An Eye Tracking Study on Symmetry and Golden Ratio in Abstract Art

Abstract

A visual stimulus that is divided in harmonic proportions is often judged as more pleasant than others. This is well known by artists that often used two main types of geometric harmonic patterns: symmetry and the golden ratio. Symmetry refers to the property of an object to have two similar halves, whereas the golden ratio consists of dividing an object in a major and a minor part so that their proportion is the same as that between the whole object and its major part. Here we investigated looking behaviour and explicit preferences for different regularities including symmetry and golden ratio. We selected four Mark Rothko’s paintings, a famous abstract expressionism artist, characterized by two main areas depicted by different colours: one symmetric (ratio between areas: 50–50%), one in golden ratio (38–62%), one in an intermediate ratio (46–54%), and one in a ratio exceeding the golden ratio (32–68%). Thirty-six healthy participants (24.75 ± 3.71 years old) completed three tasks: observation task (OT), pleasantness task (PT), and harmony task (HT). Findings for explicit ratings of pleasantness and harmony were very similar and were not significantly correlated with patterns of looking behaviour. Eye Dwell Time mainly depended on stimuli orientation (p < 0.001), but for the harmony task also by ratio and their interaction. Our results showed that the visual scanning behaviour of abstract arts primarily depends on the orientation of internal components, whereas their proportion is more important for the pleasantness and harmony explicit judgments.

1. Introduction

Symmetry is widely present in nature and the human visual system is particularly responsive to symmetry. Moreover, symmetry processing is independent of cultural backgrounds and it is considered a biological-rooted component of vision as it is reported across different contexts [1].

Many researchers regard symmetry as a process characterizing the early stages of visual elaboration. The automaticity of symmetry detection bypasses attentive resources in a way similar to a bottom-up mechanism. In cognitive psychology, bottom-up processing determines how sensory information is initially interpreted. This process begins at the sensory level, with the perception of stimuli leading to higher-level cognitive functions in the cerebral cortex. Bottom-up processing is sensory-data driven pre-attentive, automatic, and non-conscious. By contrast, a top-down process initiates with higher level functions, which flow down to lower-level functions, such as the senses [2]. Both approaches functionally serve the same purpose, i.e., to make sense of environmental stimuli.

In this sense, Latto defines symmetry as an example of “aesthetic primitive”, meaning that it is “intrinsically interesting even in the absence of narrative meaning, because it resonates with the mechanisms of the visual system processing it” [3]. In the “Eight laws of artistic experience”, Ramachandran and Hirstein listed symmetry as one of the main strategies employed by artists (more or less consciously) to activate specific visual areas of the brain in the observers [4]. Similarly, in the cognitive model of visual aesthetic judgment proposed by Leder and colleagues, symmetry is placed among other factors within the early perception stage [5,6]. If symmetry detection relies on a bottom-up process, spontaneous extraction of symmetric cues out of the environment is thought to optimize our visual processing fluency (i.e., the ease with which a stimulus is processed) through figure–ground segmentation and object identification. Symmetry processing fluency is proposed to relate to hedonic responses (i.e., pleasant feelings) and sometimes to aesthetic conscious evaluations [7]. Accordingly, previous studies reported individuals’ preferences for symmetry are due to the positive affect engendered by processing fluency yielded by the presence of symmetry in the stimuli [8,9].

Although symmetry is famously related to aesthetic valence, it is not the only geometric structure considered to have a special connection to beauty. Another proportion discovered in Greece in 5 BCE drew fascination for its properties associated with aesthetic pleasure and beauty: the golden ratio (GR), also known as phi (φ). GR is an irrational number which has been for long considered the mathematical formula through which one could reproduce the harmony of the human body in sculpture and art [10,11]. The golden ratio is obtained when an object is divided in a major and a minor part so that their proportion is the same as that between the whole object and its major part. If we consider a rectangle, the golden ratio is obtained by cutting off a square and the leftover rectangle has the same proportion as the original rectangle (a + b/a = a/b). The ratio of this proportion is always equal to GR, which is approximately 1.618. From the curve of the human ear to the human bone structure, to the growth pattern of leaves and flowers, the golden ratio can be found in many different contexts. It has been claimed that “golden rectangles” appear in various forms both in nature and art. Examples of art are found in famous ancient architecture, such as the façade of the Parthenon in Athens, and Notre Dame de Paris, as well as in visual artworks such as the Venus of Milo and the Creation of Adam by Michelangelo Buonarroti.

But if symmetry is consistently reported to be easily detected and preferred, the empirical study of the relation between golden ratio and a subjective aesthetic experience of beauty has brought contrasting results. In support of an explicit preference for GR, Fechner’s pioneering study determined that most participants visually preferred the golden ratio shape to other random proportioned rectangles [12]. However, some of the difficulties encountered in most studies on preferences for GR regard the parameters used for the assessment of aesthetic preferences, such as implicit measures or explicit/subjective reports [10,11,12,13,14]. Other difficulties are linked to inconsistencies in interpreting preferences for the golden ratio as individual preferences for GR can differ significantly depending on whether explicit or implicit measures are employed. Additionally, while GR frequently appears as a median ranking among other ratios—indicating an overall preference—it is not always the most preferred or most frequently chosen ratio, and evidence sometimes shows contrasting results [15]. Yet other difficulties are related to the categories of stimuli tested (e.g., abstract/geometric or figurative/humanoid) [16], and to the cultural background of participants (level of scholar education, artistic and mathematical knowledge/interest).

Recent studies have attempted to overcome some of these issues by using integrative approaches. Namely, De Bartolo and colleagues [16] tested preference using a set of photographs displaying different contents, from abstract stimuli (ad hoc geometric figures and bisected lines) to artistic stimuli (images of famous anthropomorphic sculptures and paintings) to natural stimuli (human figures). The stimuli were digitally manipulated so that the two parts could have three different ratios: 1.5, 1.618 (GR), and 1.8. Participants were asked to explicitly report their liking using a Likert scale while they had their eye movements recorded by an eye tracker device measuring the fixation durations—Dwell Time—on specific Areas of Interest (AoI), which has been described as an indicator of attention [17]. They found overall, statistically significant GR aesthetic preference for humanoid stimuli, but not for geometric figures, and preferences were inversely correlated to the Dwell Time spent on the division line in golden proportion. The authors interpreted the results within the ecological approach of visual perception proposed by Gibson [18], which considers GR as having some features analogous to symmetry. In this view, both symmetry and GR have geometric characteristics widely present in nature [10], and both facilitate visual processing and reduce cognitive load. Hence, both could be considered as ecological affordances [18,19,20,21,22], and may be related to the perception of beauty, as artists have well known since ancient time. However, although both these proportions were investigated for abstract stimuli [23,24], there is a lack of evidence on aesthetic preference and free viewing observation patterns for symmetry and golden ratio properties related to abstract art. Therefore, the aim of this study is to fill this gap by investigating how participants observe and judge abstract art having symmetric and golden proportions with respect to other proportions when presented in different orientations.

In previous studies, stimuli were mostly geometrical patterns or dots arrangements created ad hoc for the experiment, whereas in this study we favoured a more ecological approach and selected original artworks as stimuli. Accordingly, stimuli were created based on paintings of the abstract American Expressionist Mark Rothko (1903–1970). Rothko developed a well-recognized series of paintings, in which he juxtaposed rectangles (often two) of different colours on large-scale canvas. The structure of Rothko’s paintings was ideal for the aims of the present study, since it allows the assessment of participants’ behaviour towards abstract art while observing paintings in different proportions. Indeed, the number of his artworks containing rectangular-shaped fields, including those in symmetric or GR proportions, provided a real world set of stimuli, which allowed exploration of explicit preferences and visual behaviour in abstract art. Therefore, using an eye tracker, participants’ eye movements and fixations were recorded on specific Areas of Interest (AoI) to investigate differences in individuals’ visual observation behaviours under free viewing conditions and when performing two judgment tasks (pleasantness and harmony). We anticipated that symmetrical and Golden Ratio paintings would be judged as more pleasant and harmonious and they would also be looked at (i.e., Dwell Time) for longer as people look at what they are interested in.

2. Materials and Methods

2.1. Participants

Thirty-six participants took part in the study (mean age: 24.75 ± 3.71, 19 females). All participants gave their informed consent to the study. Participants had normal or corrected-to-normal vision and were naïve to the purpose of the study.

2.2. Stimuli

The original stimuli consisted of a set of 4 artworks by Rothko, mainly formed by 2 rectangles of different colours (the digital photos of these 4 artworks have a size of 900 × 613 pixels). Specifically, four paintings from the “rectangle” series were chosen based on the rectangle’s ratio within the canvases. We chose four paintings with four different ratios, based on the proportion between the above and below rectangles: symmetrical (S; ratio: ~50–50%, painted in 1969), Golden Ratio (GR; ratio ~38–62%, 1968), a proportion between the above two ones (R46; ratio 46–54%, 1968), and a proportion overcoming that of GR (R32; 32–68%, 1956).

The paintings were also digitally adjusted so that each artwork was presented in all ratios (i.e., S, R46, GR, and R32) to control for colour effects, and were also presented in four possible orientations [0° (original orientation), 90°, 180°, and 270°] to investigate if fixation durations and explicit preferences depend on stimuli orientation (Figure 1b). The four paintings were characterized by different colours, but our digital reproductions allowed each painting to be presented in four different ratios and four different orientations. Each participant’s answer and ocular parameter were averaged over the four paintings (and hence on the four two-colour combinations characterizing each painting) minimizing any possible effect due to colours. Thus, the total set consisted of 64 stimuli (4 artworks × 4 proportions × 4 orientations).

Stimuli were presented on a white background on a 17.3-inch monitor laptop (resolution 1920 × 1080, refresh rate 240 Hz).

2.3. Experimental Procedure

Stimulus presentation and data collection were controlled by Experiment Builder (SR Research Ltd., version 2.3.38, Mississauga, ON, Canada). Eye movements were recorded using an EyeLink 1000 device (SR Research Ltd., Oakville, ON, Canada) in remote binocular mode with a sampling rate of 1000 Hz (average accuracy ~0.25°–0.5°, spatial resolution < 0.01° RMS, as reported by the manufacturer). Data were exported using the EyeLink Data Viewer software package (SR Research Ltd., version 4.2.1, Oakville, ON, Canada).

Upon completion of the consent form, participants were invited to a silent room, following guidelines for eye movements recording with the EyeLink 1000 device. Luminance was provided only from the top. Participants sat comfortably in front of a screen, at a viewing distance of approximately 55 cm from the camera and illuminator. A chinrest was used to maintain distance and help the stabilization of the head position. The experiment consisted of three blocks of 64 trials each (tot = 192 trials). Before starting each block, participants completed a 13-point calibration–validation phase, which was also repeated at the beginning of each block, and every 16 trials.

In the first block—the free viewing observation task, OT—each trial started with a fixation point which stayed on screen until participants fixed their gaze on it and the experimenter pressed the “spacebar” (i.e., EyeLink drift correction was applied to small drifts in the calculation of gaze position that can build up over time). Then, the stimulus appeared for 5 s (recording period for each trial), and participants were asked to freely observe the painting. After each stimulus presentation, the experimenter pressed the “spacebar” to proceed to the next trial. All stimuli were presented in randomized order in each block (Figure 1a).

The other two blocks were identical to block 1, but participants were asked to provide an aesthetic judgement to each stimulus. In one block—the pleasantness block, PT—participants rated the paintings based on pleasantness (Italian version: “Quanto le è piaciuto?”; English version: “How much did you like it?”), whereas in the second block—the harmony block, HT—they rated the paintings based on harmony (Italian version: “Quanto è armonioso?”; English version: “How harmonious is it?”). Responses were provided using a scale from 0 (Not at all) to 10 (Very much). Thus, after each stimulus presentation (5 s), a response window appeared, displaying the question and response options, and stayed on screen until response (Figure 1). The free viewing observation task was always presented as the first block, whereas for pleasantness and harmony blocks were presented next, with order counterbalanced across participants. Participants were instructed to maintain position and to respond using the mouse by selecting one of the ten response options. After each block, participants had the opportunity to take a short break. The study lasted approximately 40 min.

2.4. Recordings and Data Processing

Fixation durations were retrieved from the fixation report of the EyeLink Data Viewer software (SR Research, v. 4.2.1), using the software’s default settings. All fixations shorter than 100 ms were discarded as well as the first fixation of each trial (to avoid bias due to starting gaze position at the centre in each trial, for drift correction). The AoI was created with the EyeLink Data Viewer software for each stimulus’ ratio and orientation conditions, encompassing the target area of each painting. Thus, for each stimulus, the target area of interest was defined as the upper one in the 0° orientation condition, the right one in the 90° orientation condition, the lower one in the 180° orientation condition, and the left one in the 270° orientation condition (as in Figure 1b). Dwell Time (DT) on the AoI was computed as the summation of all fixation durations in the area of interest in each trial. Computations of DT were done using the right eye data. Thus, the proportion of DT for each AoI over the Dwell Time of all fixations falling within the painting was computed for each trial. Finally, means of AoI Dwell Time proportions were computed for each participant for each condition.

To consider the differences in proportions of the areas, a normalized Dwell Time (nDT) was computed as the proportion of DT spent on the AoI minus the proportion of the AoI on the whole stimulus.

2.5. Statistical Analysis

Data are reported as mean ± standard error for DT, nDT, and explicit ratings for each condition. Separate 4 × 4 Repeated Measure Analyses of Variance (RM-ANOVA) for each task (OT: observation task, PT: pleasantness judgment task, HT: harmony judgement task) were performed on means of nDT and explicit ratings using Stimulus Ratio (4: S, R46, GR, R32) and Orientation (4: 0°, 90°, 180°, 270°) as within-subject factors. RM-ANOVA was not computed for DT because this variable is affected by a bias related to the different sizes of the AoI among the stimuli, which was compensated for using nDT. The alpha level of statistical significance was set at 5% for all the analyses, the p-value of post hoc was computed after Tukey correction. If sphericity was violated, the Greenhouse–Geisser correction was applied.

For DT a one-sample t-test was used to verify the significant differences from the expected values corresponding to the AoI percentage size. Correlations using Pearson’s coefficient (R) were computed.

3. Results

3.1. Explicit Ratings

Figure 2 shows the mean ± standard error for explicit ratings when participants were asked to judge the pleasantness or the harmony of the stimuli. In general, participants’ responses ranged from 0 to 10. It is important to underline that the standard error bars reported in Figure 2 are related to the variability between subjects, whereas the analyses were performed within subject. Figure 3 shows the relative frequency distributions of the ratings provided by subjects.

Table 1. RM-ANOVA results in terms of F, p-value, and partial eta squared (η_p²) on ratings. Bold represents p < 0.05.

Explicit Ratings	Pleasantness			Harmony
Factor	F	p	ηp2	F	p	ηp2
Ratio	2.22	0.109	0.060	8.08	0.002	0.188
Orientation	1.71	0.183	0.047	1.03	0.376	0.028
Interaction	2.20	0.022	0.059	2.77	0.027	0.073

shows the ANOVA results for the two tasks. For PT, there were no significant main effects, but a significant ratio-by-orientation interaction, F(9, 315) = 2.20, p = 0.022, η_p² = 0.059). Post hoc tests showed a significant difference at 0° as S was judged more pleasant (5.52 ± 0.308) than GR (5.08 ± 0.303, p = 0.010).

Moreover, for the HT there was a significant main effect of ratio, F(1.58, 55.47) = 8.08, p = 0.002, η_p² = 0.188, qualified by a significant ratio-by-orientation interaction, F(4.25, 148.88) = 2.77, p = 0.027, η_p² = 0.073. Post hoc tests showed that S was judged more harmonious than GR at 0° (5.81 ± 0.26 vs. 5.12 ± 0.26, p = 0.009) whereas at 90° S was judged more harmonious (6.07 ± 0.25) than both GR (5.17 ± 0.27, p = 0.017) and R32 (5.16 ± 0.27, p = 0.004).

Explicit ratings for symmetric and GR stimuli were not correlated with the respective proportions of Dwell Time on the target area of interest.

To have an idea of the distribution of individual ratings, the percentage of responses below and above the mean range in each task (respectively, below < 3 and above > 7) was computed. In PT, 9.05% of ratings were below 3 and 9.59% ratings were above 7, with 81.35% of ratings being between 3 and 7. In HT, 7.14% of ratings were below 3 and 10.48% ratings were above 7, with 82.38% of ratings being between 3 and 7. Figure 3 shows the relative frequency distributions of the ratings provided by subjects.

3.2. Eye Tracking

3.2.1. Dwell Time

Figure 4 shows the DT ((a) above panels) and nDT ((b) below panels) proportions spent on the AoI in the three different tasks, for the four ratios and the four orientations. For the observation task, an interesting result emerged for DT when not subtracting the expected proportion in specific conditions. The DT of symmetric stimuli at 90° and at 270° (with respect to the original paintings) was not significantly different from 50% (50.28%, p = 0.922 and 51.69%, p = 0.542, respectively), but when it was presented at 0° it was 59.71%, significantly different from 50% (p < 0.001) but not from 61.8% that is the longer proportion of GR (p = 0.367). When presented at 180°, the rectangle below was observed for 40.8% of time, a value significantly different from 50% (p = 0.004), but not from 38.2%, the shorter proportion of GR (p = 0.382). The same patterns were present for R46. Conversely, for GR stimuli, the rectangle above at 0° was observed for 45.95% (a value not significantly different from 50%, p = 0.254), despite it covering only 38.2% of the whole area (p = 0.033). In the other orientations, the DT was 41.56%, 34.56%, and 43.26% (90°, 180°, 270°, respectively), all values not significantly different from the percentage of covered areas (p > 0.07). For R32, the DT was significantly different from 50% for all the four orientations (p < 0.029).

For the nDT, the following results were found. For the observation task (OT), the main effect of orientation was significant. Post hoc comparisons for orientation showed significant differences for the comparisons between 0°–180° (10.42 ± 2.29 vs. −4.32 ± 2.30, respectively, p < 0.001), 0°–90° (10.42 ± 2.29 vs. 1.55 ± 2.37, p = 0.012), and 180°–270° (1.55 ± 2.37 vs. 5.46 ± 2.96, p < 0.001). The main effect of ratio and the interaction were not significant (please see

Table 2. RM-ANOVA results in terms of F, p-value, and partial eta squared (η_p²) on normalized Dwell Time. * p < 0.05.

	Observation			Pleasantness			Harmony
	F	p	ηp2	F	p	ηp2	F	p	ηp2
Ratio	2.72	0.063	0.07	1.58	0.198	0.04	9.38	<0.001 *	0.21
Orientation	8.90	<0.001 *	0.20	21.10	<0.001 *	0.38	22.98	<0.001 *	0.40
Interaction	1.21	0.300	0.03	1.64	0.104	0.04	3.29	<0.001 *	0.09

).

Similarly, for the pleasantness task (PT), the main effect of ratio was not significant, but there was again a significant main effect of orientation (see Table 2). Post hoc comparisons showed significant differences between 0° and 180° (11.15 ± 2.00 vs. −10.00 ± 2.11, p < 0.001), between 0° and 270° (11.15 ± 2.00 vs. 1.39 ± 2.18, p = 0.004), between 90° and 180° (5.55 ± 2.18 vs. −10.00 ± 2.11, p < 0.001), and between 180° and 270° (−10.00 ± 2.11 vs. 1.39 ± 2.18, p < 0.001). The interaction was not statistically significant.

Finally, for the harmony task (HT), the main effects of ratio and orientation were significant. These effects were qualified by a significant ratio-by-orientation interaction (see Table 2). Post hoc comparisons showed that DT for S at 0° was greater (15.13 ± 2.07) compared to 180° (−10.82 ± 2.46, p < 0.001) and 270° (−2.40 ± 2.16, p < 0.001). DT at 0° for R46 (20.73 ± 2.45) also was significantly greater than for GR (6.13 ± 2.94, p = 0.003). Although S at 0° was greater than GR at 0°, the difference did not reach statistical significance (p = 0.079).

3.2.2. Average Number of Fixations

To inspect whether the same results hold using an absolute (rather than a relative) fixations metric, we also conducted the same analyses on average number of fixations on the AoI. We did not analyse the directions of saccades because our stimuli clearly showed a division line and a direction that is the same for all the four different ratios. Such an analysis could assist comparing the observations of stimuli with differently oriented axes of symmetry or with rotational or radial symmetries [23].

Results were as for the pattern of DT results, except for the effect of ratio that was significant in each task, but which was due to data being not normalized on the effective size of the AoI (as instead was done on nDT). Specifically, for the observation task (OT) the main effect of ratio (F(2.51, 87.80) = 38.79, p < 0.001, η_p² = 0.53) and orientation (F(3, 105) = 11.92, p < 0.001, η_p² = 0.25) were significant. The interaction was not significant (F(9, 315) = 1.53, p = 0.138, η_p² = 0.04). Similarly, for the pleasantness task (PT), the main effect of ratio (F(3, 105) = 79.29, p < 0.001, η_p² = 0.69) and orientation (F(2.24, 78.33) = 21.60, p < 0.001, η_p² = 0.38), as well as the interaction (F(9, 315) = 1.97, p = 0.043, η_p² = 0.05), were significant.

Finally, for the harmony task (HT), the main effects of ratio (F(2.42, 84.63) = 82.40, p < 0.001, η_p² = 0.70) and orientation (F(2.10, 73.49) = 26.14, p < 0.001, η_p² = 0.43) were significant. These effects were qualified by a significant ratio-by-orientation interaction (F(9, 315) = 2.33, p = 0.015, η_p² = 0.06).

4. Discussion

In this study, we were interested in assessing participants’ explicit judgments of pleasantness and harmony as well as their looking behaviour (i.e., ocular Dwell Time) during free viewing observation of real abstract artworks and related digitally modified stimuli. We expected an overall explicit preference for symmetry and GR and anticipated that these explicit ratings would correlate with the proportion of Dwell Time spent between the two internal features (i.e., two painted rectangles). However, we found unexpected results. Firstly, the explicit ratings of pleasantness and harmony were very low and only ranged around 1 point on a 10-point scale. Secondly, neither ratio nor orientation—the two features of the paintings—directly affected the explicit ratings of pleasantness. The only small difference—smaller than 0.5 points—was between paintings with symmetry and GR at 0°. In contrast, for harmony judgements, the differences were a bit larger and were affected by both ratio and orientation. Symmetric paintings were judged as more harmonious when presented in all four orientations, especially at 90°, followed by the quasi-symmetric stimuli (R46). GR paintings were judged as poorly harmonious, and R32 paintings were judged harmonious only when presented at 0° (with the small rectangle above). Therefore, GR was not explicitly judged as more harmonious than R46 and R32.

To note, analysis of number of fixations showed a pattern similar to that for DT, and we suggest that differences between our results depended on data being not normalized on the effective size of the AoI.

It should be noted that in our study, the harmony ratings ranged between 5.07 and 6.07, suggesting that even if statistically significant, the effects were small (as indexed by the small η_p² < 0.2). These findings are in keeping with De Bartolo et al. [16], who also failed to find evidence of a preference for GR when using abstract stimuli. A preference for GR was present only for non-abstract stimuli, such as human photographs, anthropometric sculptures, and realistic paintings. However, as they did not use symmetric stimuli, their findings cannot speak as to whether GR is preferred more than symmetry.

The present findings may seem at odds with Salera et al. [24], who used dot patterns in GR proportions vs. random dot patterns and found an implicit preference for GR similar to that observed in a previous analogous study for symmetry [23]. However, this could be due to presenting symmetry and GR in the same task. In fact, Salera and colleagues [24] did not use symmetric dot patterns because it could be a confounding factor for the judgments on GR. Importantly, in a more explicit task (the Ultimatum game) they found that a symmetric division was preferred to a GR division, confirming that, when directly compared, symmetry is preferred to GR (as previously found [25]). It is well known that humans are highly sensitive to symmetry, which affects the visual exploration process, the directions of saccades, and it enhances and maintains sustained sensitivity [26,27].

Interestingly, Ouhnana and colleagues [28] showed that regular pattern could also have an after effect. That is, having seen more regular stimuli makes the following stimuli appear to have fewer regular patterns and even less regular. This effect depends on the level of regularity and is unidirectional. This regularity after effect may explain our findings. Namely, the presence of symmetric paintings reduced the perception of harmony of paintings in golden ratio.

That non-expert participants show no explicit preference for GR in the present study may be due to these preferences depending upon individuals’ art expertise. Indeed, Stieger and Swami [25] considered participants’ different backgrounds (familiar or not familiar with art) and used both implicit and explicit measures (respectively the Implicit Association Test and Likert rating scales). They asked participants to observe figurative stimuli (i.e., artistic photographs) with three different main proportions (symmetric, GR, and ¾ proportions). Their findings showed a general preference for symmetry for both implicit and explicit measures, but the explicit preference for GR correlated with participants’ background: those who knew GR showed greater preference for stimuli with this feature [25].

In sum, the first novel finding of the present study is that symmetric and quasi-symmetric (R46) stimuli are judged as more harmonious than GR. Another relatively surprising and novel finding is that from eye movements as the Dwell Time divided between the two parts of the stimuli (the two rectangles in Rothko’s paintings) were not significantly correlated with the explicit ratings. One possible account calls again upon the small variance (1 point out of 10) in the means of explicit ratings. Another is related to Dwell Time, which, differently from explicit judgments, mainly depended on the orientation of the stimulus. In fact, neither ratio alone nor with orientation affected the Dwell Time during free viewing and the pleasantness judgment task.

Although for the harmony judgment task, the trends of Dwell Time seemed similar to those observed for the free viewing task and for the pleasantness task, the effects were statistically significant for ratio (the AoI was observed for longer time for R46), orientation (the AoI was observed for longer time when above than below), and their interaction (the AoI above was less observed in GR proportion). That Dwell Time was spent on the AoI of R46 suggests that participants spent more time looking at the quasi-symmetric stimuli, perhaps to assess harmony. In fact, this finding could mimic real-world scenarios, as symmetrical patterns vary in natural settings, and oftentimes do not have perfect symmetry [29]. That is, humans’ ability to detect symmetry is more likely to stem from a generalization of an average of deviated symmetrical patterns, and not from a collection of singular perfect symmetries [30]. This may explain why more time was spent on the AoI for judging R46 slightly less harmonic than symmetric stimuli. This account is in keeping with psychophysics studies showing that people can recognize a symmetrical pattern faster within a single fixation, especially if the axis of reflection is vertical [31]. Interestingly, it is argued that this level of spontaneous expertise might have to do with our exposure and familiarity with such type of reflection. Notably, the human body (and the body of most of other animals) is per se a salient example of vertical reflection, as it is roughly the same when reflected left to right. Strong visual responses to symmetry are observed even in degraded visual conditions: people are accurate in detecting symmetric patterns, even when these are surrounded by jittered elements or are not in perfect proportions, such as the R46 stimuli in the present study [32].

The most important effect on Dwell Time was for orientation. For all the ratios, the AoI was looked at for a longer time when above (0°) than when below (180°). There are differences in upper and lower visual fields that have been reported in various tasks. Visual search, local processing, and categorical judgments were more effective in the upper visual field, whereas lower visual field is advantaged in motion analysis, global processing, and coordinate spatial judgments [33]. Despite the tasks required to provide a judgement, abstract art is often associated to a more global processing than representational art [34], so it is possible that a smaller Dwell Time was required when the AoI is the lower visual field, whereas a greater one is necessary when it is above. The significant interaction between ratio and orientation was mainly due to the GR stimuli at 0°, for which the Dwell Time on the AoI was significantly lower than R46, and close to the significant threshold with respect to symmetric stimuli. In fact, when GR stimulus is presented at 0°, the Dwell Time was balanced on the two rectangles (not significantly different from 50–50%). In contrast, for symmetric and quasi-symmetric stimuli, there was an increase of Dwell Time on the above rectangles for 0° (DT: 59.71%) and 180° (40.8%) with respect to the balanced division observed at 90° (when the symmetric stimuli were judged as the most harmonic) and 270°. These findings point to participants equally dividing the time spent on two congruent rectangles when they were presented with a vertical symmetry (left–right) but not when they were presented with symmetry along the horizontal axis (above–below). In this latter case, participants spent longer time looking at the rectangles above and the proportion between the two Dwell Time approaches GR. Conversely, in GR stimuli at 0°, the Dwell Time spent looking at the smaller rectangle above was the same as the time spent looking the bigger rectangle below. When these GR stimuli were reversed (180°) the Dwell Times were similar to those expected and proportional to the dimensions of the AoI.

These similarities between symmetry and GR in human behaviour have been already observed, for example, in locomotion: left and right steps are symmetric, whereas the stance and swing phases within the same stride are in golden proportion [35,36]. The idea that some stimulus can be visually scanned using golden proportion (even if the stimulus is not in GR) has been previously suggested [37]. Symmetry and GR could be considered as two affordances [16,18] and hence, according to the theory of internalization of ecological invariants [38], individuals could scan according to these proportions in search of regularities. Most of the symmetric stimuli to which we are exposed have a horizontal left–right refection (such as human and animal bodies, furniture, cars), whereas GR proportion is mainly on the vertical direction (with the above part smaller to the below one, such as in anthropometric dimensions or architecture of famous monuments [10,39]). This is mainly due to the gravitational field, and gravity is an internalized invariant [40]. Accordingly, Bingham and Muchinsky [41] suggested that visual affordance could be related to the need of perceiving the centre of mass of the stimulus for facilitating its “graspability”. Interestingly, in their experiment they used the same four orientation as of the present study (0°, 90°, 180°, and 270°) and found that the presence of symmetric objects in the set of stimuli also influenced individuals’ responses to the other stimuli.

Finally, we should acknowledge some limitations of the present study. The most important was that using artistic abstract paintings implied that stimuli had the borders of the rectangles not perfectly defined, including the lines at the borders of the canvas. Another possible limitation of this study is that the time of observation was not decided by the observer, but it was fixed (5 s). This limited the possibility to verify if certain stimuli were observed for longer or shorter time as we could only analyse the proportions of the Dwell Time, not their absolute time for the experimental conditions. Furthermore, our analysis was limited to Dwell Time, not considering saccades and scan paths, as these variables require a standardized procedure for parameterization, which could be problematic in our protocol due to the change in orientation of our stimuli.

Another limit of our study was that the analysis of variance was performed on values obtained by averaging four values for each participant (the four different paintings digitally modified for having the same ratio and the same orientation), which could affect the reliability of our study. However, we did not include other stimuli because the duration of our experiment ranged between 45 min and one hour, and to have balanced conditions we could only double the experimental conditions, which would have made the duration of the experiment much longer, with the risk to increase fatigue and reduce attention.

Finally, in our study, participants were not art experts, and they were simply asked to judge the pleasantness and the harmony of the observed stimuli. Because the definition of harmony in visual perception could be controversial [42] and associated to familiar stimuli [43], there is the possibility that participants associated harmony with pleasantness. This hypothesis could explain some similar results between the judgements of these two aspects, such as the absence of a significant main effect of orientation and the significant effect of the interaction of ratio per orientation. On the other hand, a significant main effect of ratio (in favour of symmetry) was found only for harmony judgments, suggesting that the two concepts could be associated by participants, but not confounded one with the other. Further studies may investigate individuals’ differences related to the level of art knowledge as done in some research [44].

At last, in our study we used abstract paintings and not artificial stimuli developed in laboratory. In our opinion, this choice might increase the ecological approach to pleasantness, because the stimuli have been already recognized as appreciated by museum visitors. On one hand, the used paintings are not perfectly symmetric or in golden proportion as artificial stimuli created by a computer could be, but, on the other hand, it increases the generalizability of our results because everyday life visual experiences are related to not-perfect stimuli, with symmetry of faces or golden ratio of bodies only approached on average.

5. Conclusions

Our results suggest that eye movements for abstract stimuli, consisting of Rothko’s two-rectangle paintings presented in different versions, varied with stimuli orientation. Participants spent more time looking at the parts above, but the judgements of pleasantness and harmony were not correlated with the differences in ocular scanning patterns, and these judgments poorly depended on the orientation of the paintings. Importantly, symmetry seemed to polarize the results, as the more the stimulus was far from symmetry, the more it was judged as less harmonious, and stimuli in GR were judged as less harmonious. Interestingly, the schema of the visual scanning path, measured in terms of proportions of Dwell Time spent on different areas, show symmetric or GR patterns, even when the stimuli are not in these proportions. Future studies should look in depth into this novel finding.