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The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation
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...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2019
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514942/ https://www.ncbi.nlm.nih.gov/pubmed/33267167 http://dx.doi.org/10.3390/e21050453 |
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author | Chen, Yanguang |
author_facet | Chen, Yanguang |
author_sort | Chen, Yanguang |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-7514942 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2019 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75149422020-11-09 The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation Chen, Yanguang Entropy (Basel) Article 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. MDPI 2019-04-30 /pmc/articles/PMC7514942/ /pubmed/33267167 http://dx.doi.org/10.3390/e21050453 Text en © 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Chen, Yanguang The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation |
title | The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation |
title_full | The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation |
title_fullStr | The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation |
title_full_unstemmed | The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation |
title_short | The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation |
title_sort | solutions to the uncertainty problem of urban fractal dimension calculation |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514942/ https://www.ncbi.nlm.nih.gov/pubmed/33267167 http://dx.doi.org/10.3390/e21050453 |
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