{
  "abstract": "Cellular automata (CA) are widely used to study how simple rules generate life-like behavior, typically through local interactions. Here, we introduce a Separable-Field Cellular Automaton (SFCA), in which conventional local-neighborhood interactions are replaced by updates governed by a normalized global coupling field. Each cell is updated according to q = n/n_max, with survival and birth controlled by threshold intervals S and B. Systematic scans over interval widths and positions revealed four outcome classes: extinction, fixed points, cycles, and long transients. The phase diagram was organized by the relative geometry of S and B: fixed points were enriched when B was contained within S, whereas long transients concentrated near the boundary between partial overlap and no overlap. A fine scan across this transition revealed a narrow long-transient ridge separating two distinct cycle-dominated regimes: a dense, high-change-rate branch approximating global period-2 alternation and a sparse, low-change-rate, stripe-like branch. Damage-spreading analyses were consistent with delayed selection between these cyclic attractor families and provided no evidence for sustained exponential trajectory separation. Finite-size analyses showed that the ridge persists across all tested lattice sizes, although its position shifts systematically with system size. These results show that structured long-lived dynamics can arise under separable global coupling with a field matrix of rank at most one, suggesting that nontrivial collective organization can persist under strongly compressed interaction architectures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.08983",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaorui Shi"
    },
    {
      "name": "Mengsha Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dqn52nab3ve2r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.08983",
  "fulltext_url": null,
  "id": "dqn52nab3ve2r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.08983",
  "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",
      "cs.FL"
    ],
    [
      "arxiv",
      "nlin.CG"
    ],
    [
      "openalex",
      "1703|Cellular Automata and Applications"
    ]
  ],
  "openalex": "W7163989329",
  "pdf_url": "https://arxiv.org/pdf/2606.08983",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dqn52nab3ve2r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2606.08983",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.08983"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nlin.CG",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Dynamics in a Low-Rank Separable Field Cellular Automaton",
  "title_text": "Dynamics in a Low-Rank Separable Field Cellular Automaton",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/dqn52nab3ve2r",
  "venue": "arXiv",
  "versions": []
}