Complex Systems

On Simple Energy—Complexity Relations for Filament Tangles and Networks Download PDF

Renzo L. Ricca
Department of Mathematics and Applications
U. Milano-Bicocca
Via Cozzi 53, 20125 Milano, Italy


Structural complexity emerges from all systems that display morphological organization. Structural complexity for an intricate tangle of filaments is measured by the average crossing number of the tangle. Direct relationships between total length, energy, and structural complexity of a tangle are established. These results are based on elementary considerations that suggest a wide range of applications from magnetic energy estimates to neural and social networks and financial markets analysis.