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Fractal Geometry in Geosciences

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Encyclopedia of Mathematical Geosciences

Part of the book series: Encyclopedia of Earth Sciences Series ((EESS))

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Definition

A fractal is an object or feature characterized by its fractal dimension that differs from the integer Euclidian dimension of the space in which the fractal is imbedded. On the one hand, fractals are often closely associated with the random variables studied in mathematical statistics; on the other hand, they are connected with the concept of “chaos” that is an outcome of some types of nonlinear processes. Fractals are phenomena measured in terms of their presence or absence in boxes belonging to arrays superimposed on the domain of study in 1-D, 2-D, or 3-D space. Several phenomena that originally were thought to be fractals turned out to multifractals, which are “measures” representing of how much of a feature is present within the boxes used for measurement. Multifractals are spatially intertwined fractals.

Introduction

The word “fractal” was coined by Mandelbrot (1975). Evertsz and Mandelbrot (1992) explain that fractals are phenomena measured in terms of their presence...

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Author information

Authors and Affiliations

  1. School of Earth Science and Engineering, Sun Yat-Sen University, Zhuhai, China

    Qiuming Cheng

  2. State Key Lab of Geological Processes and Mineral Resources, China University of Geosciences, Beijing and Wuhan, China

    Qiuming Cheng

  3. Geological Survey of Canada, Ottawa, ON, Canada

    Frits Agterberg

Authors
  1. Qiuming Cheng
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  2. Frits Agterberg
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Corresponding author

Correspondence to Qiuming Cheng .

Editor information

Editors and Affiliations

  1. System Science & Informatics Unit, Indian Statistical Institute- Bangalore Centre, Bangalore, India

    B. S. Daya Sagar

  2. Insititue of Earth Sciences, China University of Geosciences, Beijing, China

    Qiuming Cheng

  3. School of Natural and Built Environment, Queen's University Belfast, Belfast, UK

    Jennifer McKinley

  4. Canada Geological Survey, Ottawa, ON, Canada

    Frits Agterberg

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Cheng, Q., Agterberg, F. (2021). Fractal Geometry in Geosciences. In: Daya Sagar, B.S., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-26050-7_9-1

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  • DOI: https://doi.org/10.1007/978-3-030-26050-7_9-1

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