Topological invariants can be used to quantify complexity in abstract paintings

A method is proposed to quantify complexity in abstract art.Topological invariants, the Betti numbers, are used.The method is tested with the paintings of Jackson Pollock.Comparisons with other art pieces show the uniqueness of Pollocks paintings. Abstract art screams of complexity: its visual language purposely creates complex images that are a distorted artist-driven vision of the real world. Complexity can be recognized from either the composition, form, color, brightness, among other aspects. In this paper we show that it is possible to objectively assess the complexity of abstract paintings by determining the values of the Betti numbers associated with the image. These quantities, which are topological invariants, capture the amount of connectivity and spatial distribution of the paint traces. We apply this analysis to a series of abstract paintings, demonstrating that the complexity of Jackson Pollock paintings produced by his famous dripping technique, is superior compared with many other abstract paintings by different authors. Opposed to what was previously discussed considering only fractal properties, the complexity does not simply increase with time; instead, it displays a local maximum at a certain year which coincides with the time when Pollock perfected his technique. This tool has been used before to measure complexity in other scientific areas, but not for art assessment.

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