Encyclopedia of Complexity and Systems Science

2009 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Fractal Geometry, A Brief Introduction to

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DOI: https://doi.org/10.1007/978-0-387-30440-3_218
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Definition of the Subject

In this chapter we present some definitions related to the fractal concept as well asseveral methods for calculating the fractal dimension and other relevant exponents. Thepurpose is to introduce the reader to the basic properties of fractals and self‐affinestructures so that this book will be self contained. We do not give references to most of theoriginal works, but, we refer mostly to books and reviews on fractal geometry where theoriginal references can be found.

Fractal geometry isa mathematical tool for dealing with complex systems that have no characteristic lengthscale. A well‐known example is the shape ofa coastline . When we see two picturesof a coastline on two different scales, with 1 cm corresponding for example to0.1 km or 10 km, we cannot tell which scale belongs to which picture: both lookthe same, and this features characterizes also many other geographical patterns likerivers ,cracks ,mountains , andclouds . This means that the coastline is...

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Notes

Acknowledgments

We like to thank all our coworkers in this field, in particular Eva Koscielny‐Bunde, Mikhail Bogachev, Jan Kantelhardt, Jan Eichner, Diego Rybski, Sabine Lennartz, Lev Muchnik, Kazuko Yamasaki, John Schellnhuber and Hans von Storch.

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© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikGießenGermany
  2. 2.Institute of Theoretical PhysicsBar-Ilan‐UniversityRamat GanIsrael