Self-Affine Carpets on the Square Lattice

  • Authors:

  • Irene Hueter;Yuval Peres

  • Affiliations:

  • Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, USA. E-mail: hueter@math.ufl.edu.;Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel. E-mail: peres@stat.berkeley.edu.

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 1997

  • Zeta-Dimension

    MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science

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Abstract

We explore the ‘Hausdorff dimension at infinity’ for self-affine carpets defined on the square lattice. This notion of dimension (due to Barlow and Taylor), which is the correct notion from a probabilistic perspective, differs for these sets from more ‘naive’ indices of fractal dimension.