{
  "abstract": "We study the visible parts and orthogonal projections of the affine fractal percolation. We show that for the affine fractal percolation $E$, conditioned on $E \\neq \\varnothing$, almost surely the dimension of the visible part is equal to $\\min\\{1, \\dim_{\\rm H} E\\}$ from all directions except for the major contracting direction. The visible part from the major contracting direction is notably different from the other directions, and we provide a formula for its Hausdorff and box dimensions. In addition, we show that almost surely conditioned on $E \\neq \\varnothing$, $\\dim_{\\rm H} π(E) =\\min\\{ 1, \\dim_{\\rm H} E\\}$ for every orthogonal projection $π$ excluding the one onto the major contracting direction, and given $\\dim_{\\rm H} E >1$, these projections contain intervals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21768",
  "author_total": 3,
  "authors": [
    {
      "name": "Eeva Kuure"
    },
    {
      "name": "Markus Myllyoja"
    },
    {
      "name": "Aleksi Pyörälä"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2274ckndyntrg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21768",
  "fulltext_url": null,
  "id": "2274ckndyntrg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21768",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7222696203",
  "pdf_url": "https://arxiv.org/pdf/2610.21768",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2274ckndyntrg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21768",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21768"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Visible parts and projections of the affine fractal percolation",
  "title_text": "Visible parts and projections of the affine fractal percolation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/2274ckndyntrg",
  "venue": "arXiv",
  "versions": []
}