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Fractal Landscape

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Encyclopedia of Mathematical Geosciences

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

Definition

Fractals are objects with scale-invariant geometry, introduced to describe the non-Euclidian shape of natural phenomena. Fractal dimension, which is proportionate to the degree of space filled by an object withing its embedding space, is generally used to describe the fractal geometry of natural landscapes. Multifractal geometry results, if we have heterogeneity of space filling across the embedding space. Fractal properties of landscape can often be quantitatively related to the spatio-temporal scale of the associated governing natural processes, which provides novel insights into the nonlinear dynamics ubiquitous in nature.

Introduction

Many natural phenomena look similarly complex under different resolutions, a property known as scale-invariance (not to be confused with scale-independence). Without an object with a representative dimension, often referred to as a scale in the geological literature, it is impossible to determine whether the object in a picture covers a few...

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Author information

Authors and Affiliations

  1. Department of Earth and Climate Science, IISER Pune, Pune, India

    Ramendra Sahoo

Authors
  1. Ramendra Sahoo
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Corresponding author

Correspondence to Ramendra Sahoo .

Editor information

Editors and Affiliations

  1. Systems Science & Informatics Unit, Indian Statistical Institute – Bangalore Centre, Bangalore, India

    B. S. Daya Sagar

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

    Qiuming Cheng

  3. Geography, 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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Sahoo, R. (2023). Fractal Landscape. 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/10.1007/978-3-030-85040-1_121

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