Topological invariants can be used to quantify complexity in abstract paintings

Calleja, Elsa de la; Zenit, Roberto

doi:10.1016/j.knosys.2017.03.030

Cited by 7 publications

(8 citation statements)

References 51 publications

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“…The formation of these dense linear structures reflects in the decrease of the fractal dimension. It is consequence of geometrical characteristics of the structure [39,40]. For the highest salt concentration analyzed in this study the bundles percolate the system forming a quasi-two dimensional structure and the fractal dimension increases.…”

Section: B Fractal Dimension Of the Dna-salt Solutionmentioning

confidence: 82%

“…The behavior β 0 differentiate the cases (c) and (e) that show similar values for the fractal dimension D f as illustrated in the Figure 2. Even though in both cases the surface is covered, for the case (e) one structure is formed while in the case (c) many structures are present [39].…”

Section: B Fractal Dimension Of the Dna-salt Solutionmentioning

confidence: 95%

“…For the cases (a), (b) and (c) the behavior of connectivity follows the behavior of fractal dimension as illustrated in the Figure 2, increasing with the addition of salt. The relation between D f and β 0 can be explained as a function of the density of black pixels [39]. These stages show how the dsDNA are in process of link to each other.…”

Section: B Fractal Dimension Of the Dna-salt Solutionmentioning

confidence: 99%

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Topology of DNA: a honeycomb stable structure under salt effect

de la Calleja,

Bazoni,

Rocha

et al. 2017

Preprint

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Atomic Force Microscopy analysis is employed to study the geometrical and topological properties of 3000kbp DNA molecules fixed in mica substrates with M gCl2. We found that the aggregates on the substrate surface for certain salt concentrations form a honeycomb stable structure with the addition of salt. The honeycomb, and the transition to other structures, were characterized by the Betti numbers, which is a topological invariant property and by Hausdorff-Besicovitch fractal dimension PACS numbers: May be entered using the \pacs{#1} command.

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Section: B Fractal Dimension Of the Dna-salt Solutionmentioning

confidence: 82%

Section: B Fractal Dimension Of the Dna-salt Solutionmentioning

confidence: 95%

Section: B Fractal Dimension Of the Dna-salt Solutionmentioning

confidence: 99%

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Topology of DNA: a honeycomb stable structure under salt effect

de la Calleja,

Bazoni,

Rocha

et al. 2017

Preprint

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“…But first applications happened only at the turn of the twenty-first century, where the work of Taylor et al [61] showed that Pollock's paintings are characterized by an increasing fractal dimension over the course of his artistic career. This subsequently inspired the application of fractal analysis to the authenticity of paintings [62][63][64][65][66], to the evolution of artists [67,68], to the statistical properties of paintings [69] and artists [70][71][72], to art movements [73] and to other visual expressions [74][75][76]. And we would be remiss not to mention that fractal art is a fascinating subject on its own right [77].…”

Section: Visual Artsmentioning

confidence: 99%

Beauty in artistic expressions through the eyes of networks and physics

Perc

2020

J. R. Soc. Interface.

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Beauty is subjective, and as such it, of course, cannot be defined in absolute terms. But we all know or feel when something is beautiful to us personally. And in such instances, methods of statistical physics and network science can be used to quantify and to better understand what it is that evokes that pleasant feeling, be it when reading a book or looking at a painting. Indeed, recent large-scale explorations of digital data have lifted the veil on many aspects of our artistic expressions that would remain forever hidden in smaller samples. From the determination of complexity and entropy of art paintings to the creation of the flavour network and the principles of food pairing, fascinating research at the interface of art, physics and network science abounds. We here review the existing literature, focusing in particular on culinary, visual, musical and literary arts. We also touch upon cultural history and culturomics, as well as on the connections between physics and the social sciences in general. The review shows that the synergies between these fields yield highly entertaining results that can often be enjoyed by layman and experts alike. In addition to its wider appeal, the reviewed research also has many applications, ranging from improved recommendation to the detection of plagiarism.

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“…An objective quantification of an artwork presents a challenge, and as such new objective methodological approaches become a necessity 1 – 3 . The characteristics of an artwork can be quantified and compared by considering characteristics such as shape, colors and brightness 4 , 5 .…”

Section: Introductionmentioning

confidence: 99%

Kolmogorov compression complexity may differentiate different schools of Orthodox iconography

Peptenatu

Andronache

Ahammer

et al. 2022

Sci Rep

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The complexity in the styles of 1200 Byzantine icons painted between 13th and 16th from Greece, Russia and Romania was investigated through the Kolmogorov algorithmic information theory. The aim was to identify specific quantitative patterns which define the key characteristics of the three different painting schools. Our novel approach using the artificial surface images generated with Inverse FFT and the Midpoint Displacement (MD) algorithms, was validated by comparison of results with eight fractal and non-fractal indices. From the analyzes performed, normalized Kolmogorov compression complexity (KC) proved to be the best solution because it had the best complexity pattern differentiations, is not sensitive to the image size and the least affected by noise. We conclude that normalized KC methodology does offer capability to differentiate the icons within a School and amongst the three Schools.

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Topological invariants can be used to quantify complexity in abstract paintings

Cited by 7 publications

References 51 publications

Topology of DNA: a honeycomb stable structure under salt effect

Topology of DNA: a honeycomb stable structure under salt effect

Beauty in artistic expressions through the eyes of networks and physics

Kolmogorov compression complexity may differentiate different schools of Orthodox iconography

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