Universal Scale Laws for Colors and Patterns in Imagery

• Rémi Michel and Mohamed Tamaazousti
• received 12/27/2023; accepted 04/22/2024; posted 04/30/2024; Doc. ID 516720
• Abstract: Distribution of colors and patterns in images is observed through cascades that adjustspatial resolution and dynamics. Cascades of colors reveal the emergent universal propertythat Fully Colored Images (FCIs) of natural scenes adhere to the debated continuous linearlog-scale law (slope −2.00 ± 0.01) (L1). Cascades of discrete 2 × 2 patterns are derived from pixel squares reductions onto the seven unlabeled rotation-free textures (0000, 0001, 0011, 0012,0101, 0102, 01 ). They exhibit an unparalleled universal entropy maximum of 1.74 ± 0.013 atsome dynamics regardless of spatial scale (L2). Patterns also adhere to the Integral FluctuationTheorem (1.00 ± 0.01) (L3), pivotal in studies of chaotic systems. Images with fewer colorsexhibit quadratic shift and bias from L1 and L3 but adhere to L2. Randomized Hilbert fractalsFCIs better match the laws than basic-to-AI-based simulations. Those results are of interest inNeural Networks, out of equilibrium physics and spectral imagery.