Hidden evolving anisotropic order in Pollock’s drip paintings

Jackson Pollock’s action paintings (1943–1954) combined rapid drip-and-pour gestures with large-scale Lévy-flight movements, producing complex, apparently chaotic patterns. Here, directional geological entropy (DGE), a Shannon-entropy–based framework originally developed for heterogeneous geological systems, is applied to 47 digital images of Pollock’s works. The analysis reveals a previously unreported and systematic anisotropy in spatial order, with consistently higher disorder along the horizontal direction than along the vertical one. This directional asymmetry evolves over time, being strongest in early works (1943–1947) and progressively decreasing as Pollock’s technique matures. DGE also captures a transition from comparatively ordered to highly disordered patterns, followed by a regime of stable, near-maximum entropy. These findings establish DGE as a powerful alternative to fractal analysis and demonstrate its ability to uncover directional structure in complex visual patterns, extending entropy-based methods to the quantitative study of artistic heritage.