Multifractal signatures of AI, animal, nature, cave, and human art

Technical Summary: Multifractal Signatures of AI, Animal, Nature, Cave, and Human Art

Problem Statement
The study addresses the lack of systematic, quantitative comparisons across diverse categories of mark-making: artificial intelligence (AI)-generated imagery, animal paintings, prehistoric cave art, human figurative art, mathematical fractals, and natural photographs. While fractal and multifractal analysis have been applied to specific artists (e.g., Pollock, van Gogh) and natural landscapes, a unified framework comparing these distinct sources of visual texture is absent. The paper investigates whether multifractal parameters can discriminate between these categories and explores the extent to which these statistical signatures might serve as correlates for intentionality, attention, and cognitive processes, while explicitly cautioning against over-interpreting texture as direct evidence of consciousness.

Methodology
The research utilized a dataset of 142 images categorized into six groups: AI-generated art ($n=19$), animal paintings ($n=24$), prehistoric cave drawings ($n=35$), human paintings by a single artist, Nicolae Grigorescu ($n=16$), mathematical fractals ($n=23$), and natural photographs ($n=25$).

• Preprocessing: Images were converted to grayscale, cropped to a central 1:1 square to ensure isotropic scaling, and normalized to pixel intensity values between 0 and 1.
• Multifractal Analysis Pipeline: A Python-based pipeline implemented a standard partition-function approach. Images were analyzed using a box-counting method on the magnitude of intensity gradients. The process involved:
  • Partitioning images into non-overlapping boxes of varying sizes (8 logarithmically spaced scales).
  • Computing the partition function $Z(q,s)$ for moment orders $q \in [-10, 10]$.
  • Deriving the mass exponent $\tau(q)$ via linear regression in log-log space.
  • Calculating generalized fractal dimensions ($D_q$) and the singularity spectrum via Legendre transform.
• Parameters: Six key parameters were extracted: Capacity dimension ($D_0$), Information dimension ($D_1$), Correlation dimension ($D_2$), Spectrum width ($\Delta\alpha$), Singularity strength ($\alpha_0$), and Spectral asymmetry ($A$).
• Statistical Analysis: Due to frequent violations of normality (assessed via Shapiro–Wilk tests), the study employed non-parametric statistics. Global differences were tested using Kruskal–Wallis H-tests, followed by pairwise Mann–Whitney U tests with Bonferroni correction.

Key Results
The analysis revealed that while generalized dimensions ($D_0, D_1, D_2$) showed moderate variation across categories, higher-order descriptors—specifically spectrum width ($\Delta\alpha$), singularity strength ($\alpha_0$), and asymmetry ($A$)—were the primary discriminators.

1. AI-Generated Art: Exhibited the widest multifractal spectra ($\Delta\alpha = 1.382$) of all categories, significantly exceeding both natural photographs and human art (which had the narrowest spectra at $\Delta\alpha = 0.613$). AI images were statistically well-behaved (mostly normal distributions) but demonstrated "hyper-multifractal" heterogeneity. Notably, AI images clustered at low asymmetry values ($0.359$), whereas human images displayed the highest mean positive asymmetry ($1.814$) of all categories.
2. Animal Paintings: On average, animal mark-making matched natural photographs in spectrum width ($\Delta\alpha \approx 1.1$). However, significant individual variation was observed. One chimpanzee (Congo) produced images with high asymmetry and fine detail, while an elephant (Suda) produced symmetric, rhythmic textures. The category showed mixed normality, driven by these individual differences.
3. Cave Art: Displayed the highest spatial uniformity (highest $D_1$ and $D_2$ values) of any category, approaching theoretical maximums. However, the category was the most heterogeneous overall, showing strong non-normality across five of six metrics. This suggests "cave art" is not a monolithic style but varies significantly by site, substrate, and preservation conditions.
4. Human Paintings (Grigorescu): Showed the narrowest spectrum width ($\Delta\alpha = 0.613$) and the highest mean positive asymmetry ($1.814$). This high asymmetry was driven largely by a single outlier painting (Peasant Girl Resting) featuring extreme figure-ground contrast. No AI-generated image, animal painting, or photograph in the sample approached this asymmetry value; the only comparable case was one cave painting.
5. Mathematical Fractals: Characterized by the highest capacity dimension ($D_0$) and near-zero asymmetry, consistent with their deterministic, formal construction.

Significance and Claims
The paper claims that multifractal analysis provides a quantitative method for distinguishing texture signatures across biological, cultural, and synthetic sources. The primary empirical contribution is the demonstration that spectrum width, $\alpha_0$, and asymmetry are more effective discriminators than generalized dimensions.

Regarding interpretation, the author proposes a "working Aesthetic Hypothesis" where multifractal signatures are treated as candidate correlates—not proof—of intentionality, compositional organization, and motor control. The paper explicitly frames the link between texture statistics and cognitive states (e.g., flow, attention, consciousness) as speculative and heuristic. It introduces a "spectrum-of-consciousness" framework (Tables 7–9) to generate testable hypotheses but emphasizes that these associations have not been validated against independent behavioral, physiological, or neural markers.

The study concludes that:

• AI textures possess distinct, wider multifractal spectra than human or natural sources, though they share low asymmetry characteristics with natural photographs in this dataset, distinct from the high asymmetry of human art.
• Animal art cannot be treated as a uniform category; individual variation (e.g., between Congo and Suda) is substantial.
• Prehistoric cave art exhibits high spatial uniformity but significant site-specific heterogeneity, challenging the notion of a single "Paleolithic style."
• Extreme figure-ground contrast (high asymmetry) in human art was observed in the sampled artist's output and did not occur in any other category within the sample, though the author states this cannot be settled as a uniquely human cognitive achievement by texture statistics alone.

The author cautions that texture statistics alone cannot resolve the "problem of other minds" or definitively attribute conscious states to non-human makers or AI systems. The study serves as a starting point for future work that combines multifractal analysis with independent measures of engagement and cognition.