Belal Abboushi, Ihab Elzeyadi, Richard Taylor, and Margaret Sereno

Abstract

In contrast to urban environments, natural environments exhibit fractal patterns that have been widely studied to understand their restorative properties and people’s affinity for nature. Existing studies suggest that fractal patterns elicit positive perceptual and physiological responses such as visual preference, stress recovery, and enhancing the wakefully-relaxed state. In these studies, participants viewed the patterns on a computer screen and assessed their visual preference. It is unclear, however, whether the demonstrated visual preference for fractal patterns translates to higher visual interest for fractal light patterns in architectural renderings.

This paper presents the results of a study that extends empirical findings of fractal perceptual response and human impacts by examining the visual interest and mood elicited by various complexities of fractal light patterns included in architectural renderings of an interior space. In an experimental setting, 68 participants assessed-- using a repeated-measure procedure-- their perceptual response to four fractal light patterns, of varying complexities, and two non-fractal light patterns. The patterns were included in an interior space renderings that were projected on a wall, and participants were asked to select the light pattern that was more visually interesting and to assess how these patterns made them feel.

Results of this study suggest that fractal light patterns of medium-high complexity were significantly more visually interesting, as compared to other light patterns. The results suggest a different range for visual interest, compared to results from previous visual preference studies. The projection of fractal light patterns in interior spaces may be useful for creating visually interesting environments.

Introduction

In his seminal article “The restorative benefits of nature: Toward an integrative framework”, Kaplan (1995) proposed the attention restoration theory, and suggested that restorative environments have four main components: being away, e.g. psychologically getting away; fascination, which implies that small magnitudes of attentional load are required; a sense of extent; and compatibility, which implies a special resonance between the natural environment and human inclinations. These components might provide the required mechanism that links natural environments to positive psychophysiological responses. The questions, therefore, are: 1) What geometrical characteristics of natural environments are essential for these four components? and, 2) What are the mechanisms that link these characteristics to human physiological and psychological responses?

One of the approaches taken to identify important restorative characteristics of natural environments was to examine the visual geometrical characteristics of patterns found in nature. Many researchers suggested that the effects of natural scenes on attention restoration can be explained by the presence of fractal patterns which are prevalent in nature (Purcell, Peron, and Berto 2001; Joye and van den Berg 2011; Hagerhall et al. 2015; Mandelbrot, 1983). It is hypothesized that their prevalence in nature has caused the human visual system to adapt to easily process them (Taylor & Spehar, 2016), hence fractal patterns are more preferred to non-fractals ones. Previous studies suggested that fractal patterns have relaxing and restorative effects (Hagerhall et al. 2008), aesthetic appreciation (Taylor 2002), as well as stress-recovery benefits (Taylor 2006). These effects might be elicited by the perceptual response, e.g. visual preference, which Taylor (2002) refers to as ‘the aesthetic pull of fractals’. For example, Taylor (1998) conducted an experiment where participants were shown pictures of fractal and non-fractal patterns and found that 95% of participants preferred fractal over non-fractal patterns.

In interior environments, the shape of sunlight patterns in space is often influenced by exterior and/or interior obstructions such as trees. The resulting dappled shadows and sunlight patterns might have positive psychophysiological effects. However, because participants in most previous studies viewed the fractal patterns on a computer screen (Taylor et al. 2005; Hagerhall et al. 2015; Spehar et al. 2003), it is unclear whether the same positive reported response can be elicited in interior environments using fractal light patterns. When a fractal pattern is viewed on room surfaces, as opposed to on a computer screen, new variables such as projection surfaces, viewing angle, size of the pattern, space geometry, the use of light projection, light reflectance values of surfaces, and luminance variability can influence the visual preference or interest of these patterns. As a first step to bridging this gap, this study aims to examine the visual interest of fractal and non-fractal patterns in renderings of an interior space and to compare results to visual preference from previous studies.

Fractal Patterns and Complexity

Fractal patterns are shapes that display a cascade of self-similar, meandering detail as observed at various scales (Bovill 1996; Harris 2012). Fractals, typically, are characterized based on a variable called the fractal dimension (D). This parameter represents the complexity of the pattern and quantifies the fractal scaling relationship between the patterns observed at different magnifications (Spehar et al., 2003). For fractal patterns, this value lies between 1-2 and depends on the complexity of the pattern. Interestingly, the complexity of fractal patterns influences their visual preference. Previous studies have consistently found that people’s preferences peak within fractal dimensions of 1.3-1.5 (Spehar et al. 2003; Spehar and Taylor 2013; Taylor et al. 2005). Taylor and Spehar (2016) proposed a conceptual model for the interactions between people and fractal patterns called the ‘Fractal Fluency’ model, which implies that the human visual system has specifically adapted to efficiently process the mid-complexity patterns (1.3-1.5).

Fractal Patterns and Elicited Positive Responses

Aks and Sprott (1996) found that participants preferred patterns with a D value between 1.17-1.38, and suggested that aesthetic preference may reflect stable individual differences and traits such as creativity. In another study, Spehar et al. (2003) examined visual preferences for three types of fractals that were generated with different methods: natural, statistical, and human-produced fractals, which are cropped images from Pollock’s paintings “Untitled; Number 14; and Number 32”. The results show that preferences congregate within the range D=1.3-1.5, regardless of the generation method. Preferences for mid-D fractals have been confirmed by another study which involved 5000 participants (Taylor and Sprott 2008). It is important to mention that in these studies, fractal patterns were viewed on a computer screen located directly in front of each participant.

The D=1.3-1.5 range was also found to significantly reduce stress by 60% (Taylor 2006). This is the only study in which fractal patterns were printed, each measuring 3.2x6.5 feet, and mounted on a wall in front of participants. In a subsequent study, fractal patterns were found to increase alpha activity (Hagerhall et al. 2008), which is an indicator of a wakefully relaxed state. Further, these fractals generated the highest beta in the parietal lobe, which means that they generated most activation in the processing of the pattern’s spatial properties and contribute to the alertness state. Delta activity, which is an indication of a state of sleepiness and drowsiness, was lowest for fractals of D=1.3. This paper focuses on statistical fractals, which are found in nature and exhibit randomness and variety in sizes at different scales. The aforementioned brain response is better enhanced by statistical fractals, as compared to exact fractals which appear exactly the same at different magnifications (Hagerhall et al. 2015).

Hypotheses

Because of the demonstrated visual preference for mid-complexity fractal patterns (D=1.3-1.5), we hypothesize that fractals in this range are more visually interesting than other fractal and non-fractal patterns even when viewed in architectural renderings. Second, we hypothesize that this range is more likely to elicit positive mood responses, e.g. feeling Calm, Peaceful, Excited, and Stimulated.

5. Methods

   1. Participants

Participants were recruited from a pool of students enrolled in a course in the Department of Architecture at the University of Oregon. A total of 68 participants, of which 94.1% were architecture or interior architecture students. From the 68 participants (27 male and 41 female), 78% were 18-29 and 18% were 30-39 years of age. Responses from participants requiring vision correction but not wearing any during the experiment were excluded. All participants signed a consent form and, upon completion, received an extra participation credit in that course.

Visual Stimuli

Black and white fractal patterns and non-fractal patterns were used in this experiment. The selected fractal patterns included 4 coastline statistical fractal patterns (D = 1.1, 1.3, 1.5, 1.7) and two non-fractal patterns, a rectangular and a striped pattern (Fig. 1). It should be noted that all patterns were generated with an equal black-to-white ratio of 50% to control for light across different light patterns. This set of patterns was used to create 30 combinations such that each pattern is paired with every other pattern in the set, and presented twice, once on each side of the projection wall. Projection order was randomized. Participants completed their selections using wireless polling remotes each identified with a unique identifier.

Study Setting

The experiment was conducted in a windowless lecture hall in the afternoon during the Spring term. An overhead projector was used to project the renderings on a white wall located in front of participants. Projection area of each light pattern was 7 x 7 feet. Participants were seated in front of the projection wall such that each participant has a clear unobstructed view. Electric lighting in the room was set to allow for a clear contrast between light pattern projections and room surfaces. The luminance values of white and black areas of the patterns were 45 cd/m² and 9 cd/m², respectively. Lighting levels remained constant for the entire duration of the experiment (Fig.2).

Assessing Visual Interest and Mood

For assessing the visual interest of light patterns, the stimulus slides were projected using the two-alternative forced-choice (2AFC) paired-comparison procedure. On the other hand, for assessing mood, a rating procedure was used. The 2AFC procedure was used in previous studies and has been considered superior to other procedures for assessing visual interest and preference (Spehar et al., 2015). Participants were given 17 seconds to make their assessment and instructed to follow an impulsive first-impression selection. After each assessment, a neutral gray color was shown for five seconds. Responses were collected from all participants at the same time. The time required to complete viewing and assessments was 40 minutes.

Feelings provoked by light patterns are assessed using four descriptions: Calm, Peaceful, Stimulated, and Excited. These four parameters were selected based on previous studies by Russell and Pratt (1980) and (Boubekri, Hull, & Boyer, 1991). After explaining the experimental procedure, assessments were collected using a wireless polling system (iClicker), by selecting a letter A/B of the pattern that is more visually interesting (“Which light pattern is more visually interesting?”), and by selecting the level to which a pattern makes them feel on a 5-point scale, e.g. “Does this light pattern make you feel PEACEFUL?” The scale was: “Not at all, A little, Moderately, Quite a bit, and Extremely (Fig.3).

Results

The data were analyzed using Stata software where the Wilcoxon signed ranks test was used to examine whether distributions were similar or significantly different. The results showed that visual interest was highest for the fractal pattern of D=1.7, and was lowest for the rectangular pattern. Specifically, the visual interest for D=1.7 was significantly higher than D=1.5 and D=1.3. As can be seen in Error: Reference source not found, the visual interest gradually increased as the fractal dimension increased. Unexpectedly, the visual interest for the Striped pattern was significantly higher than that for the D=1.1 pattern. With regards to mood response, means for Calm and Peaceful judgments were lowest for the Striped pattern (1.33 and 1.16) and highest for the Rectangular (1.88) and D=1.5 (1.9) patterns, respectively. On the other hand, means for Excited and Stimulated were lowest for the rectangular pattern (0.37 and 0.65), respectively.

The four mood indices (Calm, Peaceful, Excited, and Stimulated) were measured on a linear 5-point Likert-type scale that ranged from “Not at all”, “a little”, “Moderately”, “Quite a bit”, and “extremely”. These five levels were converted to a numerical scale 0-4, respectively, for statistical analyses. The four mood variables for each light pattern were factor-analyzed to confirm the two main indices proposed by Russell & Pratt (1980). Exploratory factor analysis using Principal Components Analysis for factor extraction and Varimax with Kaiser Normalization as a rotation method were used. These analyses were separately conducted on each pattern. The factor loadings indicated the existence of two underlying indexes, Relaxation and Excitement, with eigenvalues generally higher than 1 as recommended by Berman & Wang (2012). The load bearings were used to calculate each index as a weighted average (Error: Reference source not found). Overall, ‘Calm’ and ‘Peaceful’ had high load bearings on the Relaxation index ranging from 0.79-0.93, while the Excited and Stimulated variables had high load bearings on the Excitement index ranging from 0.77-0.93.

Discussion

Unlike previous studies, which found that fractals of D=1.3 were considered more visually preferred than fractals of D=1.7, this study found that fractals of D=1.7 were more visually interesting than fractals of D=1.3. A number of explanations might suggest this shift from previous findings. It is possible that the spatial projection of light patterns in the interior space renderings caused this difference. It is also possible that visual interest (which was assessed in the current study) is a different construct than visual preference (which was assessed in previous studies). Another rationale related to the Euclidean space framing the rendered image where the fractal is being rendered might have altered the perception of the fractal complexity. A recent study addressed this issue (Abboushi, Elzeyadi, Taylor, & Sereno, 2019) and found that preference and interest might be different but related constructs. In future studies, it would be helpful to include D=1.9 fractals to compare against existing psychological studies as well as test the impact of viewing the fractal rendered space on a computer screen and on a projected wall simultaneously. Figure 6 shows visual interest results of the current study along with visual preference from previous studies that examined visual preference on a computer screen.

[CHART] Figure 1: The visual interest results from the current study and visual preference results from previous studies.

Fractal light patterns maintained a better balance between Relaxation and Excitement, as compared to the two non-fractal patterns. While the use of a linear scale to assess mood limited comparison to circumplex models of affect, like the one presented by Boubekri, Hull, and Boyer (1991), it can still be inferred that fractal light patterns of D=1.5 and D=1.7 triggered the highest levels of Excitement. On the other hand, in line with the results of another study (Abboushi et al., 2019), the striped light pattern rated lowest in Relaxation and moderate in Excitement. The rectangular light pattern is rather dull because it was rated low in Excitement and moderate in Relaxation. Nonetheless, currently, there are not enough studies to suggest that a balance between relaxation and excitement is a positive characteristic. This might depend on the activity and space type. For example, in some spaces, it might be desired to increase relaxation and reduce excitement.

Conclusion

This study examined the visual interest and mood response to different light patterns in architectural renderings. Fractal and non-fractal light patterns with different degrees of complexity were projected on a wall to test their impact on participant’s visual interest and mood. Wireless polling was used to collect responses from all participants at the same time, which ensured that all participants were subject to the same experimental settings and procedures. Results of this study suggest that medium-high complexity fractal light patterns D=1.5 and D=1.7 were significantly more visually interesting compared to fractal light patterns of D=1.1, D=1.3, and the two non-fractal light patterns.

Regarding mood response, the rectangular light pattern was rated lowest in excitement, whereas the Striped pattern was rated lowest in Relaxation. Fractal light patterns, on the other hand, received higher ratings for both Relaxation and Excitement. Further studies are needed to determine levels of excitement and relaxation desired for different tasks and to examine variability in mood response.

This experiment has expanded empirical evidence with regards to fractal light patterns and their applicability in architectural space renderings and virtual environments. Future studies should examine spatial variables, light intensity, glare and views, and their effects on visual interest and mood response. Implications of such studies would inform the design of future façade systems and glare control mechanisms, such as internal and external shades not only to enhance occupant’s mood but also to improve the quality of interior spaces.

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