The quantification of visual aesthetics and complexity have a long history, the latter previously operationalized via the application of compression algorithms. Here we generalize and extend the compression approach beyond simple complexity measures to quantify algorithmic distance in historical and contemporary visual media. The proposed "ensemble" approach works by compressing a large number of transformed versions of a given input image, resulting in a vector of associated compression ratios. This approach is more efficient than other compression-based algorithmic distances, and is particularly suited for the quantitative analysis of visual artifacts, because human creative processes can be understood as algorithms in the broadest sense. Unlike comparable image embedding methods using machine learning, our approach is fully explainable through the transformations. We demonstrate that the method is cognitively plausible and fit for purpose by evaluating it against human complexity judgments, and on automated detection tasks of authorship and style. We show how the approach can be used to reveal and quantify trends in art historical data, both on the scale of centuries and in rapidly evolving contemporary NFT art markets. We further quantify temporal resemblance to disambiguate artists outside the documented mainstream from those who are deeply embedded in Zeitgeist. Finally, we note that compression ensembles constitute a quantitative representation of the concept of visual family resemblance, as distinct sets of dimensions correspond to shared visual characteristics otherwise hard to pin down. Our approach provides a new perspective for the study of visual art, algorithmic image analysis, and quantitative aesthetics more generally.

To 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.