12,509 research outputs found
The fractal urban coherence in biourbanism: the factual elements of urban fabric
This article is available online and will be inserted in also printed format in the Journal in October 2013.During the last few decades, modern urban fabric lost some very important elements, only because urban design and planning turned out to be stylistic aerial views or new landscapes of iconic technological landmarks. Biourbanism attempts to re-establish lost values and balance, not only in urban fabric, but also in reinforcing human-oriented design principles in either micro or macro scale. Biourbanism operates as a catalyst of theories and practices in both architecture and urban design to guarantee high standards in services, which are currently fundamental to the survival of communities worldwide. Human life in cities emerges during connectivity via geometrical continuity of grids and fractals, via path connectivity among highly active nodes, via exchange/movement of people and, finally via exchange of information (networks). In most human activities taking place in central areas of cities, people often feel excluded from design processes in the built environment. This paper aims at exploring the reasons for which, fractal cities, which have being conceived as symmetries and patterns, can have scientifically proven and beneficial impact on human fitness of body and mind; research has found that, brain traumas caused by visual agnosia become evident when patterns disappear from either 2D or 3D emergences in architectural and urban design.ADT Fund
Fractal Descriptors in the Fourier Domain Applied to Color Texture Analysis
The present work proposes the development of a novel method to provide
descriptors for colored texture images. The method consists in two steps. In
the first, we apply a linear transform in the color space of the image aiming
at highlighting spatial structuring relations among the color of pixels. In a
second moment, we apply a multiscale approach to the calculus of fractal
dimension based on Fourier transform. From this multiscale operation, we
extract the descriptors used to discriminate the texture represented in digital
images. The accuracy of the method is verified in the classification of two
color texture datasets, by comparing the performance of the proposed technique
to other classical and state-of-the-art methods for color texture analysis. The
results showed an advantage of almost 3% of the proposed technique over the
second best approach.Comment: Chaos, Volume 21, Issue 4, 201
Multifractal and Network Analysis of Phase Transition
Many models and real complex systems possess critical thresholds at which the
systems shift from one sate to another. The discovery of the early warnings of
the systems in the vicinity of critical point are of great importance to
estimate how far a system is from a critical threshold. Multifractal Detrended
Fluctuation analysis (MF-DFA) and visibility graph method have been employed to
investigate the fluctuation and geometrical structures of magnetization time
series of two-dimensional Ising model around critical point. The Hurst exponent
has been confirmed to be a good indicator of phase transition. Increase of the
multifractality of the time series have been observed from generalized Hurst
exponents and singularity spectrum. Both Long-term correlation and broad
probability density function are identified to be the sources of
multifractality of time series near critical regime. Heterogeneous nature of
the networks constructed from magnetization time series have validated the
fractal properties of magnetization time series from complex network
perspective. Evolution of the topology quantities such as clustering
coefficient, average degree, average shortest path length, density,
assortativity and heterogeneity serve as early warnings of phase transition.
Those methods and results can provide new insights about analysis of phase
transition problems and can be used as early warnings for various complex
systems.Comment: 23 pages, 11 figure
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Macaques preferentially attend to visual patterns with higher fractal dimension contours.
Animals' sensory systems evolved to efficiently process information from their environmental niches. Niches often include irregular shapes and rough textures (e.g., jagged terrain, canopy outlines) that must be navigated to find food, escape predators, and master other fitness-related challenges. For most primates, vision is the dominant sensory modality and thus, primates have evolved systems for processing complicated visual stimuli. One way to quantify information present in visual stimuli in natural scenes is evaluating their fractal dimension. We hypothesized that sensitivity to complicated geometric forms, indexed by fractal dimension, is an evolutionarily conserved capacity, and tested this capacity in rhesus macaques (Macaca mulatta). Monkeys viewed paired black and white images of simulated self-similar contours that systematically varied in fractal dimension while their attention to the stimuli was measured using noninvasive infrared eye tracking. They fixated more frequently on, dwelled for longer durations on, and had attentional biases towards images that contain boundary contours with higher fractal dimensions. This indicates that, like humans, they discriminate between visual stimuli on the basis of fractal dimension and may prefer viewing informationally rich visual stimuli. Our findings suggest that sensitivity to fractal dimension may be a wider ability of the vertebrate vision system
Multiresolution analysis of active region magnetic structure and its correlation with the Mt. Wilson classification and flaring activity
Two different multi-resolution analyses are used to decompose the structure
of active region magnetic flux into concentrations of different size scales.
Lines separating these opposite polarity regions of flux at each size scale are
found. These lines are used as a mask on a map of the magnetic field gradient
to sample the local gradient between opposite polarity regions of given scale
sizes. It is shown that the maximum, average and standard deviation of the
magnetic flux gradient for alpha, beta, beta-gamma and beta-gamma-delta active
regions increase in the order listed, and that the order is maintained over all
length-scales. This study demonstrates that, on average, the Mt. Wilson
classification encodes the notion of activity over all length-scales in the
active region, and not just those length-scales at which the strongest flux
gradients are found. Further, it is also shown that the average gradients in
the field, and the average length-scale at which they occur, also increase in
the same order. Finally, there are significant differences in the gradient
distribution, between flaring and non-flaring active regions, which are
maintained over all length-scales. It is also shown that the average gradient
content of active regions that have large flares (GOES class 'M' and above) is
larger than that for active regions containing flares of all flare sizes; this
difference is also maintained at all length-scales.Comment: Accepted for publication in Solar Physic
Slim Fractals: The Geometry of Doubly Transient Chaos
Traditional studies of chaos in conservative and driven dissipative systems
have established a correspondence between sensitive dependence on initial
conditions and fractal basin boundaries, but much less is known about the
relation between geometry and dynamics in undriven dissipative systems. These
systems can exhibit a prevalent form of complex dynamics, dubbed doubly
transient chaos because not only typical trajectories but also the (otherwise
invariant) chaotic saddles are transient. This property, along with a manifest
lack of scale invariance, has hindered the study of the geometric properties of
basin boundaries in these systems--most remarkably, the very question of
whether they are fractal across all scales has yet to be answered. Here we
derive a general dynamical condition that answers this question, which we use
to demonstrate that the basin boundaries can indeed form a true fractal; in
fact, they do so generically in a broad class of transiently chaotic undriven
dissipative systems. Using physical examples, we demonstrate that the
boundaries typically form a slim fractal, which we define as a set whose
dimension at a given resolution decreases when the resolution is increased. To
properly characterize such sets, we introduce the notion of equivalent
dimension for quantifying their relation with sensitive dependence on initial
conditions at all scales. We show that slim fractal boundaries can exhibit
complex geometry even when they do not form a true fractal and fractal scaling
is observed only above a certain length scale at each boundary point. Thus, our
results reveal slim fractals as a geometrical hallmark of transient chaos in
undriven dissipative systems.Comment: 13 pages, 9 figures, proof corrections implemente
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