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6 - Iterated Function Systems

from Part Two - Examples

Published online by Cambridge University Press:  13 October 2020

Jonathan M. Fraser
Jonathan M. Fraser
Affiliation:
University of St Andrews, Scotland
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Summary

One of the most important and widely used methods for constructing fractal sets is via iterated function systems. These were introduced in a celebrated article of Hutchinson from 1980. We consider the special case of self-similar sets in Chapter 7, self-affine sets in Chapter 8, and self-conformal sets in Section 9.1, but in this chapter we introduce the theory of iterated function systems and their attractors in full generality.

Keywords

iterated function systemattractorinvariant measuresymbolic spacequasi-self-similarityAhlfors regularitysimultaneous realisation problemopen set conditionstrong separation condition
Type
Chapter
Information
Assouad Dimension and Fractal Geometry , pp. 81 - 92
Publisher: Cambridge University Press
Print publication year: 2020

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  • Iterated Function Systems
  • Jonathan M. Fraser, University of St Andrews, Scotland
  • Book: Assouad Dimension and Fractal Geometry
  • Online publication: 13 October 2020
  • Chapter DOI: https://doi.org/10.1017/9781108778459.007
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  • Iterated Function Systems
  • Jonathan M. Fraser, University of St Andrews, Scotland
  • Book: Assouad Dimension and Fractal Geometry
  • Online publication: 13 October 2020
  • Chapter DOI: https://doi.org/10.1017/9781108778459.007
Available formats
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  • Iterated Function Systems
  • Jonathan M. Fraser, University of St Andrews, Scotland
  • Book: Assouad Dimension and Fractal Geometry
  • Online publication: 13 October 2020
  • Chapter DOI: https://doi.org/10.1017/9781108778459.007
Available formats
×