Mandelbrot percolation and some of its generalizations: a survey

Abstract In this survey, we collect some results regarding the Mandelbrot percolation fractal and some of its natural generalizations. We discuss projections and connectivity in detail. We also touch upon porosity, visibility, differences of independent Mandelbrot percolations (i.e. projections of products of independent percolations) and Assouad-type dimensions. In the appendix, some more general constructions are explored.