Nature-Inspired Scale-Rich Networks Achieving Near-Optimal Transport

Natural systems such as leaf venation, vascular networks, and river basins demonstrate how hierarchical architectures combining branching and loops achieve efficient, robust transport while minimizing material use. Inspired by these biological principles, we design and fabricate Scale-Rich networks generated by sequentially adding thinner elements, forming a self-organized, scale-free architecture in which thickness, length, and connectivity follow power-law distributions in the dual graph. These networks coordinate transport pathways across multiple length scales, creating heterogeneous structures that balance efficiency and stability. We experimentally and numerically investigated their thermal properties under steady-state heat flux. The Scale-Rich networks exhibit near-optimal power-law scaling of heat flux distributions (exponent ≈ –0.56), closely matching theoretical predictions for minimal energy dissipation (exponent = -0.5), and outperform periodic and random lattices in conductivity per unit mass. Our approach shows how non-periodic, hierarchical design principles enable efficient transport using less material, providing a versatile design platform for thermal management in electronics and aerospace, or efficient material flow in microfluidic devices and tissue engineering.