Abstract
This non-technical introduction tries to place fractal geometry into the development of contemporary mathematics. Fractals were introduced by Mandelbrot to model irregular phenomena in nature. Many of them were known before as mathematical counterexamples. The essential model assumption is self-similarity which makes it possible to describe fractals by parameters which are called dimensions or exponents. Most fractals are constructed from dynamical systems. Measures and probability theory play an important part in the study of fractals.
Workshop on Fractals and Wavelets at Rajagiri School, Kochi, India, 9 Nov 2013.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Barnsley, M.F.: Fractals Everywhere. Academic, Cambridge (1988)
Edgar, G.A.: Classics on Fractals. Addison-Wesley, Reading (1993)
Falconer, K.J.: Fractal Geometry: Mathematical Foundations and Applications. Wiley, Chichester (1990)
Hutchinson, J.E.: Fractals and self-similarity. Indiana Univ. Math. J. 30, 713–747 (1981)
Mandelbrot, B.B.: The Fractal Geometry of Nature. Freeman, San Francisco (1982)
Mandelbrot, B.B.: The Fractalist: Memoir of a Scientific Maverick. Pantheon, New York (2012)
Peitgen, H.O., Jürgens, H., Saupe, D.: Chaos and Fractals. Springer, New York (1992)
Prusinkiewisz, P., Lindenmayer, A.: The Fractal Beauty of Plants. Springer, New York (1992)
Schroeder, M.R.: Fractals, Chaos, Power Laws. Freeman, New York (1991)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Bandt, C. (2014). Introduction to Fractals. In: Bandt, C., Barnsley, M., Devaney, R., Falconer, K., Kannan, V., Kumar P.B., V. (eds) Fractals, Wavelets, and their Applications. Springer Proceedings in Mathematics & Statistics, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-08105-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-08105-2_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08104-5
Online ISBN: 978-3-319-08105-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)