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.

Neuron arbor geometry is sensitive to the limited-range fractal properties of their dendrites.

Fractal geometry is a well-known model for capturing the multi-scaled complexity of many natural objects. By analyzing three-dimensional images of pyramidal neurons in the rat hippocampus CA1 region, we examine how the individual dendrites within the neuron arbor relate to the fractal properties of the arbor as a whole. We find that the dendrites reveal unexpectedly mild fractal characteristics quantified by a low fractal dimension. This is confirmed by comparing two fractal methods-a traditional "coastline" method and a novel method that examines the dendrites' tortuosity across multiple scales. This comparison also allows the dendrites' fractal geometry to be related to more traditional measures of their complexity. In contrast, the arbor's fractal characteristics are quantified by a much higher fractal dimension. Employing distorted neuron models that modify the dendritic patterns, deviations from natural dendrite behavior are found to induce large systematic changes in the arbor's structure and its connectivity within a neural network. We discuss how this sensitivity to dendrite fractality impacts neuron functionality in terms of balancing neuron connectivity with its operating costs. We also consider implications for applications focusing on deviations from natural behavior, including pathological conditions and investigations of neuron interactions with artificial surfaces in human implants.

Comparison of fractal and grid electrodes for studying the effects of spatial confinement on dissociated retinal neuronal and glial behavior.

Understanding the impact of the geometry and material composition of electrodes on the survival and behavior of retinal cells is of importance for both fundamental cell studies and neuromodulation applications. We investigate how dissociated retinal cells from C57BL/6J mice interact with electrodes made of vertically-aligned carbon nanotubes grown on silicon dioxide substrates. We compare electrodes with different degrees of spatial confinement, specifically fractal and grid electrodes featuring connected and disconnected gaps between the electrodes, respectively. For both electrodes, we find that neuron processes predominantly accumulate on the electrode rather than the gap surfaces and that this behavior is strongest for the grid electrodes. However, the 'closed' character of the grid electrode gaps inhibits glia from covering the gap surfaces. This lack of glial coverage for the grids is expected to have long-term detrimental effects on neuronal survival and electrical activity. In contrast, the interconnected gaps within the fractal electrodes promote glial coverage. We describe the differing cell responses to the two electrodes and hypothesize that there is an optimal geometry that maximizes the positive response of both neurons and glia when interacting with electrodes.

Investigating Fractal Analysis as a Diagnostic Tool That Probes the Connectivity of Hippocampal Neurons.

Many of nature's fractal objects benefit from the favorable functionality that results from their pattern repetition at multiple scales. Our recent research focused on the importance of fractal scaling in establishing connectivity between neurons. Fractal dimension D A of the neuron arbors was shown to relate to the optimization of competing functional constraints-the ability of dendrites to connect to other neurons versus the costs associated with building the dendrites. Here, we consider whether pathological states of neurons might affect this fractal optimization and if changes in D A might therefore be used as a diagnostic tool in parallel with traditional measures like Sholl analyses. We use confocal microscopy to obtain images of CA1 pyramidal neurons in the coronal plane of the dorsal rat hippocampus and construct 3-dimensional models of the dendritic arbors using Neurolucida software. We examine six rodent groups which vary in brain condition (whether they had lesions in the anterior thalamic nuclei, ATN) and experience (their housing environment and experience in a spatial task). Previously, we showed ATN lesions reduced spine density in hippocampal CA1 neurons, whereas enriched housing increased spine density in both ATN lesion and sham rats. Here, we investigate whether ATN lesions and experience also effect the complexity and connectivity of CA1 dendritic arbors. We show that sham rats exposed to enriched housing and spatial memory training exhibited higher complexity (as measured by D A ) and connectivity compared to other groups. When we categorize the rodent groups into those with or without lesions, we find that both categories achieve an optimal balance of connectivity with respect to material cost. However, the D A value used to achieve this optimization does not change between these two categories, suggesting any morphological differences induced by the lesions are too small to influence the optimization process. Accordingly, we highlight considerations associated with applying our technique to publicly accessible repositories of neuron images with a broader range of pathological conditions.

Controlled assembly of retinal cells on fractal and Euclidean electrodes.

Controlled assembly of retinal cells on artificial surfaces is important for fundamental cell research and medical applications. We investigate fractal electrodes with branches of vertically-aligned carbon nanotubes and silicon dioxide gaps between the branches that form repeating patterns spanning from micro- to milli-meters, along with single-scaled Euclidean electrodes. Fluorescence and electron microscopy show neurons adhere in large numbers to branches while glial cells cover the gaps. This ensures neurons will be close to the electrodes' stimulating electric fields in applications. Furthermore, glia won't hinder neuron-branch interactions but will be sufficiently close for neurons to benefit from the glia's life-supporting functions. This cell 'herding' is adjusted using the fractal electrode's dimension and number of repeating levels. We explain how this tuning facilitates substantial glial coverage in the gaps which fuels neural networks with small-world structural characteristics. The large branch-gap interface then allows these networks to connect to the neuron-rich branches.

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.

Investigation of Fractal Carbon Nanotube Networks for Biophilic Neural Sensing Applications.

We propose a carbon-nanotube-based neural sensor designed to exploit the electrical sensitivity of an inhomogeneous fractal network of conducting channels. This network forms the active layer of a multi-electrode field effect transistor that in future applications will be gated by the electrical potential associated with neuronal signals. Using a combination of simulated and fabricated networks, we show that thin films of randomly-arranged carbon nanotubes (CNTs) self-assemble into a network featuring statistical fractal characteristics. The extent to which the network's non-linear responses will generate a superior detection of the neuron's signal is expected to depend on both the CNT electrical properties and the geometric properties of the assembled network. We therefore perform exploratory experiments that use metallic gates to mimic the potentials generated by neurons. We demonstrate that the fractal scaling properties of the network, along with their intrinsic asymmetry, generate electrical signatures that depend on the potential's location. We discuss how these properties can be exploited for future neural sensors.

The Roles of an Aluminum Underlayer in the Biocompatibility and Mechanical Integrity of Vertically Aligned Carbon Nanotubes for Interfacing with Retinal Neurons.

Retinal implant devices are becoming an increasingly realizable way to improve the vision of patients blinded by photoreceptor degeneration. As an electrode material that can improve restored visual acuity, carbon nanotubes (CNTs) excel due to their nanoscale topography, flexibility, surface chemistry, and double-layer capacitance. If vertically aligned carbon nanotubes (VACNTs) are biocompatible with retinal neurons and mechanically robust, they can further improve visual acuity-most notably in subretinal implants-because they can be patterned into high-aspect-ratio, micrometer-size electrodes. We investigated the role of an aluminum (Al) underlayer beneath an iron (Fe) catalyst layer used in the growth of VACNTs by chemical vapor deposition (CVD). In particular, we cultured dissociated retinal cells for three days in vitro (DIV) on unfunctionalized and oxygen plasma functionalized VACNTs grown from a Fe catalyst (Fe and Fe + Pl preparations, where Pl signifies the plasma functionalization) and an Fe catalyst with an Al underlayer (Al/Fe and Al/Fe + Pl preparations). The addition of the Al layer increased the mechanical integrity of the VACNT interface and enhanced retinal neurite outgrowth over the Fe preparation. Unexpectedly, the extent of neurite outgrowth was significantly greater in the Al/Fe than in the Al/Fe+Pl preparation, suggesting plasma functionalization can negatively impact biocompatibility for some VACNT preparations. Additionally, we show our VACNT growth process for the Al/Fe preparation can support neurite outgrowth for up to 7 DIV. By demonstrating the retinal neuron biocompatibility, mechanical integrity, and pattern control of our VACNTs, this work offers VACNT electrodes as a solution for improving the restored visual acuity provided by modern retinal implants.

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.

Nature's Fractal Similarities: Integrating Art and Science.

This year's cover artist, Clinton Marstall, creates fractal imagery by photographing natural patterns. He then uses a pen to highlight the patterns and projects them on to a canvas for painting. Using this precision technique, he integrates a number of biomorphic images into a unique amalgum of multi-scaled complexity.

Modeling the Improved Visual Acuity Using Photodiode Based Retinal Implants Featuring Fractal Electrodes.

Electronically restoring vision to patients blinded by severe retinal degenerations is rapidly becoming a realizable feat through retinal implants. Upon receiving an implant, previously blind patients can now detect light, locate objects, and determine object motion direction. However, the restored visual acuity (VA) is still significantly below the legal blindness level (VA < 20/200). The goal of this research is to optimize the inner electrode geometry in photovoltaic subretinal implants in order to restore vision to a VA better than blindness level. We simulated neural stimulation by 20 µm subretinal photovoltaic implants featuring square or fractal inner electrodes by: (1) calculating the voltage generated on the inner electrode based on the amount of light entering the photodiode, (2) mapping how this voltage spreads throughout the extracellular space surrounding retinal bipolar neurons, and (3) determining if these extracellular voltages are sufficient for neural stimulation. By optimizing the fractal inner electrode geometry, we show that all neighboring neurons can be stimulated using an irradiance of 12 mW/mm2, while the optimized square only stimulates ~10% of these neurons at an equivalent irradiance. The 20 µm fractal electrode can thus theoretically restore VA up to 20/80, if other limiting factors common to retinal degenerations, such as glia scarring and rewiring of retinal circuits, could be reduced. For the optimized square to stimulate all neighboring neurons, the irradiance has to be increased by almost 300%, which is very near the maximum permissible exposure safety limit. This demonstration that fractal electrodes can stimulate targeted neurons for long periods using safe irradiance levels highlights the possibility for restoring vision to a VA better than the blindness level using photodiode-based retinal implants.

Taxonomy of Individual Variations in Aesthetic Responses to Fractal Patterns.

In two experiments, we investigate group and individual preferences in a range of different types of patterns with varying fractal-like scaling characteristics. In Experiment 1, we used 1/f filtered grayscale images as well as their thresholded (black and white) and edges only counterparts. Separate groups of observers viewed different types of images varying in slope of their amplitude spectra. Although with each image type, the groups exhibited the "universal" pattern of preference for intermediate amplitude spectrum slopes, we identified 4 distinct sub-groups in each case. Sub-group 1 exhibited a typical peak preference for intermediate amplitude spectrum slopes ("intermediate"; approx. 50%); sub-group 2 exhibited a linear increase in preference with increasing amplitude spectrum slope ("smooth"; approx. 20%), while sub-group 3 exhibited a linear decrease in preference as a function of the amplitude spectrum slope ("sharp"; approx. 20%). Sub-group 4 revealed no significant preference ("other"; approx. 10%). In Experiment 2, we extended the range of different image types and investigated preferences within the same observers. We replicate the results of our first experiment and show that individual participants exhibit stable patterns of preference across a wide range of image types. In both experiments, Q-mode factor analysis identified two principal factors that were able to explain more than 80% of interindividual variations in preference across all types of images, suggesting a highly similar dimensional structure of interindividual variations in preference for fractal-like scaling characteristics.

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.

Beauty and the beholder: the role of visual sensitivity in visual preference.

For centuries, the essence of aesthetic experience has remained one of the most intriguing mysteries for philosophers, artists, art historians and scientists alike. Recently, views emphasizing the link between aesthetics, perception and brain function have become increasingly prevalent (Ramachandran and Hirstein, 1999; Zeki, 1999; Livingstone, 2002; Ishizu and Zeki, 2013). The link between art and the fractal-like structure of natural images has also been highlighted (Spehar et al., 2003; Graham and Field, 2007; Graham and Redies, 2010). Motivated by these claims and our previous findings that humans display a consistent preference across various images with fractal-like statistics, here we explore the possibility that observers' preference for visual patterns might be related to their sensitivity for such patterns. We measure sensitivity to simple visual patterns (sine-wave gratings varying in spatial frequency and random textures with varying scaling exponent) and find that they are highly correlated with visual preferences exhibited by the same observers. Although we do not attempt to offer a comprehensive neural model of aesthetic experience, we demonstrate a strong relationship between visual sensitivity and preference for simple visual patterns. Broadly speaking, our results support assertions that there is a close relationship between aesthetic experience and the sensory coding of natural stimuli.

Temporal Structure of Human Gaze Dynamics Is Invariant During Free Viewing.

We investigate the dynamic structure of human gaze and present an experimental study of the frequency components of the change in gaze position over time during free viewing of computer-generated fractal images. We show that changes in gaze position are scale-invariant in time with statistical properties that are characteristic of a random walk process. We quantify and track changes in the temporal structure using a well-defined scaling parameter called the Hurst exponent, H. We find H is robust regardless of the spatial complexity generated by the fractal images. In addition, we find the Hurst exponent is invariant across all participants, including those with distinct changes to higher order visual processes due to neural degeneration. The value we find for H of 0.57 shows that the gaze dynamics during free viewing of fractal images are consistent with a random walk process with persistent movements. Our research suggests the human visual system may have a common strategy that drives the dynamics of human gaze during exploration.

The routine use of chest radiographs after chest tube removal in children who have had cardiac surgery.

BACKGROUND: It is routine to obtain a chest radiograph (CXR) after removal of a chest tube (CT) to assess for pneumothorax. Retrospective studies have shown that clinical signs were present in most children with pneumothorax and were an indication for a CXR. OBJECTIVE: Our objective was to determine if clinical indicators of pneumothorax are sufficient predictors of the need for CT reinsertion in children who have had a CT removed after cardiac surgery. METHODS: The prospective study included a physical assessment before CT removal, using a two-person technique, which was repeated 2 hours after CT removal. Based on assessment findings, a decision was made regarding whether a CXR was indicated. The routine CXR was then obtained and read by a pediatric intensivist who was blinded to the decision of the investigator. RESULTS: Sixty CTs were removed in 53 children. No false-positive predictions were made, because none of the children was predicted to have a pneumothorax requiring chest tube reinsertion, and none developed a significant pneumothorax (95% confidence interval: 0, 5%). CONCLUSIONS: The low rate of pneumothoraces in this study may be been related to how the CT was placed in surgery, the type of CT used, or the method of removal. In this study the risk of developing a pneumothorax requiring CT reinsertion after CT removal was at most 5% and therefore low enough to consider obtaining a CXR for symptomatic children only.

Femoral central venous catheters are not associated with higher rates of infection in the pediatric critical care population.

BACKGROUND: Adult data show a difference in central venous catheter (CVC) infection rates between 3 major sites: subclavian (SC), internal jugular (IJ), and femoral veins. We hypothesized that in patients in pediatric intensive care units (PICUs), there is no difference in rates of CVC infection among these three sites, but specifically the femoral compared to all other sites. METHODS: In this retrospective cohort study, data from January 1999 to January 2008 were collected prospectively for internal review and quality assurance. All PICU patients with a CVC were enrolled. The rate of CVC infection was determined using Cox regression survival analysis to account for various durations of CVC placement at the various sites, then adjusted for severity of illness, number of lumens, and patient age. Mortality was compared in patients with a CVC infection versus those without. RESULTS: A total of 4,512 patients with a CVC were enrolled. No site was associated with an increased risk of infection compared with the other sites, with hazard ratios of 0.951 (95% confidence interval [CI], 0.612-1.478) for the SC site, 0.956 (95% CI, 0.593-1.541) for the IJ site, and 1.120 (95% CI, 0.753-1.665) for the femoral site. No significant association between mortality and presence of CVC infection was found when adjusted for age, severity of illness, and duration of CVC placement. An association was found between the presence of a CVC infection and prolonged PICU length of stay (3.98 days longer; P < .001). CONCLUSION: Femoral CVCs are not associated with higher rates of infection in the PICU. In addition, the presence of CVC infection does not affect mortality, but is associated with longer PICU admission.

Perceptual and Physiological Responses to Jackson Pollock's Fractals.

Fractals have been very successful in quantifying the visual complexity exhibited by many natural patterns, and have captured the imagination of scientists and artists alike. Our research has shown that the poured patterns of the American abstract painter Jackson Pollock are also fractal. This discovery raises an intriguing possibility - are the visual characteristics of fractals responsible for the long-term appeal of Pollock's work? To address this question, we have conducted 10 years of scientific investigation of human response to fractals and here we present, for the first time, a review of this research that examines the inter-relationship between the various results. The investigations include eye tracking, visual preference, skin conductance, and EEG measurement techniques. We discuss the artistic implications of the positive perceptual and physiological responses to fractal patterns.