Unified Metrics for Characterizing the Fractal Nature of Geographic Features

Peichao Gao, Zhao Liu, Gang Liu, Hongrui Zhao and Xiaoxiao Xie

Annals of the American Association of Geographers, 2017, vol. 107, issue 6, 1315-1331

Abstract: The term fractal is used to describe an object displaying self-similarity at different scales. This self-similarity can be measured by either the power-law exponent or the ht-index, which is a recently proposed method for characterizing the fractal nature of geographic features. Although increasingly popular in geography, the ht-index is not sensitive to changes or evolutions of fractals, limiting its usefulness as an alternative “fractal dimension” to the power-law exponent. Two improvements to the ht-index were suggested in the literature, namely, the cumulative rate of growth (the CRG index) and the ratio of areas in a rank-size plot (the RA index). The CRG index is sensitive but not monotonic, however, with respect to the evolution of fractals. The RA index is both sensitive and monotonic but not interpretable in fractal terms. In this article, two novel metrics, referred to as unified metrics, are proposed by combining advantages of the ht-index and all of its improvements, being simultaneously easy to interpret, monotonic with respect to the evolution of fractals, and sensitive to changes in the evolution. The usefulness of unified metrics was demonstrated by both numerical experiments and case studies. Given that the idea behind the ht-index has led to a relaxed, emerging popular definition of fractals, the proposed unified metrics have great potential to be used as the standard fractal dimension along with such a definition.

Date: 2017
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1080/24694452.2017.1310022 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:raagxx:v:107:y:2017:i:6:p:1315-1331

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/raag21

DOI: 10.1080/24694452.2017.1310022

Access Statistics for this article

Annals of the American Association of Geographers is currently edited by Jennifer Cassidento

More articles in Annals of the American Association of Geographers from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().