  Intricate patterns in abstract art many times can be wrongly characterized as
being complex. Complexity can be an indicator of the internal dynamic of the
whole system, regardless of the type of system in question, including art
creation. In this investigation, we use two different techniques to objectively
quantify complexity in abstract images: the fractal dimension and the value of
the Betti numbers. We first validate our technique by considering synthetic
images with a random distribution of dots, to then apply it to a series of `Net
obsession' paintings by Yayoi Kusama. Surprisingly, we found that although the
fractal dimension of her works in this series is comparable to those by Jackson
Pollock in his dripping period, which could indicate a high level of
complexity, the value of the Betti numbers do show disconnectedness and not
high complexity. This is intuitively in agreement with the visual assessment of
such works.
