Fractal Universality of Network Intelligence - From Planck Length to Cosmic Web, from Mycelium to Cities

Version 3.0 — Conceptual Synthesis and Research Agenda This interdisciplinary catalog documents convergent structural patterns across 30 systems spanning 87 orders of magnitude — from quantum-scale phenomena (QCD vacuum, nuclear fragmentation, quantum spacetime) through biological networks (brain, mycelium, immune system, vascular systems) to large-scale structures (cities, Internet, cosmic web). Rather than asserting a unified theory, this work proposes a research program: that complex systems operating under resource constraints and connectivity requirements may exhibit convergent structural signatures, including scale-free distributions, fractal organization, 1/f temporal spectra, and hierarchical network topology. We explore the hypothesis that these features could in some cases be described within a constrained entropy maximization framework (S = −Σ pᵢ log pᵢ, subject to connectivity and energy constraints). This is proposed as a unifying hypothesis, not a demonstrated derivation. Important caveats: The quantities compared across systems (mass fractions, volume fractions, occupation probabilities) are not directly commensurable. Observed similarities may reflect shared constraints, selection effects, or coincidence. Universality class membership is not assumed and remains to be tested. Key testable prediction: Spectral dimension measurements of brain functional connectivity, mycelial networks, and communication infrastructures may reveal scaling regimes consistent with those observed in certain critical percolation models (e.g., ds ≈ 4/3 under specific conditions). Falsification protocols are included. 81 peer-reviewed references. Epistemic status marked throughout (ESTABLISHED / OBSERVED / HYPOTHESIS / SPECULATIVE). Research coordination and conceptual synthesis: Jean-François Bourrel, CEO Groupe EDDY, Paris. Literature review and structural formalization: Claude (Anthropic, Opus 4.5).