The Universal Boundary–Bandwidth Law

Abstract Across biological, geological, atmospheric, and plasma systems, recurring morphologies—folds, branches, filaments, and waves—arise from a shared control principle. When transport demand (of matter, energy, charge, or information) exceeds local bandwidth within a resistant medium, systems preserve coherence by extending boundary length while maintaining interior order. Near-hexagonal packing functions as the carrier lattice for isotropic stress sharing and neighbour stability. Folding, branching, and filamentation are not expressions of excess growth or randomness, but phase-preserving responses that maintain ratio coherence under constraint. This law unifies phenomena spanning cortical folding, plant roots, soft-body locomotion, lightning, and plasma filaments without invoking scale-specific mechanisms. Keywords hexagonal packing; bandwidth limitation; boundary dynamics; folding; branching; filamentation; coherence preservation; ratio thresholds; transport networks; self-organization