{
  "abstract": "FINDING: The Douady-Couder experiment demonstrates that phyllotaxis (Fibonacci spirals in plants) emerges from a purely dynamical system — a magnetic fluid droplet falling in a viscous oil bath with periodic magnetic forcing — without any genetic or biological instruction, revealing a physical self-organization principle.\n\nMATH: - **Core model**: The system is a one-dimensional map of successive primordia (new growth units) placed at angular increments. The key parameter is the **divergence angle** δ between successive primordia. - **Golden angle**: δ = 2π/φ² = 2π(1 − 1/φ) = 2π × 0.381966... ≈ 137.5077° — the unique angle that maximizes spacing efficiency (no two primordia align radially). - **Fibonacci numbers**: The number of visible spirals (parastichies) in each direction are consecutive Fibonacci numbers (e.g., 34 and 55), because the continued fraction of φ = [1;1,1,1,...] gives the best rational approximations via Fibonacci ratios Fₙ₊₁/Fₙ → φ. - **Dynamical instability**\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3yb7z23f13xap.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587096",
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  "id": "3yb7z23f13xap",
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  "landing_url": "https://zenodo.org/records/23587096",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3yb7z23f13xap.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:52Z",
      "native_id": "23587096",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23587096"
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  "subjects": [],
  "title": "Physical Self-Organization Drives Fibonacci Phyllotaxis in Dynamical Systems — E8 Intelligence Research",
  "title_text": "Physical Self-Organization Drives Fibonacci Phyllotaxis in Dynamical Systems — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:52Z",
  "url": "https://research.draconitic.com/paper/3yb7z23f13xap",
  "venue": "Zenodo",
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}