Creative Brain and Abstract Art: a quantitative study on Kandinskij paintings

In this paper, we speculate that abstract art can become an useful paradigm for both studying the relationship between neuroscience and art, and as a benchmark problem for the researches on Autonomous Machine Learning (AML) in brain-like computation. In particular, we are considering the case of some Kandinskij's oeuvres. There, it seems to see a deliberate willingness of introducing some effects today's hugely studied in the neuroscience, namely, for the retrieval of mental visual images or the neural correlates underlying visual tasks. The genial use of colours, geometry and vague forms generates very complex pictures that, we claim, excite preferentially mid-hierarchic levels of the bottom-up/top-down architecture of the brain, widely recognized as a possible framework for implementing AML. We introduce a quantitative metric for confirming the intuitive and psychological ranking of complexity given to paintings and pictures, the Artistic Complexity. The paintings of the artist are analysed, by selecting appropriately the oeuvres in order to point out different aspects of the topic. The concept of non-extensive Tsallis entropy is also introduced in an information-theoretic perspective, to cope with long-range interactions, as is done in spectral analysis of the human brain EEG. fMRI experimentations are sought to justify our speculations.