Drip Paintings and Fractal Analysis

It has been claimed [1-6] that fractal analysis can be applied to unambiguously characterize works of art such as the drip paintings of Jackson Pollock. This academic issue has become of more general interest following the recent discovery of a cache of disputed Pollock paintings. We definitively demonstrate here, by analyzing paintings by Pollock and others, that fractal criteria provide no information about artistic authenticity. This work has also led to two new results in fractal analysis of more general scientific significance. First, the composite of two fractals is not generally scale invariant and exhibits complex multifractal scaling in the small distance asymptotic limit. Second the statistics of box-counting and related staircases provide a new way to characterize geometry and distinguish fractals from Euclidean objects

Multi-fractal analysis of weighted networks

In many real complex networks, the fractal and self-similarity properties have been found. The fractal dimension is a useful method to describe fractal property of complex networks. Fractal analysis is inadequate if only taking one fractal dimension to study complex networks. In this case, multifractal analysis of complex networks are concerned. However, multifractal dimension of weighted networks are less involved. In this paper, multifractal dimension of weighted networks is proposed based on box-covering algorithm for fractal dimension of weighted networks (BCANw). The proposed method is applied to calculate the fractal dimensions of some real networks. Our numerical results indicate that the proposed method is efficient for analysis fractal property of weighted networks

Comment on "Drip Paintings and Fractal Analysis", arXiv:0710.4917v2, by K. Jones-Smith, H. Mathur and L.M. Krauss

In a recent manuscript (arXiv:0710.4917v2), Jones-Smith et al. attempt to use the well-established box-counting technique for fractal analysis to "demonstrate conclusively that fractal criteria are not useful for authentication". Here, in response to what we view to be an extremely simplistic misrepresentation of our earlier work by Jones-Smith et al., we reiterate our position regarding the potential of fractal analysis for artwork authentication. We also point out some of the flaws in the analysis presented in by Jones-Smith et al.Comment: Comment on arXiv:0710.4917v2 [cond-mat.stat-mech