Ht-Index for Quantifying the Fractal or Scaling Structure of Geographic Features

@article{Jiang2013HtIndexFQ,
  title={Ht-Index for Quantifying the Fractal or Scaling Structure of Geographic Features},
  author={Bin Jiang and Junjun Yin},
  journal={Annals of the Association of American Geographers},
  year={2013},
  volume={104},
  pages={530 - 540}
}
  • B. JiangJunjun Yin
  • Published 4 May 2013
  • Sociology
  • Annals of the Association of American Geographers
Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is dubious, is mainly attributed to the strict definition of fractal dimension as a measure or index for characterizing the complexity of fractals. In this article, we propose an alternative, ht-index, to quantify the fractal or scaling structure of geographic features. A geographic feature has ht-index (h) if the pattern of far… 
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123 Citations
Highly Influential Citations
14
Background Citations
70
Methods Citations
34
Results Citations
3

123 Citations

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References

SHOWING 1-10 OF 34 REFERENCES

The Fractal Nature of Geographic Phenomena

Abstract Fractal concepts have attracted substantial popular attention in the past few years. The key ideas originated in studies of map data, and many of the applications continue to be concerned…

Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping

Fractional Brownian surfaces have been widely discussed as an appropriate model for the statistical behavior of topographic surfaces. The fractals model proposes that topographic surfaces are…

Scaling and allometry in the building geometries of Greater London

Abstract.Many aggregate distributions of urban activities such as city sizes reveal scaling but hardly any work exists on the properties of spatial distributions within individual cities,…

Scaling of Geographic Space as a Universal Rule for Map Generalization

Map generalization is a process of producing maps at different levels of detail by retaining essential properties of the underlying geographic space. In this article, we explore how the map…

On the Issues of Scale, Resolution, and Fractal Analysis in the Mapping Sciences*

Scale and resolution have long been key issues in geography. The rapid development of analytical cartography, GIS, and remote sensing (the mapping sciences) in the last decade has forced the issues…

Scaling of geographic space from the perspective of city and field blocks and using volunteered geographic information

An analogy between a country and a city (or a city or geographic space in general) and a complex organism like the human body or the human brain is drawn to further elaborate on the power of this block perspective in reflecting the structure or patterns of geographic space.

Scale-Dependence And Self-Similarity In Cartographic Lines

This paper provides a typology of two classes of geometry for cartographic lines, based on the well-known Richardson plots. The first class contains objects having self-similar geometry, features…

Scaling and universality in the micro-structure ofurban space

How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension

Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable. However, many are statistically "selfsimilar," meaning that each portion can be…

Self-organized natural roads for predicting traffic flow: a sensitivity study

It was found that there exists a tipping point from segment-based to road-based network topology in terms of correlation between ranking metrics and their traffic and to the great surprise, this correlation is significantly improved if a selfish rather than utopian strategy is adopted in forming the self-organized natural roads.