Quantum Randomness, Turing Degrees, and Algorithmic Fractal Growth — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
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(ω) ≥ n − O(1) for prefix-free Kolmogorov complexity; Levin-Schnorr theorem: ω ML-random iff ω passes all Σ01 tests; quantum analogue: ρ ML-random iff ρ is incompressible under quantum prefix-free complexity KQ(ρ) ≥ n − O(1); Turing patterns: reaction-diffusion ∂t u = Du ∇2 u + f(u,v), ∂t v = Dv ∇2 v + g(u,v), instability when Dv/Du > 1 and wavelength λ ∝ √(D/(reaction rate)); fractal dimension D = limϵ→ 0 (log N(ϵ))/log(1/ϵ). | CONNECTION: Fractal self-similarity ratio 1/3 (Cantor) and 1/2 (Koch) — but deeper: Turing degree partial order has a
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026quantum,
title = {{Quantum Randomness, Turing Degrees, and Algorithmic Fractal Growth — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23635000},
url = {https://zenodo.org/records/23635000},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Randomness, Turing Degrees, and Algorithmic Fractal Growth — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23635000
UR - https://zenodo.org/records/23635000
AB - 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(ω) ≥ n − O(1) for prefix-free Kolmogorov complexity; Levin-Schnorr theorem: ω ML-random iff ω passes all Σ^0_1 tests; quantum analogue: ρ ML-random iff ρ is incompressible under quantum prefix-free complexity K_Q(ρ) ≥ n − O(1); Turing patterns: reaction-diffusion ∂_t u = D_u ∇^2 u + f(u,v), ∂_t v = D_v ∇^2 v + g(u,v), instability when D_v/D_u > 1 and wavelength λ ∝ √(D/(reaction rate)); fractal dimension D = lim_ϵ→ 0 (log N(ϵ))/log(1/ϵ). | CONNECTION: Fractal self-similarity ratio 1/3 (Cantor) and 1/2 (Koch) — but deeper: Turing degree partial order has a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -