The dimensions of inhomogeneous self-affine sets

Stuart Andrew Burrell, Jonathan MacDonald Fraser

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1 Citation (Scopus)


We prove that the upper box dimension of an inhomogeneous self-affine set is bounded above by the maximum of the affinity dimension and the dimension of the condensation set. In addition, we determine sufficient conditions for this upper bound to be attained, which, in part, constitutes an exploration of the capacity for the condensation set to mitigate dimension drop between the affinity dimension and the corresponding homogeneous attractor. Our work improves and unifies previous results on general inhomogeneous attractors, low-dimensional affine systems, and inhomogeneous self-affine carpets, while providing inhomogeneous analogues of Falconer’s seminal results on homogeneous self-affine sets.
Original languageEnglish
Article number313-324
JournalAnnales Academiae Scientiarum Fennicae-Mathematica
Issue number1
Early online date23 Dec 2019
Publication statusPublished - 2020


  • Inhomogenous attractor
  • Self-affine set
  • Box dimension
  • Affinity dimension


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