Dimensions of popcorn-like pyramid sets

Amlan Banaji, Haipeng Chen

Research output: Contribution to journalArticlepeer-review


This article concerns the dimension theory of the graphs of a family of functions which include the well-known 'popcorn function' and its pyramid-like higher-dimensional analogues. We calculate the box and Assouad dimensions of these graphs, as well as the intermediate dimensions, which are a family of dimensions interpolating between Hausdorff and box dimension. As tools in the proofs, we use the Chung–Erdős inequality from probability theory, higher-dimensional Duffin–Schaeffer type estimates from Diophantine approximation, and a bound for Euler's totient function. As applications we obtain bounds on the box dimension of fractional Brownian images of the graphs, and on the Hölder distortion between different graphs.
Original languageEnglish
Pages (from-to)151-168
Number of pages18
JournalJournal of Fractal Geometry
Issue number1
Publication statusPublished - 10 Apr 2023


  • Popcorn function
  • Box dimension
  • Assouad dimension
  • Intermediate dimensions


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