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<p>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.</p>

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Mandelbrot percolation and some of its generalizations: a survey

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月26日

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  • Vilma Orgoványi,
  • Károly Simon

摘要

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.