Predicting beauty: Fractal dimension and visual complexity in art

Forsythe, Alexandra; Nadal, Marcos; Sheehy, Noel; Cela‐Conde, Camilo J.; Sawey, Martin

doi:10.1348/000712610x498958

Cited by 178 publications

(251 citation statements)

References 54 publications

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“…Moreover, Redies et al used the Histogram of Orientation Gradients (HOG) approach to calculate two other aesthetic measures, complexity and anisotropy. In support of previously published ideas, their results showed that intermediate levels of complexity characterize visual artworks on average [Berlyne 1974;Forsythe et al 2011]. The anisotropy of orientation gradients in visual artworks is about as low as in images of diverse natural patterns and scenes (see also [Koch et al 2010]).…”

Section: Introductionsupporting

confidence: 79%

“…This type of research is in line with the notion that aesthetic artworks share specific and universal properties, which reflect functions of the human visual system in particular and of the human brain in general [Zeki 1999;Reber et al 2004;Redies 2007]. Over the years, different research groups proposed several properties that characterize aesthetic paintings [Birkhoff 1933;Arnheim 1954;Berlyne 1974;Graham and Field 2007;Redies et al 2007;Rigau et al 2008;Forsythe et al 2011]. For example, Redies et al [Redies et al 2007] and Graham and Field [Graham and Field 2007] have shown that, on average, log-log plots of the radially averaged 1d power spectrum of greyscale images tend to drop according to a power law, similar to results that have been described for natural scenes [Field et al 1987;Burton and Moorhead 1987].…”

Section: Introductionsupporting

confidence: 62%

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How self-similar are artworks at different levels of spatial resolution?

Amirshahi

Redies

Denzler

2013

Proceedings of the Symposium on Computational Aesthetics

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Recent research has shown that a large variety of aesthetic paintings are highly self-similar. The degree of self-similarity seen in artworks is close to that observed for complex natural scenes, to which low-level visual coding in the human visual system is adapted. In this paper, we introduce a new measure of self-similarity, which we will refer to as the Weighted Self-Similarity (WSS). Using PHOG, which is a state-of-the-art technique from computer vision, WSS is derived from a measure that has been previously linked to aesthetic paintings and represents self-similarity on a single level of spatial resolution. In contrast, WSS takes into account the similarity values at multiple levels of spatial resolution. The values are linked to each other by using a weighting factor so that the overall self-similarity of an image reflects how self-similarity changes at different spatial levels. Compared to the previously proposed metric, WSS has the advantage that it also takes into account differences between selfsimilarity at different levels of spatial resolution with respect to one another.An analysis of a large image dataset of aesthetic artworks (the JenAesthetics dataset) and other categories of images reveals that artworks, on average, show a relatively high WSS. Similarly, high values for WSS were obtained for images of natural patterns that can be described as being fractal (for example, images of clouds, branches or lichen growth patterns). The analysis of the JenAesthetics dataset, which consists of paintings of Western provenance, yielded similar values of WSS for different art styles. In conclusion, self-similarity is uniformly high across different levels of spatial resolution in the artworks analyzed in the present study.

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Section: Introductionsupporting

confidence: 79%

Section: Introductionsupporting

confidence: 62%

How self-similar are artworks at different levels of spatial resolution?

Amirshahi

Redies

Denzler

2013

Proceedings of the Symposium on Computational Aesthetics

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“…Hagerhall, Purcell, and Taylor [46] found that fractal characteristics of landscape silhouette outlines reliably predict landscape preferences. Fractal characteristics provide a consistent measure of complexity, and were shown to account for judgments of perceived beauty in visual art [47]. Here, we make the prediction that the "symmetry of things in a thing" in 2D fractal objects plays a decisive role in our perception of their aesthetic content and thereby influences visual preference judgments.…”

Section: Nature-inspired Design and The Symmetry Of "Things In A Thing"mentioning

confidence: 86%

Affine Geometry, Visual Sensation, and Preference for Symmetry of Things in a Thing

Dresp-Langley

2016

Symmetry

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Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and geometry of symmetry is controlled by numerical parameters, which act in analogy with a biological organism's DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional (2D) design parameters, affine geometry and shape symmetry for visual or tactile shape sensation and perception-based decision making in populations of experts and non-experts. It will be shown that 2D fractal symmetry, referred to herein as the "symmetry of things in a thing", results from principles very similar to those of affine projection. Results from experiments on aesthetic and visual preference judgments in response to 2D fractal trees with varying degrees of asymmetry are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (on a scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from "symmetry of things in a thing" significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion.

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“…This is especially important in aesthetics research, where there have been claims of universality in preference for patterns of moderately low complexity [23,26,[34][35][36][37]. To test this hypothesis, it is necessary to be able to translate the units of measurement of researchers who alternately use D [22,25,26,28,29,31,[33][34][35][36][37][38][39][40], β [14,24,30,32,[41][42][43][44][45][46], or, infrequently, both [23,27]. The crux of the problem, perhaps, is that D is a general parameter that quantifies complexity in a variety of patterns, whereas β is limited (at least in practice) in its ability to quantify some patterns' complexity.…”

Section: D(mountain Edgementioning

confidence: 99%

Relationship between Fractal Dimension and Spectral Scaling Decay Rate in Computer-Generated Fractals

et al. 2016

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Two measures are commonly used to describe scale-invariant complexity in images: fractal dimension (D) and power spectrum decay rate (β). Although a relationship between these measures has been derived mathematically, empirical validation across measurements is lacking. Here, we determine the relationship between D and β for 1-and 2-dimensional fractals. We find that for 1-dimensional fractals, measurements of D and β obey the derived relationship. Similarly, in 2-dimensional fractals, measurements along any straight-line path across the fractal's surface obey the mathematically derived relationship. However, the standard approach of vision researchers is to measure β of the surface after 2-dimensional Fourier decomposition rather than along a straight-line path. This surface technique provides measurements of β that do not obey the mathematically derived relationship with D. Instead, this method produces values of β that imply that the fractal's surface is much smoother than the measurements along the straight lines indicate. To facilitate communication across disciplines, we provide empirically derived equations for relating each measure of β to D. Finally, we discuss implications for future research on topics including stress reduction and the perception of motion in the context of a generalized equation relating β to D.

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Predicting beauty: Fractal dimension and visual complexity in art

Cited by 178 publications

References 54 publications

How self-similar are artworks at different levels of spatial resolution?

How self-similar are artworks at different levels of spatial resolution?

Affine Geometry, Visual Sensation, and Preference for Symmetry of Things in a Thing

Relationship between Fractal Dimension and Spectral Scaling Decay Rate in Computer-Generated Fractals

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