Structural Universality in Natural Systems: A Comparative Analysis of Ten Diverse Classifications Branching-Type Structural Analogy in Ten Unrelated Systems

Abstract

We compare ten systems with no direct physical or informational connection: special numbers, as well as Mersenne and Wagstaff numbers (mathematics), stable isotopes of chemical elements (nuclear physics), genetic code degeneracy (molecular biology), Bravais crystallographic lattices (crystallography), the Hertzsprung–Russell diagram (astrophysics), the quark system of the Standard Model (high-energy physics), the SCOP protein fold classification (structural biology), the Nickel–Strunz mineral classification (geochemistry), and the ionic radius system (crystal chemistry). The comparison is conducted along five structural parameters: dominant branch, dwarf branches, the role of “simple” structure-forming elements, two-level structure, and the presence of “gaps” — objects that should exist according to the logic of the system but are absent. In all ten systems, the same branching “blueprint” is found. Additionally, five systems not conforming to the pattern (clouds, blood groups, the Mendeleev periodic table, tectonic plates, human races) are analyzed, allowing the boundaries of applicability of the discovered principle to be outlined. The goal of this work is not to prove a fundamental connection between the systems, but to test the hypothesis of a general topological principle of organization of bounded classification systems, independent of the specific mechanism.