Projections of fractal percolations

Michal Rams; Károly Simon

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arXiv · 1306.3844

Projections of fractal percolations

Michal Rams·Károly Simon

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Abstract

In this paper we study the radial and orthogonal projections and the distance sets of the random Cantor sets $E\subset \mathbb{R}^2 $ 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 \textbf{every} line, the radial projection with \textbf{every} center, and distance set from \textbf{every} point contain intervals.

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Michal Rams, Károly Simon. 2013-06-17. Projections of fractal percolations. https://arxiv.org/abs/1306.3844

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