Unified Metrics for Characterizing the Fractal Nature of Geographic Features
Bibliographic Data
| ID | 3775475 |
|---|---|
| Authors | Penghui Gao (0000-0003-1714-779X, Tsinghua University), Zhao Liu (0000-0002-8434-4016), Liu Zhao (0009-0002-9593-7332, Tsinghua University), Gang Liu (0000-0003-2613-7286, Chengdu University of Technology), Hongrui Zhao (0000-0003-4930-5166, Tsinghua University), Xiaoxiao Xie (0009-0002-8947-3842, Tsinghua University) |
| Year | 2017 |
| Volume | 107 |
| Issue | 6 |
| Pages | 1315-1331 |
| Publication date | 2017-11-02 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | Annals of the American Association of Geographers (JOURNAL) |
| Journal identifiers | ISSN: 2469-4452 • E-ISSN: 2469-4460 |
| Publisher | Informa UK Limited (PUBLISHER • GB) |
| DOI | 10.1080/24694452.2017.1310022 |
| OpenAlex | W2620643032 |
| Language | EN |
| Citations received | 10 |
| References cited | 45 |
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
Combinatorics · Exponent · Fractal · Fractal analysis · Fractal dimension · Fractal dimension on networks · Mathematical analysis · Mathematical economics · Monotonic function · Physics · Power index · Statistical physics · Computer Science · Human Mobility and Location-Based Analysis · Land Use and Ecosystem Services · Mathematics · Urban Design and Spatial Analysis
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Study on Fractal Characteristics of Migration-Population Flow—Evidence from Egypt
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Patterns of Socioeconomic Segregation in the Capital Cities of Fast-Track Reforming Postsocialist Countries
Temporal Scaling Behavior of Avian Influenza A (H5N1)
The Fractal Nature of Geographic Phenomena
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Spatial Analysis of Shoreline Erosion, Delaware Bay, New Jersey
Urban Indicators of China from Radiance-Calibrated Digital DMSP-OLS Nighttime Images
Fractality and Self-Similarity in the Structure of Road Networks
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Neoliberalism, Corporations, and Power
Moving Agent Pedestrians Through Space and Time
Mapping Block-Level Urban Areas for All Chinese Cities
| Unique citing works | 10 |
|---|---|
| Citations per year | 1,25 |
| Citation span | 2018 - 2024 (7) |
| Citation velocity | recent |
| Highly cited | No |
| Citation types | Neutral: 5 |