Dimensions of Self-affine Sets: A Survey

Part of the Trends in Mathematics book series (TM)


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.


Hausdorff Dimension Iterate Function System Multifractal Analysis Fractal Interpolation Bernoulli Measure 
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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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of St AndrewsSt AndrewsScotland

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