Physical Self-Organization Drives Fibonacci Phyllotaxis in Dynamical Systems — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
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.
MATH: - **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**
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026physical,
title = {{Physical Self-Organization Drives Fibonacci Phyllotaxis in Dynamical Systems — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23587096},
url = {https://zenodo.org/records/23587096},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Physical Self-Organization Drives Fibonacci Phyllotaxis in Dynamical Systems — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23587096
UR - https://zenodo.org/records/23587096
AB - 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. MATH: - **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** Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -