jats:titleAbstract</jats:title>jats:pTo the human eye, different images appear more or less complex, but capturing this intuition in a single aesthetic measure is considered hard. Here, we propose a computationally simple, transparent method for modeling aesthetic complexity as a multidimensional algorithmic phenomenon, which enables the systematic analysis of large image datasets. The approach captures visual family resemblance via a multitude of image transformations and subsequent compressions, yielding explainable embeddings. It aligns well with human judgments of visual complexity, and performs well in authorship and style recognition tasks. Showcasing the functionality, we apply the method to 125,000 artworks, recovering trends and revealing new insights regarding historical art, artistic careers over centuries, and emerging aesthetics in a contemporary NFT art market. Our approach, here applied to images but applicable more broadly, provides a new perspective to quantitative aesthetics, connoisseurship, multidimensional meaning spaces, and the study of cultural complexity.</jats:p>