Penrose Tilings and Quantum Biology: A Golden Ratio Gap — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-14
DOI
https://doi.org/10.5281/zenodo.22742261
Primary Topic
Quasicrystal Structures and Properties
Type
preprint
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preprint

Penrose Tilings and Quantum Biology: A Golden Ratio Gap — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
preprint

Penrose Tilings and Quantum Biology: A Golden Ratio Gap — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Penrose tilings are aperiodic, self-similar, and encode golden-ratio-based quasicrystalline order; recent work formalizes their parameter spaces, C*-algebras, and sofic structure, while a separate variational QFT method uses Gaussian approximations—no direct quantum-biology link found in these abstracts. | MATH: Golden ratio φ = (1+√5)/2 ≈ 1.618; inverse φ⁻¹ = φ−1 ≈ 0.618; φ² = φ+1 ≈ 2.618; Penrose rhombi angles: 36°/72° (thin) and 72°/108° (thick) — all multiples of 36° = π/5, yielding 5-fold rotational symmetry (crystallographically forbidden in periodic lattices). The "golden angle" 137.5° = 360° × (1 − 1/φ) = 360° × 0.381966... ≈ 137.5077° — this is the irrational rotation angle generating quasiperiodic phyllotaxis. Penrose tiling inflation factor: φ (each tile inflates by φ). C*-algebra K-theory for hyperbolic Penrose tilings: K₀ ≅ Z[φ] (as abelian group), K₁ ≅ Z (from arXiv:0905.1932). | CONNECTION: Direct geometric harmony: φ, φ⁻¹, φ² all appear; 0.382 = 1/φ² ≈ 0.381966 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
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