{
  "abstract": "FINDING: Sunflower seed heads and related phyllotactic systems converge on the golden angle 137.5077…°, producing Fibonacci-numbered spiral counts (13, 21, 34, 55, 89) as the optimal packing solution.\n\nMATH: - Golden angle: α = 360° · (1 − 1/φ) = 360°/φ² ≈ 137.507764…° - Equivalently α = 360° · (2 − φ) = 360° · 0.381966… = 137.5077…° - Golden ratio: φ = (1+√5)/2 = 1.6180339887… - Fibonacci recurrence: F(n) = F(n−1) + F(n−2); F(n+1)/F(n) → φ - Continued fraction: φ = [1;1,1,1,…] — slowest-converging irrational ⇒ most irrational number - Parastichy counts (m,n) are consecutive Fibonacci numbers; visible spiral families satisfy m/n → φ - Divergence angle error tolerance: packing remains near-optimal for α within ~±0.1° of 137.5°; deviation produces visible radial gaps - Douady–Couder experiment: ferrofluid droplets in a rotating radial magnetic field spontaneously select α ≈ 137.5° at high injection rate (dynamic self-organization, not genetic encoding)\n\nCONNECTION: - 0.381966 = 1/φ² = 2\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/4mjxdkg2b13vm.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23658804",
  "fulltext_url": null,
  "id": "4mjxdkg2b13vm",
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  "landing_url": "https://zenodo.org/records/23658804",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
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  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4mjxdkg2b13vm.ris",
  "sources": [
    {
      "first_seen": "2026-11-09T12:21:31Z",
      "native_id": "23658804",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23658804"
    }
  ],
  "subjects": [],
  "title": "Golden Angle 137.5° and Fibonacci Spirals Optimize Sunflower Seed Packing — E8 Intelligence Research",
  "title_text": "Golden Angle 137.5° and Fibonacci Spirals Optimize Sunflower Seed Packing — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-09T12:21:31Z",
  "url": "https://research.draconitic.com/paper/4mjxdkg2b13vm",
  "venue": "Zenodo",
  "versions": []
}