Projections of fractal percolations

Michał Rams, Károly Simon

Research output: Contribution to journalArticle

13 Citations (Scopus)


In this paper we study the radial and orthogonal projections and the distance sets of the random Cantor sets E ⊂ ℝ2, which are called Mandelbrot percolation or percolation fractals. We prove that the following assertion holds almost surely: if the Hausdorff dimension of E is greater than 1 then the orthogonal projection to every line, the radial projection with every centre, and the distance set from every point contain intervals.

Original languageEnglish
Pages (from-to)530-545
Number of pages16
JournalErgodic Theory and Dynamical Systems
Issue number2
Publication statusPublished - Sep 11 2015

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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