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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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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DOI: https://doi.org/10.1007/978-0-8176-8400-6_6
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