text
Keywords: fractal; prefractal; multifractals; self-affine fractals; fractal cities; fractal dimension measurement fractal; prefractal; multifractals; self-affine fractals; fractal cities; fractal dimension measurement
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Chen, Y. The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation. Entropy 2019, 21, 453.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top