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Intricate patterns in abstract art many times can be wrongly characterized asbeing complex. Complexity can be an indicator of the internal dynamic of thewhole system, regardless of the type of system in question, including artcreation. In this investigation, we use two different techniques to objectivelyquantify complexity in abstract images: the fractal dimension and the value ofthe Betti numbers. We first validate our technique by considering syntheticimages with a random distribution of dots, to then apply it to a series of `Netobsession' paintings by Yayoi Kusama. Surprisingly, we found that although thefractal dimension of her works in this series is comparable to those by JacksonPollock in his dripping period, which could indicate a high level ofcomplexity, the value of the Betti numbers do show disconnectedness and nothigh complexity. This is intuitively in agreement with the visual assessment ofsuch works.

Fractal dimension and topological invariants as methods to quantify complexity in Yayoi Kusama's paintings