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Further Developments in Fractals and Related Fields pp 115–134Cite as

Birkhäuser

Dimensions of Self-affine Sets: A Survey

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Abstract

Self-affine sets may be expressed as unions of reduced scale affine copies of themselves. We survey general and specific constructions of self-affine sets and in particular the problem of finding or estimating their Hausdorff or box-counting dimensions. The structure and dimensional properties of self-affine sets are somewhat subtle, for example, their dimensions need not vary continuously in the defining transformations.

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Author information

Authors and Affiliations

  1. Mathematical Institute, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland

    Kenneth Falconer

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  1. Kenneth Falconer
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Correspondence to Kenneth Falconer .

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Editors and Affiliations

  1. , LAGA, Université Paris 13, avenue J.B. Clément 99, Villetaneuse, 93430, France

    Julien Barral

  2. , Laboratoire d'Analyse et de Mathématique, Université Paris-Est Créteil - Val de Ma, Avenue du Général de Gaulle 61, Créteil Cedex, 94010, France

    Stéphane Seuret

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Falconer, K. (2013). Dimensions of Self-affine Sets: A Survey. In: Barral, J., Seuret, S. (eds) Further Developments in Fractals and Related Fields. Trends in Mathematics. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8400-6_6

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