Aesthetic Responses to Exact Fractals Driven by Physical Complexity

Fractal Fluency: Processing of Fractal Stimuli Across Sight, Sound, and Touch

People are continually exposed to the rich complexity generated by the repetition of fractal patterns at different size scales. Fractals are prevalent in natural scenery and also in patterns generated by artists and mathematicians. In this chapter, we will investigate the powerful significance of fractals for the human senses. In particular, we propose that fractals with mid-range complexity play a unique role in our visual experiences because the visual system has adapted to these prevalent natural patterns. This adaptation is evident at multiple stages of the visual system, ranging from data acquisition by the eye to processing of this data in the higher visual areas of the brain. Based on these results, we will discuss a fluency model in which the visual system processes mid-complexity fractals with relative ease. This fluency optimizes the observer's capabilities (such as enhanced attention and pattern recognition) and generates an aesthetic experience accompanied by a reduction in the observer's physiological stress levels. In addition to reviewing people's responses to viewing fractals, we will compare these responses to recent research focused on fractal sounds and fractal surface textures. We will extend our fractal fluency model to allow for stimuli across multiple senses.

Bringing nature indoors: characterizing the unique contribution of fractal structure and the effects of Euclidean context on perception of fractal patterns

Imbuing the benefits of natural design into humanmade spaces, installations of fractal patterns have been employed to shape occupant experience. Previous work has demonstrated consistent trends for fractal judgments in the presence of design elements. The current study identifies the extent to which underlying pattern structure and perceptions of pattern complexity drive viewer judgments, and how response trends are altered with the incorporation of Euclidean context reminiscent of indoor spaces. This series of studies first establishes that pattern appeal, interest, naturalness, and relaxation have a fundamentally inverse relationship with perceptions of pattern complexity and that the presence of fractal structure contributes uniquely and positively to pattern perception. Subsequently, the addition of Euclidean structure establishes a discrete pattern boundary that alters fractal perceptions of interest and excitement but not the remaining judgments. The presence of consistent subpopulations, particularly those that contradict overarching perceptual trends is supported across studies, and further emphasizes the importance of adjusting pattern selection to consider the greatest number of possible viewers. Through informed pattern selection, designs can be installed to maximize desired experience of a space while minimizing negative impressions bound to arise in a minority of occupants. This set of studies demonstrates that through control of perceived pattern complexity and whether an emphasis is placed on pattern boundaries, fractal patterns can serve to establish predictable experiences of humanmade spaces in order to inject the benefits of nature into manufactured environments.

The Order & Complexity Toolbox for Aesthetics (OCTA): A systematic approach to study the relations between order, complexity, and aesthetic appreciation

Do individuals prefer stimuli that are ordered or disordered, simple or complex, or that strike the right balance of order and complexity? Earlier research mainly focused on the separate influence of order and complexity on aesthetic appreciation. When order and complexity were studied in combination, stimulus manipulations were often not parametrically controlled, only rather specific types of order (i.e., balance or symmetry) were usually studied, and/or the multidimensionality of order and complexity was largely ignored. Progress has also been limited by the lack of an easy way to create reproducible and expandible stimulus sets, including both order and complexity manipulations. The Order & Complexity Toolbox for Aesthetics (OCTA), a Python toolbox that is also available as a point-and-click Shiny application, aims to fill this gap. OCTA provides researchers with a free and easy way to create multi-element displays varying qualitatively (i.e., different types) and quantitatively (i.e., different levels) in order and complexity, based on regularity and variety along multiple element features (e.g., shape, size, color, orientation). The standard vector-based output is ideal for experiments on the web and the creation of dynamic interfaces and stimuli. OCTA will not only facilitate reproducible stimulus construction and experimental design in research on order, complexity, and aesthetics. In addition, OCTA can be a very useful tool in any type of research using visual stimuli, or even to create digital art. To illustrate OCTA's potential, we propose several possible applications and diverse questions that can be addressed using OCTA.

Statistical image properties predict aesthetic ratings in abstract paintings created by neural style transfer

Artificial intelligence has emerged as a powerful computational tool to create artworks. One application is Neural Style Transfer, which allows to transfer the style of one image, such as a painting, onto the content of another image, such as a photograph. In the present study, we ask how Neural Style Transfer affects objective image properties and how beholders perceive the novel (style-transferred) stimuli. In order to focus on the subjective perception of artistic style, we minimized the confounding effect of cognitive processing by eliminating all representational content from the input images. To this aim, we transferred the styles of 25 diverse abstract paintings onto 150 colored random-phase patterns with six different Fourier spectral slopes. This procedure resulted in 150 style-transferred stimuli. We then computed eight statistical image properties (complexity, self-similarity, edge-orientation entropy, variances of neural network features, and color statistics) for each image. In a rating study, we asked participants to evaluate the images along three aesthetic dimensions (Pleasing, Harmonious, and Interesting). Results demonstrate that not only objective image properties, but also subjective aesthetic preferences transferred from the original artworks onto the style-transferred images. The image properties of the style-transferred images explain 50 – 69% of the variance in the ratings. In the multidimensional space of statistical image properties, participants considered style-transferred images to be more Pleasing and Interesting if they were closer to a “sweet spot” where traditional Western paintings (JenAesthetics dataset) are represented. We conclude that NST is a useful tool to create novel artistic stimuli that preserve the image properties of the input style images. In the novel stimuli, we found a strong relationship between statistical image properties and subjective ratings, suggesting a prominent role of perceptual processing in the aesthetic evaluation of abstract images.

Does Amount of Information Support Aesthetic Values?

Obtaining information from the world is important for survival. The brain, therefore, has special mechanisms to extract as much information as possible from sensory stimuli. Hence, given its importance, the amount of available information may underlie aesthetic values. Such information-based aesthetic values would be significant because they would compete with others to drive decision-making. In this article, we ask, "What is the evidence that amount of information support aesthetic values?" An important concept in the measurement of informational volume is entropy. Research on aesthetic values has thus used Shannon entropy to evaluate the contribution of quantity of information. We review here the concepts of information and aesthetic values, and research on the visual and auditory systems to probe whether the brain uses entropy or other relevant measures, specially, Fisher information, in aesthetic decisions. We conclude that information measures contribute to these decisions in two ways: first, the absolute quantity of information can modulate aesthetic preferences for certain sensory patterns. However, the preference for volume of information is highly individualized, with information-measures competing with organizing principles, such as rhythm and symmetry. In addition, people tend to be resistant to too much entropy, but not necessarily, high amounts of Fisher information. We show that this resistance may stem in part from the distribution of amount of information in natural sensory stimuli. Second, the measurement of entropic-like quantities over time reveal that they can modulate aesthetic decisions by varying degrees of surprise given temporally integrated expectations. We propose that amount of information underpins complex aesthetic values, possibly informing the brain on the allocation of resources or the situational appropriateness of some cognitive models.

What Happens in Your Brain When You Walk Down the Street? Implications of Architectural Proportions, Biophilia, and Fractal Geometry for Urban Science

This article reviews current research in visual urban perception. The temporal sequence of the first few milliseconds of visual stimulus processing sheds light on the historically ambiguous topic of aesthetic experience. Automatic fractal processing triggers initial attraction/avoidance evaluations of an environment’s salubriousness, and its potentially positive or negative impacts upon an individual. As repeated cycles of visual perception occur, the attractiveness of urban form affects the user experience much more than had been previously suspected. These perceptual mechanisms promote walkability and intuitive navigation, and so they support the urban and civic interactions for which we establish communities and cities in the first place. Therefore, the use of multiple fractals needs to reintegrate with biophilic and traditional architecture in urban design for their proven positive effects on health and well-being. Such benefits include striking reductions in observers’ stress and mental fatigue. Due to their costs to individual well-being, urban performance, environmental quality, and climatic adaptation, this paper recommends that nontraditional styles should be hereafter applied judiciously to the built environment.

The Perceived Beauty of Convex Polygon Tilings: The Influence of Regularity, Curvature, and Density

Polygon tilings in natural and man-made objects show great variety. Unlike previous studies that have mainly focused on their classification and production methods, this study aimed at exploring factors that may contribute to the perceived beauty of convex polygon tilings. We analyze the dimensions of regularity, curvature, and density, as well as individual differences. Triangle tilings and hexagon tilings were tested in Experiment 1 and 2, respectively. The results showed that the perceived beauty of convex polygon tilings can be enhanced by higher levels of regularity and nonobvious local curvature. Surprisingly, the effect of density appeared to be different, with the dense triangle tilings and the less dense hexagon tilings scoring higher than the reverse. We discuss a possible explanation based on trypophobia caused by different types of polygons, as well as the observers' personality trait of agreeableness.

Aesthetics and Psychological Effects of Fractal Based Design

Highly prevalent in nature, fractal patterns possess self-similar components that repeat at varying size scales. The perceptual experience of human-made environments can be impacted with inclusion of these natural patterns. Previous work has demonstrated consistent trends in preference for and complexity estimates of fractal patterns. However, limited information has been gathered on the impact of other visual judgments. Here we examine the aesthetic and perceptual experience of fractal ‘global-forest’ designs already installed in humanmade spaces and demonstrate how fractal pattern components are associated with positive psychological experiences that can be utilized to promote occupant wellbeing. These designs are composite fractal patterns consisting of individual fractal ‘tree-seeds’ which combine to create a ‘global fractal forest.’ The local ‘tree-seed’ patterns, global configuration of tree-seed locations, and overall resulting ‘global-forest’ patterns have fractal qualities. These designs span multiple mediums yet are all intended to lower occupant stress without detracting from the function and overall design of the space. In this series of studies, we first establish divergent relationships between various visual attributes, with pattern complexity, preference, and engagement ratings increasing with fractal complexity compared to ratings of refreshment and relaxation which stay the same or decrease with complexity. Subsequently, we determine that the local constituent fractal (‘tree-seed’) patterns contribute to the perception of the overall fractal design, and address how to balance aesthetic and psychological effects (such as individual experiences of perceived engagement and relaxation) in fractal design installations. This set of studies demonstrates that fractal preference is driven by a balance between increased arousal (desire for engagement and complexity) and decreased tension (desire for relaxation or refreshment). Installations of these composite mid-high complexity ‘global-forest’ patterns consisting of ‘tree-seed’ components balance these contrasting needs, and can serve as a practical implementation of biophilic patterns in human-made environments to promote occupant wellbeing.

Parametric Cortical Representations of Complexity and Preference for Artistic and Computer-Generated Fractal Patterns Revealed by Single-Trial EEG Power Spectral Analysis

Fractals are self-similar patterns that repeat at different scales, the complexity of which are expressed as a fractional Euclidean dimension D between 0 (a point) and 2 (a filled plane). The drip paintings of American painter Jackson Pollock (JP) are fractal in nature, and Pollock's most illustrious works are of the high-D (~1.7) category. This would imply that people prefer more complex fractal patterns, but some research has instead suggested people prefer lower-D fractals. Furthermore, research has suggested that parietal and frontal brain activity tracks the complexity of fractal patterns, but previous research has artificially binned fractals depending on fractal dimension, rather than treating fractal dimension as a parametrically varying value. We used white layers extracted from JP artwork as stimuli, and constructed statistically matched 2-dimensional random Cantor sets as control stimuli. We recorded the electroencephalogram (EEG) while participants viewed the JP and matched random Cantor fractal patterns. Participants then rated their subjective preference for each pattern. We used a single-trial analysis to construct within-subject models relating subjective preference to fractal dimension D, as well as relating D and subjective preference to single-trial EEG power spectra. Results indicated that participants preferred higher-D images for both JP and Cantor stimuli. Power spectral analysis showed that, for artistic fractal images, parietal alpha and beta power parametrically tracked complexity of fractal patterns, while for matched mathematical fractals, parietal power tracked complexity of patterns over a range of frequencies, but most prominently in alpha band. Furthermore, parietal alpha power parametrically tracked aesthetic preference for both artistic and matched Cantor patterns. Overall, our results suggest that perception of complexity for artistic and computer-generated fractal images is reflected in parietal-occipital alpha and beta activity, and neural substrates of preference for complex stimuli are reflected in parietal alpha band activity.

The Potential of Biophilic Fractal Designs to Promote Health and Performance: A Review of Experiments and Applications

Fractal objects are prevalent in natural scenery. Their repetition of patterns at increasingly fine magnifications creates a rich complexity. Fractals displaying mid-range complexity are the most common and include trees, clouds, and mountains. The “fractal fluency” model states that human vision has adapted to process these mid-range fractals with ease. I will first discuss fractal fluency and demonstrate how it enhances the observer’s visual capabilities by focusing on experiments that have important practical consequences for improving the built environment. These enhanced capabilities generate an aesthetic experience and physiological stress reduction. I will discuss strategies for integrating fractals into building designs to induce positive impacts on the observer. Examples include fractal solar panels, fractal window shades, and fractal floor patterns. These applications of fractal fluency represent a fundamental and potentially impactful form of salutogenesis.

Symmetry Modulates the Amplitude Spectrum Slope Effect on Visual Preference

Within the spectrum of a natural image, the amplitude of modulation decreases with spatial frequency. The speed of such an amplitude decrease, or the amplitude spectrum slope, of an image affects the perceived aesthetic value. Additionally, a human observer would consider a symmetric image more appealing than they would an asymmetric one. We investigated how these two factors jointly affect aesthetic preferences by manipulating both the amplitude spectrum slope and the symmetric level of images to assess their effects on aesthetic preference on a 6-point Likert scale. Our results showed that the preference ratings increased with the symmetry level but had an inverted U-shaped relation to amplitude spectrum slope. In addition, a strong interaction existed between symmetry level and amplitude spectrum slope on preference rating, in that symmetry can amplify the amplitude spectrum slope’s effects. A quadratic function of the spectrum slope can describe such effects. That is, preference is an inverted U-shaped function of spectrum slope whose intercept is determined by the number of symmetry axes. The modulation depth of the quadratic function manifests the interaction between the two factors.

Aesthetic Perception of Line Patterns: Effect of Edge-Orientation Entropy and Curvilinear Shape

Curvilinearity is a perceptual feature that robustly predicts preference ratings for a variety of visual stimuli. The predictive effect of curved/angular shape overlaps, to a large degree, with regularities in second-order edge-orientation entropy, which captures how independent edge orientations are distributed across an image. For some complex line patterns, edge-orientation entropy is actually a better predictor for what human observers like than curved/angular shape. The present work was designed to disentangle the role of the two features in artificial patterns that consisted of either curved or angular line elements. We systematically varied these patterns across two more dimensions, edge-orientation entropy and the number of lines. Eighty-three participants rated the stimuli along three aesthetic dimensions (pleasing, harmonious, and complex). Results showed that curved/angular shape was a stronger predictor for ratings of pleasing and harmonious if the stimuli consisted of a few lines that were clearly discernible. By contrast, edge-orientation entropy was a stronger predictor for the ratings if the stimuli showed many lines, which merged into a texture. No such differences were obtained for complexity ratings. Our findings are in line with results from neurophysiological studies that the processing of shape and texture, respectively, is mediated by different cortical mechanisms.

Global Image Properties Predict Ratings of Affective Pictures

Affective pictures are widely used in studies of human emotions. The objects or scenes shown in affective pictures play a pivotal role in eliciting particular emotions. However, affective processing can also be mediated by low-level perceptual features, such as local brightness contrast, color or the spatial frequency profile. In the present study, we asked whether image properties that reflect global image structure and image composition affect the rating of affective pictures. We focused on 13 global image properties that were previously associated with the esthetic evaluation of visual stimuli, and determined their predictive power for the ratings of five affective picture datasets (IAPS, GAPED, NAPS, DIRTI, and OASIS). First, we used an SVM-RBF classifier to predict high and low ratings for valence and arousal, respectively, and achieved a classification accuracy of 58–76% in this binary decision task. Second, a multiple linear regression analysis revealed that the individual image properties account for between 6 and 20% of the variance in the subjective ratings for valence and arousal. The predictive power of the image properties varies for the different datasets and type of ratings. Ratings tend to share similar sets of predictors if they correlate positively with each other. In conclusion, we obtained evidence from non-linear and linear analyses that affective pictures evoke emotions not only by what they show, but they also differ by how they show it. Whether the human visual system actually uses these perceptive cues for emotional processing remains to be investigated.

Fractal solar panels: Optimizing aesthetic and electrical performances

Solar energy technologies have been plagued by their limited visual appeal. Because the electrical power generated by solar panels increases with their surface area and therefore their occupancy of the observer’s visual field, aesthetics will play an increasingly critical role in their future success in urban environments. Inspired by previous psychology research highlighting the aesthetic qualities of fractal patterns, we investigated panel designs featuring fractal electrodes. We conducted behavioral studies which compared observers’ preferences for fractal and conventional bus-bar electrode patterns, along with computer simulations which compared their electrical performances. This led us to develop a hybrid electrode pattern which best combines the fractal and bus-bar designs. Here we show that the new hybrid electrode matches the electrical performance of bus-bars in terms of light transmission and minimizing electrical power losses, while benefiting from the superior aesthetics of fractal patterns. This innovative integration of psychology and engineering studies provides a framework for developing novel electrode patterns with increased implementation and acceptance.

Aesthetic Image Statistics Vary with Artistic Genre

Research to date has not found strong evidence for a universal link between any single low-level image statistic, such as fractal dimension or Fourier spectral slope, and aesthetic ratings of images in general. This study assessed whether different image statistics are important for artistic images containing different subjects and used partial least squares regression (PLSR) to identify the statistics that correlated most reliably with ratings. Fourier spectral slope, fractal dimension and Shannon entropy were estimated separately for paintings containing landscapes, people, still life, portraits, nudes, animals, buildings and abstracts. Separate analyses were performed on the luminance and colour information in the images. PLSR fits showed shared variance of up to 75% between image statistics and aesthetic ratings. The most important statistics and image planes varied across genres. Variation in statistics may reflect characteristic properties of the different neural sub-systems that process different types of image.

The Perceived Beauty of Regular Polygon Tessellations

Beauty judgments for regular polygon tessellations were examined in two experiments. In experiment 1 we tested the three regular and eight semi-regular tilings characterized by a single vertex. In experiment 2 we tested the 20 demi-regular tilings containing two vertices. Observers viewed the tessellations at different random orientations inside a circular aperture and rated them using a numeric 1–7 scale. The data from the first experiment show a peak in preference for tiles with two types of polygons and for five polygons around a vertex. Triangles were liked more than other geometric shapes. The results from the second experiment demonstrate a preference for tessellations with a greater number of different kinds of polygons in the overall pattern and for tiles with the greatest difference in the number of polygons between the two vertices. Ratings were higher for tiles with circular arrangements of elements and lower for those with linear arrangements. Symmetry group p6m was liked the most and groups cmm and pmm were liked the least. Taken as a whole the results suggest a preference for complexity and variety in terms of both vertex qualities and symmetric transformations. Observers were sensitive to both the underlying mathematical properties of the patterns as well as their emergent organization.

Macaques preferentially attend to visual patterns with higher fractal dimension contours

Animals' sensory systems evolved to efficiently process information from their environmental niches. Niches often include irregular shapes and rough textures (e.g., jagged terrain, canopy outlines) that must be navigated to find food, escape predators, and master other fitness-related challenges. For most primates, vision is the dominant sensory modality and thus, primates have evolved systems for processing complicated visual stimuli. One way to quantify information present in visual stimuli in natural scenes is evaluating their fractal dimension. We hypothesized that sensitivity to complicated geometric forms, indexed by fractal dimension, is an evolutionarily conserved capacity, and tested this capacity in rhesus macaques (Macaca mulatta). Monkeys viewed paired black and white images of simulated self-similar contours that systematically varied in fractal dimension while their attention to the stimuli was measured using noninvasive infrared eye tracking. They fixated more frequently on, dwelled for longer durations on, and had attentional biases towards images that contain boundary contours with higher fractal dimensions. This indicates that, like humans, they discriminate between visual stimuli on the basis of fractal dimension and may prefer viewing informationally rich visual stimuli. Our findings suggest that sensitivity to fractal dimension may be a wider ability of the vertebrate vision system.

Edge-Orientation Entropy Predicts Preference for Diverse Types of Man-Made Images

We recently found that luminance edges are more evenly distributed across orientations in large subsets of traditional artworks, i.e., artworks are characterized by a relatively high entropy of edge orientations, when compared to several categories of other (non-art) images. In the present study, we asked whether edge-orientation entropy is associated with aesthetic preference in a wide variety of other man-made visual patterns and scenes. In the first (exploratory) part of the study, participants rated the aesthetic appeal of simple shapes, artificial ornamental patterns, facades of buildings, scenes of interior architecture, and music album covers. Results indicated that edge-orientation entropy predicts aesthetic ratings for these stimuli. However, the magnitude of the effect depended on the type of images analyzed, on the range of entropy values encountered, and on the type of aesthetic rating (pleasing, interesting, or harmonious). For example, edge-orientation entropy predicted about half of the variance when participants rated facade photographs for pleasing and interesting, but only for 3.5% of the variance for harmonious ratings of music album covers. We also asked whether edge-orientation entropy relates to the well-established human preference for curved over angular shapes. Our analysis revealed that edge-orientation entropy was as good or an even better predictor for the aesthetic ratings than curvilinearity. Moreover, entropy could substitute for shape, at least in part, to predict the aesthetic ratings. In the second (experimental) part of this study, we generated complex line stimuli that systematically varied in their edge-orientation entropy and curved/angular shape. Here, edge-orientation entropy was a more powerful predictor for ratings of pleasing and harmonious than curvilinearity, and as good a predictor for interesting. Again, the two image properties shared a large portion of variance between them. In summary, our results indicate that edge-orientation entropy predicts aesthetic ratings in diverse man-made visual stimuli. Moreover, the preference for high edge-orientation entropy shares a large portion of predicted variance with the preference for curved over angular stimuli.

Preference for Fractal-Scaling Properties Across Synthetic Noise Images and Artworks

A large number of studies support the notion that synthetic images within a certain intermediate fractal-scaling range possess an intrinsic esthetic value. Interestingly, the fractal-scaling properties that define this intermediate range have also been found to characterize a vast collection of representational, abstract, and graphic art. While some have argued that these statistic properties only serve to maximize the visibility of the artworks' spatial structure, others argue that they are intrinsically tied to the artworks' esthetic appeal. In this study, we bring together these two threads of research and make a direct comparison between visual preference for varying fractal-scaling characteristics in both synthetic images and artworks. Across two studies, viewers ranked and rated sets of synthetic noise images and artworks that systematically varied in fractal dimension for liking, pleasantness, complexity, and interestingness. We analyzed both average and individual patterns of preference between the two image classes. Average preference peaked for intermediate fractal dimension values for both categories, but individual patterns of preferences for both high and low values also emerged. Correlational analyses indicated that individual preferences between the two image classes remained moderately consistent and were improved when the fractal dimensions between synthetic images and artworks were more closely matched. Overall, these findings further support the role of fractal-scaling statistics both as a key determinant of an object's esthetic value and as a valuable predictor of individual differences in esthetic preference.

Visual Complexity and Affect: Ratings Reflect More Than Meets the Eye

Pictorial stimuli can vary on many dimensions, several aspects of which are captured by the term 'visual complexity.' Visual complexity can be described as, "a picture of a few objects, colors, or structures would be less complex than a very colorful picture of many objects that is composed of several components." Prior studies have reported a relationship between affect and visual complexity, where complex pictures are rated as more pleasant and arousing. However, a relationship in the opposite direction, an effect of affect on visual complexity, is also possible; emotional arousal and valence are known to influence selective attention and visual processing. In a series of experiments, we found that ratings of visual complexity correlated with affective ratings, and independently also with computational measures of visual complexity. These computational measures did not correlate with affect, suggesting that complexity ratings are separately related to distinct factors. We investigated the relationship between affect and ratings of visual complexity, finding an 'arousal-complexity bias' to be a robust phenomenon. Moreover, we found this bias could be attenuated when explicitly indicated but did not correlate with inter-individual difference measures of affective processing, and was largely unrelated to cognitive and eyetracking measures. Taken together, the arousal-complexity bias seems to be caused by a relationship between arousal and visual processing as it has been described for the greater vividness of arousing pictures. The described arousal-complexity bias is also of relevance from an experimental perspective because visual complexity is often considered a variable to control for when using pictorial stimuli.

Computational and Experimental Approaches to Visual Aesthetics

Aesthetics has been the subject of long-standing debates by philosophers and psychologists alike. In psychology, it is generally agreed that aesthetic experience results from an interaction between perception, cognition, and emotion. By experimental means, this triad has been studied in the field of experimental aesthetics, which aims to gain a better understanding of how aesthetic experience relates to fundamental principles of human visual perception and brain processes. Recently, researchers in computer vision have also gained interest in the topic, giving rise to the field of computational aesthetics. With computing hardware and methodology developing at a high pace, the modeling of perceptually relevant aspect of aesthetic stimuli has a huge potential. In this review, we present an overview of recent developments in computational aesthetics and how they relate to experimental studies. In the first part, we cover topics such as the prediction of ratings, style and artist identification as well as computational methods in art history, such as the detection of influences among artists or forgeries. We also describe currently used computational algorithms, such as classifiers and deep neural networks. In the second part, we summarize results from the field of experimental aesthetics and cover several isolated image properties that are believed to have a effect on the aesthetic appeal of visual stimuli. Their relation to each other and to findings from computational aesthetics are discussed. Moreover, we compare the strategies in the two fields of research and suggest that both fields would greatly profit from a joined research effort. We hope to encourage researchers from both disciplines to work more closely together in order to understand visual aesthetics from an integrated point of view.

Statistical Image Properties in Large Subsets of Traditional Art, Bad Art, and Abstract Art

Several statistical image properties have been associated with large subsets of traditional visual artworks. Here, we investigate some of these properties in three categories of art that differ in artistic claim and prestige: (1) Traditional art of different cultural origin from established museums and art collections (oil paintings and graphic art of Western provenance, Islamic book illustration and Chinese paintings), (2) Bad Art from two museums that collect contemporary artworks of lesser importance (© Museum Of Bad Art [MOBA], Somerville, and Official Bad Art Museum of Art [OBAMA], Seattle), and (3) twentieth century abstract art of Western provenance from two prestigious museums (Tate Gallery and Kunstsammlung Nordrhein-Westfalen). We measured the following four statistical image properties: the fractal dimension (a measure relating to subjective complexity); self-similarity (a measure of how much the sections of an image resemble the image as a whole), 1st-order entropy of edge orientations (a measure of how uniformly different orientations are represented in an image); and 2nd-order entropy of edge orientations (a measure of how independent edge orientations are across an image). As shown previously, traditional artworks of different styles share similar values for these measures. The values for Bad Art and twentieth century abstract art show a considerable overlap with those of traditional art, but we also identified numerous examples of Bad Art and abstract art that deviate from traditional art. By measuring statistical image properties, we quantify such differences in image composition for the first time.

Subjective Ratings of Beauty and Aesthetics: Correlations With Statistical Image Properties in Western Oil Paintings

For centuries, oil paintings have been a major segment of the visual arts. The JenAesthetics data set consists of a large number of high-quality images of oil paintings of Western provenance from different art periods. With this database, we studied the relationship between objective image measures and subjective evaluations of the images, especially evaluations on aesthetics (defined as artistic value) and beauty (defined as individual liking). The objective measures represented low-level statistical image properties that have been associated with aesthetic value in previous research. Subjective rating scores on aesthetics and beauty correlated not only with each other but also with different combinations of the objective measures. Furthermore, we found that paintings from different art periods vary with regard to the objective measures, that is, they exhibit specific patterns of statistical image properties. In addition, clusters of participants preferred different combinations of these properties. In conclusion, the results of the present study provide evidence that statistical image properties vary between art periods and subject matters and, in addition, they correlate with the subjective evaluation of paintings by the participants.

An Explanation for the Role of the Amygdala in Aesthetic Judgments

It has been proposed that the top-down guidance of feature-based attention is the basis for the involvement of the amygdala in various tasks requiring emotional decision-making (Jacobs et al., 2012a). Aesthetic judgments are correlated with particular visual features and can be considered emotional in nature (Jacobs et al., 2016). Moreover, we have previously shown that various aesthetic judgments result in observers preferentially attending to different visual features (Jacobs et al., 2010). Here, we argue that—together—this explains why the amygdalae become active during aesthetic judgments of visual materials. We discuss potential implications and predictions of this theory that can be tested experimentally.

High entropy of edge orientations characterizes visual artworks from diverse cultural backgrounds

We asked whether "good composition" or "visual rightness" of artworks manifest themselves in a particular arrangement of basic image features, such as oriented luminance edges. Specifically, we analysed the layout of edge orientations in images from a collection of >1600 paintings of Western provenance by comparing pairwise the orientation of each edge in an image with the orientations of all other edges in the same image. From the resulting orientation histograms, we calculated Shannon entropy and parallelism (i.e., the degree to which lines are parallel in the image). For comparison, we analysed the same second-order image properties in photographs of diverse natural patterns and man-made objects and scenes. Results showed that Shannon entropy of relative orientations of edge pairs was high and parallelism was low for the paintings and some of the natural patterns, but differed from other sets of photographs, including other man-made stimuli. The differences were also observed when images were matched for image content. Moreover, high entropy of edge orientations was found in traditional artworks produced by different techniques, in artworks that represented different content matter and art genres, as well as in artworks from other cultural backgrounds (East Asian and Islamic). In conclusion, we found that high entropy of edge orientations characterizes diverse sets of traditional artworks from various cultural backgrounds.

Seeing shapes in seemingly random spatial patterns: Fractal analysis of Rorschach inkblots

Rorschach inkblots have had a striking impact on the worlds of art and science because of the remarkable variety of associations with recognizable and namable objects they induce. Originally adopted as a projective psychological tool to probe mental health, psychologists and artists have more recently interpreted the variety of induced images simply as a signature of the observers’ creativity. Here we analyze the relationship between the spatial scaling parameters of the inkblot patterns and the number of induced associations, and suggest that the perceived images are induced by the fractal characteristics of the blot edges. We discuss how this relationship explains the frequent observation of images in natural scenery.

Aesthetics by Numbers: Links between Perceived Texture Qualities and Computed Visual Texture Properties

Our world is filled with texture. For the human visual system, this is an important source of information for assessing environmental and material properties. Indeed-and presumably for this reason-the human visual system has regions dedicated to processing textures. Despite their abundance and apparent relevance, only recently the relationships between texture features and high-level judgments have captured the interest of mainstream science, despite long-standing indications for such relationships. In this study, we explore such relationships, as these might be used to predict perceived texture qualities. This is relevant, not only from a psychological/neuroscience perspective, but also for more applied fields such as design, architecture, and the visual arts. In two separate experiments, observers judged various qualities of visual textures such as beauty, roughness, naturalness, elegance, and complexity. Based on factor analysis, we find that in both experiments, ~75% of the variability in the judgments could be explained by a two-dimensional space, with axes that are closely aligned to the beauty and roughness judgments. That a two-dimensional judgment space suffices to capture most of the variability in the perceived texture qualities suggests that observers use a relatively limited set of internal scales on which to base various judgments, including aesthetic ones. Finally, for both of these judgments, we determined the relationship with a large number of texture features computed for each of the texture stimuli. We find that the presence of lower spatial frequencies, oblique orientations, higher intensity variation, higher saturation, and redness correlates with higher beauty ratings. Features that captured image intensity and uniformity correlated with roughness ratings. Therefore, a number of computational texture features are predictive of these judgments. This suggests that perceived texture qualities-including the aesthetic appreciation-are sufficiently universal to be predicted-with reasonable accuracy-based on the computed feature content of the textures.