{
  "abstract": "The hat and spectre monotiles, discovered in 2023, tile the plane only aperiodically. Cellular automata are studied here on patches generated by finite-state transducers, so that every experiment regenerates deterministically from a small record. Within edge-adjacency semi-totalistic rules, exhaustive and evolutionary searches find only mortal travelers: gliders are absent. Guided by a reproduction of the known Penrose-tiling glider, the rule space is extended to vertex neighborhoods and to priority-table rules whose non-quiescent states are visible to neighbors. Evolutionary search then discovers gliders on both monotilings; tracked by a sliding window that regenerates the patch along the flight, they travel one million rings at constant speed and heading. All headings are quantized, to millidegrees, onto a six-spoke compass: the fast axes of the tiling's graph metric. An ablation shows both rule-space extensions are individually necessary. All results replay exactly in an accompanying interactive essay.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22579",
  "author_total": 1,
  "authors": [
    {
      "name": "James Edmond"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dxfry5hdy35cz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22579",
  "fulltext_url": null,
  "id": "dxfry5hdy35cz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22579",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "nlin.CG"
    ],
    [
      "openalex",
      "1703|Cellular Automata and Applications"
    ]
  ],
  "openalex": "W7214052076",
  "pdf_url": "https://arxiv.org/pdf/2609.22579",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dxfry5hdy35cz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2609.22579",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22579"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.CG",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Gliders on Aperiodic Monotilings: Cellular Automata on the Hat and Spectre",
  "title_text": "Gliders on Aperiodic Monotilings: Cellular Automata on the Hat and Spectre",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/dxfry5hdy35cz",
  "venue": "arXiv",
  "versions": []
}