Enhancing stylistic discrimination in digital art: a multi-channel fractal descriptor for large-scale image analysis

The quantitative characterization of artistic styles has traditionally relied on subjective visual appraisal or simplified color metrics. Previous large-scale studies have used fractal geometry to analyze luminance patterns (grayscale); however, the intrinsic structural organization embedded within chromatic channels remains largely unexplored. This study addresses this limitation by implementing a multi-channel fractal dimension (FD) analysis using the RGB Differential Box-Counting algorithm on a massive dataset of 60,000 paintings across ten distinct styles (ArtBench-10). The primary contribution of this work is the identification of a stylistically dependent complexity gain (ΔFD) that emerges when chromatic information is integrated into the analysis. Furthermore, the analysis shows a limited linear association between the RGB fractal dimension and Shannon entropy, indicating that structural complexity and statistical disorder represent distinct stylistic dimensions not captured by entropy-based proxies alone. Results show that while luminance captures the outline of a style, ΔFD provides a unique signature for painterly techniques where color defines the topology. Furthermore, the analysis identifies the Renaissance as the statistical centroid of the dataset with the lowest stylistic divergence, explaining its ambiguity in classification tasks compared to high-divergence styles like Ukiyo-e and Surrealism. A stratified 5-fold cross-validated classification experiment shows an 18.71% relative improvement in discriminative performance over the grayscale fractal baseline (accuracy gain from 15.15% to 17.98%). Overall, chromatic fractal analysis is thus proposed as a necessary extension to existing models for a comprehensive understanding of visual complexity in digital heritage.