Distribution of colors and patterns in images is observed through cascades
that adjust spatial resolution and dynamics. Cascades of colors reveal the
emergent universal property that Fully Colored Images (FCIs) of natural scenes
adhere to the debated continuous linear log-scale law (slope $-2.00 \pm 0.01$)
(L1). Cascades of discrete $2 \times 2$ patterns are derived from pixel squares
reductions onto the seven unlabeled rotation-free textures (0000, 0001, 0011,
0012, 0101, 0102, 0123). They exhibit an unparalleled universal entropy maximum
of $1.74 \pm 0.013$ at some dynamics regardless of spatial scale (L2). Patterns
also adhere to the Integral Fluctuation Theorem ($1.00 \pm 0.01$) (L3), pivotal
in studies of chaotic systems. Images with fewer colors exhibit quadratic shift
and bias from L1 and L3 but adhere to L2. Randomized Hilbert fractals FCIs
better match the laws than basic-to-AI-based simulations. Those results are of
interest in Neural Networks, out of equilibrium physics and spectral imagery.

图像的色彩和纹理分布通过空间分辨率和动力学的级联调整得以观察。这些级联过程揭示了自然场景中完全彩色图像遵循持续线性对数标度法则的普遍属性，并且图案的熵具有不可比拟的普遍熵最大值，还有重要的神经网络、非平衡物理和光谱图像领域的研究价值。

图像中色彩和图案的通用比例定律

Universal Scale Laws for Colors and Patterns in Imagery

We study the phenomenon of categorical perception within the quantum
measurement process. The mechanism underlying this phenomenon consists in
dilating stimuli being perceived to belong to different categories and
contracting stimuli being perceived to belong to the same category. We show
that, due to the naturally different way in determining the distance between
pure states compared to the distance between density states, the phenomenon of
categorical perception is rooted in the structure of the quantum measurement
process itself. We apply our findings to the situation of visual perception of
colors and argue that it is possible to consider colors as light quanta for
human visual perception in a similar way as photons are light quanta for
physical measurements of light frequencies. In our approach we see perception
as a complex encounter between the existing physical reality, the stimuli, and
the reality expected by the perciever, resulting in the experience of the
percepts. We investigate what that means for the situation of two colors, which
we call Light and Dark, given our findings on categorical perception within the
quantum measurement process.

我们研究了量子测量过程中的范畴感知现象，发现传统的范畴感知机制与量子测量过程的结构有关。我们将这一发现应用于颜色的视觉感知，并认为颜色可以像光子一样被视为人类视觉感知的光量。通过将现实物理、刺激和感知者期望之间的复杂互动看作是感知的基础，我们探究了这对我们所称的 “光” 和 “暗” 两种颜色的情况。