29 citations · 100 across the 28 of their papers we have counts for
4 papers · 1 filter
The geometry of fractal percolation
Michal Rams, Károly Simon
A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger v…
Projections of fractal percolations
Michal Rams, Károly Simon
In this paper we study the radial and orthogonal projections and the distance sets of the random Cantor sets which are called Mandelbrot percolation or per…
The dimension of projections of fractal percolations
Michal Rams, Károly Simon
\emph{Fractal percolation} or \emph{Mandelbrot percolation} is one of the most well studied families of random fractals. In this paper we study some of the geometric measure theore…
Slicing the Sierpiński gasket
Balázs Bárány, Andrew Ferguson, Károly Simon
We investigate the dimension of intersections of the Sierpiński gasket with lines. Our first main result describes a countable, dense set of angles that are exceptional for Marstra…