Quantifying Visual Complexity in Generative AI-Designed User Interfaces: Information-Theoretic and Structural Associations with Perceived Cognitive Load and Task Performance

Generative artificial intelligence is increasingly used to produce user interface designs, yet the usability and task-performance implications of AI-generated interfaces remain insufficiently quantified. This study proposes a reproducible evaluation framework combining computational visual complexity metrics with human-centered interface assessment. Twelve user interfaces were evaluated across four scenarios: a mobile health dashboard, a learning management system dashboard, an e-commerce shopping cart, and a university student information portal. Each scenario included three design conditions: human-designed reference interfaces, raw AI-generated interfaces, and prompt-optimized AI-generated interfaces. Computational metrics included grayscale Shannon entropy, spatial edge density, RGB color entropy, RMS contrast, robust contrast, and white-space ratio. A within-subject user study with 62 participants measured perceived cognitive load, perceived visual complexity, task ease, interface evaluation time, and task accuracy. Friedman tests revealed significant differences among the interface conditions for all five user-centered outcomes, with very large effect sizes. Raw AI-generated interfaces were associated with the highest perceived cognitive load, highest perceived visual complexity, lowest task ease, and longest interface evaluation times. Within the tested stimulus set, prompt-optimized AI-generated interfaces showed more favorable user-centered outcomes than raw AI interfaces but remained statistically distinct from human-designed references in perceived cognitive load, perceived visual complexity, task ease, and interface evaluation time. Task accuracy reached 100% for both human-designed and prompt-optimized AI interfaces, whereas raw AI interfaces achieved 63.10%. Interface-level correlations between computational visual metrics and user outcomes were weak to moderate, suggesting that pixel-level visual complexity measures capture only part of the perceived usability burden. Overall, these findings support the potential value of prompt-based HCI constraints in AI-generated interface design, while robust evaluation should integrate computational metrics with human-centered testing.