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.

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.

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.

The Effects of Three-Dimensional Context on Shape Perception.

Humans have a unique ability to perceive shape in different ways. Although we naturally estimate objective (physical) shape in our daily interactions with the world, we are also capable of estimating projective (retinal) shape, especially when attempting to accurately draw objects and scenes. In four experiments, we demonstrated robust effects of 3D context on shape perception. Using a binocular stereo paradigm, we presented rectangular surfaces of varying widths alone or embedded in a polyhedron. We investigated how context, judgment type, and angle affected width estimates. We found that the presence of even a small amount of 3D context aids objective judgments but hinders projective judgments, whereas a lack of context had the opposite effect. Context facilitated objective shape assessments by improving estimates of surface orientation. These results demonstrate that the typical presence of 3D context aids shape perception (shape constancy) while simultaneously making the projective judgments necessary for realistic drawing more difficult.

Representation of shape, space, and attention in monkey cortex.

Attentional deficits are core to numerous developmental, neurological, and psychiatric disorders. At the single-cell level, much knowledge has been garnered from studies of shape and spatial properties, as well as from numerous demonstrations of attentional modulation of those properties. Despite this wealth of knowledge of single-cell responses across many brain regions, little is known about how these cellular characteristics relate to population level representations and how such representations relate to behavior; in particular, how these cellular responses relate to the representation of shape, space, and attention, and how these representations differ across cortical areas and streams. Here we will emphasize the role of population coding as a missing link for connecting single-cell properties with behavior. Using a data-driven intrinsic approach to population decoding, we show that both 'what' and 'where' cortical visual streams encode shape, space, and attention, yet demonstrate striking differences in these representations. We suggest that both pathways fully process shape and space, but that differences in representation may arise due to their differing functions and input and output constraints. Moreover, differences in the effects of attention on shape and spatial population representations in the two visual streams suggest two distinct strategies: in a ventral area, attention or task demands modulate the population representations themselves (perhaps to expand or enhance one part at the expense of other parts) while in a dorsal area, at a population representation level, attention effects are weak and nearly non-existent, perhaps in order to maintain veridical representations needed for visuomotor control. We show that an intrinsic approach, as opposed to theory-driven and labeled approaches, is useful for understanding how representations develop and differ across brain regions. Most importantly, these approaches help link cellular properties more tightly with behavior, a much-needed step to better understand and interpret cellular findings and key to providing insights to improve interventions in human disorders.

Aesthetic Responses to Exact Fractals Driven by Physical Complexity.

Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality, symmetry, recursion, and the number of segments in the generator. Across two studies, a variety of fractal patterns were visually presented to human participants to determine the typical response to exact fractals. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as fractal dimension increases. For the majority of individuals, preference increased with dimension. We replicated these results for other exact fractal patterns in a second study. In the second study, we also tested the effects of symmetry and recursion by presenting asymmetric dragon fractals, symmetric dragon fractals, and Sierpinski carpets and Koch snowflakes, which have radial and mirror symmetry. We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in a pattern that lacked mirror or radial symmetry, while others were less discriminating. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a pattern. Conceptualizations such as Berlyne's and Redies' theories of aesthetics also provide a suitable framework for interpretation of our data with respect to the individual differences that we detect. Future studies that incorporate physiological methods to measure the human aesthetic response to exact fractal patterns would further elucidate our responses to such timeless patterns.

Navigation performance in virtual environments varies with fractal dimension of landscape.

Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans' ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D. In Experiment 2, participants completed a map-reading and location-judgment task in separate sets of fractal landscapes. In both experiments, task performance was highest at the low-to-mid range of D, which was previously reported as most preferred and discriminable in studies of fractal aesthetics and discrimination, respectively, supporting a theory of visual fluency. The applicability of these findings to architecture, urban planning, and the general design of constructed spaces is discussed.

Characteristics of Eye-Position Gain Field Populations Determine Geometry of Visual Space.

We have previously demonstrated differences in eye-position spatial maps for anterior inferotemporal cortex (AIT) in the ventral stream and lateral intraparietal cortex (LIP) in the dorsal stream, based on population decoding of gaze angle modulations of neural visual responses (i.e., eye-position gain fields). Here we explore the basis of such spatial encoding differences through modeling of gain field characteristics. We created a population of model neurons, each having a different eye-position gain field. This population was used to reconstruct eye-position visual space using multidimensional scaling. As gain field shapes have never been well-established experimentally, we examined different functions, including planar, sigmoidal, elliptical, hyperbolic, and mixtures of those functions. All functions successfully recovered positions, indicating weak constraints on allowable gain field shapes. We then used a genetic algorithm to modify the characteristics of model gain field populations until the recovered spatial maps closely matched those derived from monkey neurophysiological data in AIT and LIP. The primary differences found between model AIT and LIP gain fields were that AIT gain fields were more foveally dominated. That is, gain fields in AIT operated on smaller spatial scales and smaller dispersions than in LIP. Thus, we show that the geometry of eye-position visual space depends on the population characteristics of gain fields, and that differences in gain field characteristics for different cortical areas may underlie differences in the representation of space.

Recovering stimulus locations using populations of eye-position modulated neurons in dorsal and ventral visual streams of non-human primates.

We recorded visual responses while monkeys fixated the same target at different gaze angles, both dorsally (lateral intraparietal cortex, LIP) and ventrally (anterior inferotemporal cortex, AIT). While eye-position modulations occurred in both areas, they were both more frequent and stronger in LIP neurons. We used an intrinsic population decoding technique, multidimensional scaling (MDS), to recover eye positions, equivalent to recovering fixated target locations. We report that eye-position based visual space in LIP was more accurate (i.e., metric). Nevertheless, the AIT spatial representation remained largely topologically correct, perhaps indicative of a categorical spatial representation (i.e., a qualitative description such as "left of" or "above" as opposed to a quantitative, metrically precise description). Additionally, we developed a simple neural model of eye position signals and illustrate that differences in single cell characteristics can influence the ability to recover target position in a population of cells. We demonstrate for the first time that the ventral stream contains sufficient information for constructing an eye-position based spatial representation. Furthermore we demonstrate, in dorsal and ventral streams as well as modeling, that target locations can be extracted directly from eye position signals in cortical visual responses without computing coordinate transforms of visual space.

Monkeys in space: primate neural data suggest volumetric representations.

The target article does not consider neural data on primate spatial representations, which we suggest provide grounds for believing that navigational space may be three-dimensional rather than quasi-two-dimensional. Furthermore, we question the authors' interpretation of rat neurophysiological data as indicating that the vertical dimension may be encoded in a neural structure separate from the two horizontal dimensions.

Semantic size of abstract concepts: it gets emotional when you can't see it.

Size is an important visuo-spatial characteristic of the physical world. In language processing, previous research has demonstrated a processing advantage for words denoting semantically "big" (e.g., jungle) versus "small" (e.g., needle) concrete objects. We investigated whether semantic size plays a role in the recognition of words expressing abstract concepts (e.g., truth). Semantically "big" and "small" concrete and abstract words were presented in a lexical decision task. Responses to "big" words, regardless of their concreteness, were faster than those to "small" words. Critically, we explored the relationship between semantic size and affective characteristics of words as well as their influence on lexical access. Although a word's semantic size was correlated with its emotional arousal, the temporal locus of arousal effects may depend on the level of concreteness. That is, arousal seemed to have an earlier (lexical) effect on abstract words, but a later (post-lexical) effect on concrete words. Our findings provide novel insights into the semantic representations of size in abstract concepts and highlight that affective attributes of words may not always index lexical access.

Population coding and the labeling problem: extrinsic versus intrinsic representations.

Current population coding methods, including weighted averaging and Bayesian estimation, are based on extrinsic representations. These require that neurons be labeled with response parameters, such as tuning curve peaks or noise distributions, which are tied to some external, world-based metric scale. Firing rates alone, without this external labeling, are insufficient to represent a variable. However, the extrinsic approach does not explain how such neural labeling is implemented. A radically different and perhaps more physiological approach is based on intrinsic representations, which have access only to firing rates. Because neurons are unlabeled, intrinsic coding represents relative, rather than absolute, values of a variable. We show that intrinsic coding has representational advantages, including invariance, categorization, and discrimination, and in certain situations it may also recover absolute stimulus values.

Size matters: bigger is faster.

A largely unexplored aspect of lexical access in visual word recognition is "semantic size"--namely, the real-world size of an object to which a word refers. A total of 42 participants performed a lexical decision task on concrete nouns denoting either big or small objects (e.g., bookcase or teaspoon). Items were matched pairwise on relevant lexical dimensions. Participants' reaction times were reliably faster to semantically "big" versus "small" words. The results are discussed in terms of possible mechanisms, including more active representations for "big" words, due to the ecological importance attributed to large objects in the environment and the relative speed of neural responses to large objects.

Shape selectivity in primate frontal eye field.

Previous neurophysiological studies of the frontal eye field (FEF) in monkeys have focused on its role in saccade target selection and gaze shift control. It has been argued that FEF neurons indicate the locations of behaviorally significant visual stimuli and are not inherently sensitive to specific features of the visual stimuli per se. Here, for the first time, we directly examined single cell responses to simple, two-dimensional shapes and found that shape selectivity exists in a substantial number of FEF cells during a passive fixation task or during the sample, delay (memory), and eye movement periods in a delayed match to sample (DMTS) task. Our data demonstrate that FEF neurons show sensory and mnemonic selectivity for stimulus shape features whether or not they are behaviorally significant for the task at hand. We also investigated the extent and localization of activation in the FEF using a variety of shape stimuli defined by static or dynamic cues employing functional magentic resonance imaging (fMRI) in anesthetized and paralyzed monkeys. Our fMRI results support the electrophysiological findings by showing significant FEF activation for a variety of shape stimuli and cues in the absence of attentional and motor processing. This shape selectivity in FEF is comparable to previous reports in the ventral pathway, inviting a reconsideration of the functional organization of the visual system.

Three-dimensional shape representation in monkey cortex.

Using fMRI in anesthetized monkeys, this study investigates how the primate visual system constructs representations of three-dimensional (3D) shape from a variety of cues. Computer-generated 3D objects defined by shading, random dots, texture elements, or silhouettes were presented either statically or dynamically (rotating). Results suggest that 3D shape representations are highly localized, although widely distributed, in occipital, temporal, parietal, and frontal cortices and may involve common brain regions regardless of shape cue. This distributed network of areas cuts across both "what" and "where" processing streams, reflecting multiple uses for 3D shape representation in perception, recognition, and action.