Calculating box dimension with the method of types

István Kolossváry*

*Corresponding author for this work

Research output: Working paperPreprint


This paper presents a general procedure based on using the method of types to calculate the box dimension of sets. The approach unifies and simplifies multiple box counting arguments. In particular, we use it to generalize the formula for the box dimension of self-affine carpets of Gatzouras-Lalley and of Bara\'nski type to their higher dimensional sponge analogues. In addition to a closed form, we also obtain a variational formula which resembles the Ledrappier-Young formula for Hausdorff dimension.
Original languageEnglish
Number of pages14
Publication statusSubmitted - 22 Feb 2021


  • Box dimension
  • Method of types
  • Self-affine sponge
  • Ledrappier-Young formula


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