An analysis of silk density in spider webs

This study explores the structural complexity of spider webs through information-theoretic and harmonicity-based frameworks to quantify spatial patterns in silk density across different web regions and reveal the underlying resource allocation strategies. Currently, there is no normalized approach for describing web structure and complexity, particularly for sheet webs, and this methodology allows for non-destructive scanning and quantification of web characteristics. By analysing the entropy of silk density distributions, a single scalar that captures the heterogeneity of material investment across the entire web, we observed that the entropy values follow a normal distribution with a mean of 1.24 $\pm$ 0.22 bits when using 10 quantization levels. In the second part of the paper, by measuring the harmonicity of the silk density, we reveal that the silk density at a given point can be inferred from its neighbours, with an average harmonicity value of 0.0039 $\pm$ 0.0017 (fraction of total points in point cloud data). The harmonic behaviour is notable for its maximum principle, suggesting that the strongest parts of the web appear at the boundaries, aligning with existing knowledge of spider web construction. These findings provide a new technique for quantifying web-building strategies and offer new insights into spider behaviour and evolution.