{
  "abstract": "FINDING: Martin-Löf randomness extends to quantum states via algorithmic incompressibility, linking Turing degrees to infinite-dimensional Hilbert space structure; Turing patterns and fractal growth share algorithmic generative principles. | MATH: Martin-Löf test: \\(K(\\omega) \\geq n - O(1)\\) for prefix-free Kolmogorov complexity; Levin-Schnorr theorem: \\(\\omega\\) ML-random iff \\(\\omega\\) passes all \\(\\Sigma^0_1\\) tests; quantum analogue: \\(\\rho\\) ML-random iff \\(\\rho\\) is incompressible under quantum prefix-free complexity \\(K_Q(\\rho) \\geq n - O(1)\\); Turing patterns: reaction-diffusion \\(\\partial_t u = D_u \\nabla^2 u + f(u,v)\\), \\(\\partial_t v = D_v \\nabla^2 v + g(u,v)\\), instability when \\(D_v/D_u > 1\\) and wavelength \\(\\lambda \\propto \\sqrt{D/(\\text{reaction rate})}\\); fractal dimension \\(D = \\lim_{\\epsilon\\to 0} \\frac{\\log N(\\epsilon)}{\\log(1/\\epsilon)}\\). | CONNECTION: Fractal self-similarity ratio \\(1/3\\) (Cantor) and \\(1/2\\) (Koch) — but deeper: Turing degree partial order has a\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
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        0
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      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/eze1gecxnf84v.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635000",
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  "id": "eze1gecxnf84v",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eze1gecxnf84v.ris",
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      "first_seen": "2026-11-08T12:22:00Z",
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  "subjects": [],
  "title": "Quantum Randomness, Turing Degrees, and Algorithmic Fractal Growth — E8 Intelligence Research",
  "title_text": "Quantum Randomness, Turing Degrees, and Algorithmic Fractal Growth — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:22:00Z",
  "url": "https://research.draconitic.com/paper/eze1gecxnf84v",
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