Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Fractals Meet Chaos

  • Tony CrillyEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_225-3

Definition of the Subject

Though “Chaos” and “Fractals” are yoked together to form “Fractals and Chaos” they have had separate lines of development. And though the names are modern, the mathematical ideas which lie behind them have taken more than a century to gain the prominence they enjoy today. Chaos carries an applied connotation and is linked to differential equations which model physical phenomena. Fractals is directly linked to subsets of Euclidean space which have a fractional dimension, which may be obtained by the iteration of functions.

This brief survey seeks to highlight some of the significant points in the history of both of these subjects. There are brief academic histories of the field. A history of Chaos has been shown attention (Aubin and Dahan Dalmedico 2002; Holmes 2005), while an account of the early history of the iteration of complex functions (up to Julia and Fatou) is given in Alexander (1994). A broad survey of the whole field of fractals is given in Chabert...


Fractal Dimension Topological Dimension Hausdorff Dimension Strange Attractor Period Doubling 
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 2015

Authors and Affiliations

  1. 1.MathematicsMiddlesex UniversityLondonUK