Work

Mandelbrot percolation and some of its generalizations: a survey

Year: 2025

Type: article

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.

Source: Research in the Mathematical Sciences

DOI: 10.1007/s40687-025-00523-9

Authors: Vilma Orgoványi, Károly Simon

Institutions: Budapest University of Technology and Economics, Hungarian Research Network, HUN-REN Alfréd Rényi Institute of Mathematics

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,090

Funders: Budapesti Műszaki és Gazdaságtudományi Egyetem, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal