  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.
