Order-Fractal transition in abstract paintings

TL;DR

This study analyzes the fractal order in Jackson Pollock's paintings using Hausdorff-Besicovitch fractal dimension, revealing a transition from disorder to order over time and suggesting fractal dimension as a potential authentication parameter.

Contribution

It introduces a fractal-order transition framework for analyzing Pollock's paintings and correlates fractal dimensions with the chronological evolution of his artwork.

Findings

Fractal dimension values range close to two, indicating a transition from disorder to order.

Self-similarity observed in specific paintings, dependent on observation scale.

Fractal spectrum similarities suggest fractal dimension could aid in artwork authentication.

Abstract

We report the degree of order of twenty-two Jackson Pollock's paintings using \emph{Hausdorff-Besicovitch fractal dimension}. Through the maximum value of each multi-fractal spectrum, the artworks are classify by the year in which they were painted. It has been reported that Pollock's paintings are fractal and it increased on his latest works. However our results show that fractal dimension of the paintings are on a range of fractal dimension with values close to two. We identify this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-order transition through its dark paint strokes in Pollocks' paintings, as structured lines following a power law measured by fractal dimension. We obtain self-similarity in some specific Pollock's paintings, that reveal an important dependence on the scale of observation. We also characterize by its fractal spectrum, the called \emph{Teri's Find}. We obtained similar spectrums between \emph{Teri's Find} and \emph{Number 5} from Pollock, suggesting that fractal dimension cannot be completely rejected as a quantitative parameter to authenticate this kind of artworks.