Structural analysis of bio-inspired spatial systems: network efficiency of fractal morphologies

Abstract

Biological systems with tree-like morphological features emerge as nature's solution to an adaptive spatial exploration problem. The morphological complexity of these systems is often described in terms of its fractality, however, the network topology plays a relevant role behind the system's biological function. Therefore, here we considered a structural analysis of bio-inspired spatial systems based on fractal and network approaches in order to identify the features that could make tree-like morphologies better at exploring space under limited matter, energy and information. We considered connected clusters of particles in two-dimensions: the Ballistic and Diffusion-Limited Aggregation stochastic fractals, the Viscek and Hexaflake deterministic fractals, and the Kagome and Hexagonal lattices. We characterized their structure in terms of the range (linear extension), coverage (plane-filling), cost (assembly connections), configurational complexity (local connectivity), and efficiency (network communication). We found that tree-like systems have a lower configurational complexity and an invariant structural cost for different fractal dimensions, however, they are also fragile and inefficient. Nevertheless, this efficiency can become similar to that of an hexagonal lattice, at a similar cost, by considering euclidean connectivity beyond first neighbors. These results provide relevant insights into the interplay between the morphological and network properties of complex spatial systems.