Structural stability and thermodynamics of artistic composition.

Inspired by the way that digital artists zoom out of the canvas to assess the visual impact of their works, we introduce a conceptually simple yet effective metric for quantifying the clarity of digital images. This metric contrasts original images with progressively "melted" counterparts, produced by randomly flipping adjacent pixel pairs. It measures the presence of stable structures, assigning the value zero to completely uniform or random images and finite values for those with discernible patterns. This metric respects the color diversity of the original image and withstands image compression and color quantization. Its suitability for diverse image analysis problems is demonstrated through its effective evaluation of textural images, the identification of structural transitions in physical systems like the Potts model, and its consistency with color theory in digital arts. This allows us to demonstrate that color in visual art functions as a state variable, akin to the spin configuration in magnets, driving artistic designs to transition between states with distinct clarity. When combined with the Shannon entropy, which quantifies color diversity, the structural stability metric can serve as a navigation tool for artists to explore pathways on the complex structural information landscape toward the completion of their artwork. As a practical demonstration, we apply our metric to refine and optimize an emote design for a video game. The structural stability metric emerges as a versatile tool for extracting nuanced structural information from digital images, which may enhance decision-making and data analysis across scientific and creative domains.