Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Fractal Structures in Condensed Matter Physics

  • Tsuneyoshi Nakayama
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_229-3

Definition of the Subject

The idea of fractals is based on self-similarity, which is a symmetry property of a system characterized by invariance under an isotropic scale transformation on certain length scales. The term scale invariance has the implication that objects look the same on different scales of observations. While the underlying concept of fractals is quite simple, the concept is used for an extremely broad range of topics, providing a simple description of highly complex structures found in nature. The term fractalwas first introduced by Benoit B. Mandelbrot in 1975, who gave a definition on fractals in a simple manner “A fractal is a shape made of parts similar to the whole in some way.” Thus far, the concept of fractals has been extensively used to understand the behaviors of many complex systems or has been applied from physics, chemistry, and biology for applied sciences and technological purposes. Examples of fractal structures in condensed matter physics are...

Keywords

Fractal Dimension Hausdorff Dimension Fractal Network Fractal Structure Silica Aerogel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Hokkaido UniversitySapporoJapan