The Assouad dimension of randomly generated fractals

Jonathan MacDonald Fraser, Jun Jie Miao, Sascha Troscheit

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

We consider several dierent models for generating random fractals including random self-similar sets, random self-affine carpets, and Mandelbrot percolation. In each setting we compute either the almost sure or the Baire typical Assouad dimension and consider some illustrative examples. Our results reveal a phenomenon common to each of our models: the Assouad dimension of a randomly generated fractal is generically as big as possible and does not depend on the measure theoretic or topological structure of the sample space. This is in stark contrast to the other commonly studied notions of dimension like the Hausdor or packing dimension.
Original languageEnglish
Pages (from-to)982-1011
JournalErgodic Theory and Dynamical Systems
Volume38
Issue number3
Early online date22 Sept 2016
DOIs
Publication statusPublished - May 2018

Keywords

  • Assouad dimension
  • Random fractal
  • Self-similar set
  • Self-affine carpet
  • Mandelbrot percolation
  • Baire category

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