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A proprietary fractal image compression algorithm and the Joint Photographic Experts Group (JPEG) industry standard algorithm for image compression are compared. In every case, the JPEG algorithm was superior to the fractal method at a given compression ratio according to a root mean square criterion and a peak signal to noise criterion.
The dependence of product generation with the Peclet and Reynolds number in a numerically simulated, reacting, two dimensional, temporally growing mixing layer is used to compute the fractal dimension of passive scalar interfaces. A transition from a low dimension of 4/3 to a higher one of 5/3 is identified and shown to be associated to the kinematic distortion on the flow field during the first pairing interaction. It is suggested that the structures responsible for this transition are non-deterministic, non-random, inhomogeneous fractals. Only the large scales are involved. No further transition is found for Reynolds numbers up to 20,000.
Biologically generated cellular patterns, sometimes called bioconvective patterns, are found to cluster into aggregates which follow fractal growth dynamics akin to diffusion-limited aggregation (DLA) models. The pattern formed is self-similar with fractal dimension of 1.66 +/-0.038. Bioconvective DLA branching results from thermal roughening which shifts the balance between ordering viscous forces and disordering cell motility and random diffusion. The phase diagram for pattern morphology includes DLA, boundary spokes, random clusters, and reverse clusters.
The concepts of fractal geometry are applied to the analysis of 0.4-micron alumina constrained to agglomerate in two dimensions. Particles were trapped at the bottom surface of a drop of a dilute suspension, and the agglomeration process was directly observed, using an inverted optical microscope. Photographs were digitized and analyzed, using three distinct approaches. The results indicate that the agglomerates are fractal, having a dimension of approximately 1.5, which agrees well with the predictions of the diffusion-limited cluster-cluster aggregation model.
Images acquired by NASA's Calibrated Airborne Multispectral Scanner are used to compute the fractal dimension as a function of spatial resolution. Three methods are used to determine the fractal dimension: Shelberg's (1982, 1983) line-divider method, the variogram method, and the triangular prism method. A description of these methods and the result of applying these methods to a remotely-sensed image is also presented. The scanner data was acquired over western Puerto Rico in January, 1990 over land and water. The aim is to study impacts of man-induced changes on land that affect sedimentation into the near-shore environment. The data were obtained over the same area at three different pixel sizes: 10 m, 20 m, and 30 m.
The MSS, SPOT, and AVHRR imagery of Ugandan forests were analyzed to assess the information content related to deforestation and tropical habitat fragmentation, focusing primarily on the Kibale and Mabira Forests. Analysis of actual and simulated AVHRR imagery showed that it might be possible to monitor major changes in forest extent with the relatively coarse spatial resolution of AVHRR imagery (about 1 km) provided ancillary data were available. The fractal dimension of the forest edges, measured with the Landsat and SPOT imagery, was consistently about 1.7 or 1.8. This high fractal dimension was due to the coplex pattern of clearings, remnant forest stands, and jagged forest edges caused by repeated human encroachment over centuries.
Many natural structures possess self-similar multiscales which can be characterized by power law spectra. Under appropriate conditions, knowledge of the strength of these scale sizes provides information on the physical processes which formed these objects. In this paper, we investigate wave interactions with continuous fractal layers which model geological and variegated structures. Since fractal characteristics of the layers are embedded in the scattered field, they can be retrieved under appropriate conditions. This inversion can be performed in either the frequency or the time domain as desired.
The dependence of product generation on Peclet and Reynolds numbers in a numerically simulated, reacting, two dimensional, temporally growing mixing layer is related theoretically to the fractal dimension of the passive scalar interfaces. This relation is verified using product generation measurements and dimensions derived from a standard box counting technique. A transition from a low initial dimension to a higher one of approximately 5/3 is identified and shown to be associated to the kinematic distortion on the flow field during the first pairing interaction. It is suggested that the structures responsible for this transition are non-deterministic, non-random, inhomogeneous fractals. Only the large scales are involved. No further transitions, either in the spectra of the vorticity field or in the mixing behavior, are found for Reynolds numbers up to 90,000.
Fractal dimension for a few lava flow margins on the gently sloping flanks of Alba Patera were measured using the structured walk method. Fractal behavior was observed at scales ranging from 20 to 100 pixels. The upper limit of the linear part of log(margin length) vs. log(scale) profile correlated well to the margin length. The lower limit depended on resolution and flow properties.
The surface roughness of the Vastitas Borealis Formation on Mars was analyzed with fractal statistics. Root mean square slopes and fractal dimensions were calculated for 74 topographic profiles. Results have implications for radar scattering models.
Stochastic fractal models of clouds are often used to study 3D radiative effects and their influence on the remote sensing of cloud properties. Since it is important that the cloud models produce a correct radiative response, some researchers require the model parameters to match observed cloud properties such as scale-independent optical thickness variability. Unfortunately, matching these properties does not necessarily imply that the cloud models will cause the right 3D radiative effects. First, the matched properties alone only influence the 3D effects but do not completely determine them. Second, in many cases the retrieved cloud properties have been already biased by 3D radiative effects, and so the models may not match the true real clouds. Finally, the matched cloud properties cannot be considered independent from the scales at which they have been retrieved. This paper proposes an approach that helps ensure that fractal cloud models are realistic and produce the right 3D effects. The technique compares the results of radiative transfer simulations for the model clouds to new direct observations of 3D radiative effects in satellite images.
The term "magnetic complexity" has not been sufficiently quantified. To accomplish this, we must understand the relationship between the observed magnetic field of solar active regions and fractal dimension measurements. Using data from the Marshall Space Flight Center's vector magnetograph ranging from December 1991 to July 2001, we compare the results of several methods of calculating a fractal dimension, e.g., Hurst coefficient, the Higuchi method, power spectrum, and 2-D Wavelet Packet Analysis. In addition, we apply these methods to synthetic data, beginning with representations of very simple dipole regions, ending with regions that are magnetically complex.
Fluctuations in the duration of the gait cycle (the stride interval) display fractal dynamics and long-range correlations in healthy young adults. We hypothesized that these stride-interval correlations would be altered by changes in neurological function associated with aging and certain disease states. To test this hypothesis, we compared the stride-interval time series of 1) healthy elderly subjects and young controls and of 2) subjects with Huntington's disease and healthy controls. Using detrended fluctuation analysis we computed alpha, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. The scaling exponent alpha was significantly lower in elderly subjects compared with young subjects (elderly: 0.68 +/- 0.14; young: 0.87 +/- 0.15; P < 0.003). The scaling exponent alpha was also smaller in the subjects with Huntington's disease compared with disease-free controls (Huntington's disease: 0.60 +/- 0.24; controls: 0.88 +/-0.17; P < 0.005). Moreover, alpha was linearly related to degree of functional impairment in subjects with Huntington's disease (r = 0.78, P < 0.0005). These findings demonstrate that strike-interval fluctuations are more random (i.e., less correlated) in elderly subjects and in subjects with Huntington's disease. Abnormal alterations in the fractal properties of gait dynamics are apparently associated with changes in central nervous system control.
The characterization of forested areas is frequently required in resource management practice. Passive remotely sensed data, which are much more accessible and cost effective than are active data, have rarely, if ever, been used to characterize forest structure directly, but rather they usually focus on the estimation of indirect measurement of biomass or canopy coverage. In this study, some spatial analysis techniques are presented that might be employed with Landsat TM data to analyze forest structure characteristics. A case study is presented wherein fractal dimensions, along with a simple spatial autocorrelation technique (Moran s I), were related to stand density parameters of the Oakmulgee National Forest located in the southeastern United States (Alabama). The results of the case study presented herein have shown that as the percentage of smaller diameter trees becomes greater, and particularly if it exceeds 50%, then the canopy image obtained from Landsat TM data becomes sufficiently homogeneous so that the spatial indices reach their lower limits and thus are no longer determinative. It also appears, at least for the Oakmulgee forest, that the relationships between the spatial indices and forest class percentages within the boundaries can reasonably be considered linear. The linear relationship is much more pronounced in the sawtimber and saplings cases than in samples dominated by medium sized trees (poletimber). In addition, it also appears that, at least for the Oakmulgee forest, the relationships between the spatial indices and forest species groups (Hardwood and Softwood) percentages can reasonably be considered linear. The linear relationship is more pronounced in the forest species groups cases than in the forest classes cases. These results appear to indicate that both fractal dimensions and spatial autocorrelation indices hold promise as means of estimating forest stand characteristics from remotely sensed images. However, additional work is needed to confirm that the boundaries identified for Oakmulgee forest and the linear nature of the relationship between image complexity indices and forest characteristics are generally evident in other forests. In addition, the effects of other parameters such ,as topographic relief and image distortion due to sun angle and cloud cover, for example, need to be examined.
This study compares heat flux performance of a Loop Heat Pipe (LHP) wick structure fabricated from compressed carbon foam with that of a wick structure fabricated from sintered soda lime glass. Each wick was used in an LHP containing a fractal based evaporator. The Fractal Loop Heat Pipe (FLHP) was designed and manufactured by Mikros Manufacturing Inc. The compressed carbon foam wick structure was manufactured by ERG Aerospace Inc., and machined to specifications comparable to that of the initial soda lime glass wick structure. Machining of the compressed foam as well as performance testing was conducted at the United States Naval Academy. Performance testing with the sintered soda lime glass wick structures was conducted at NASA Goddard Space Flight Center. Heat input for both wick structures was supplied via cartridge heaters mounted in a copper block. The copper heater block was placed in contact with the FLHP evaporator which had a circular cross-sectional area of 0.88 cm(sup 2). Twice distilled, deionized water was used as the working fluid in both sets of experiments. Thermal performance data was obtained for three different Condenser/Subcooler temperatures under degassed conditions. Both wicks demonstrated comparable heat flux performance with a maximum of 75 W/cm observed for the soda lime glass wick and 70 W /cm(sup 2) for the compressed carbon foam wick.
Purpose: Our hypothesis predicts that blood vessels within the retina increase in density during early-stage nonproliferative diabetic retinopathy (NPDR), based on previous results of a small retrospective study. For the current prospective study, the remodeling of arteries and veins during progression of early NPDR is assessed by a repertoire of parameters that includes the fractal dimension (D(sub f) ). In complex structures such as branching vascular trees, D(sub f) is a sensitive measure of space-filing capacity. The renin-angiotensin system (RAS) is implicated in DR pathogenesis and the function of circulating angiogenic cells (CACs), a critical bone marrow-derived population instrumental in vascular repair. Methods: Arterial and venous branching patterns were extracted from images of 6 normal controls and 3 early NPDR subjects (2 moderate, 1 mild) acquired by Heidelberg Spectralis (Registered Trademark) OCT following fluorescein angiography (FA). The vascular branching patterns were analyzed by NASAs VESsel GENeration Analysis (VESGEN) software, in which skeletonized representations were generated automatically to yield D(sub f) by the box-counting method. For binary 2D images, D(sub f) varies between limiting Euclidean dimensions of 1 and 2. Peripheral blood of diabetics and controls was collected for CD34+ CAC isolation. The gene expression of RAS in CACs was assessed by qPCR for Mas receptor to Ang-(1-7). The vasoreparative function of the CACs was measured by migration ability toward CXCL12 (SDF-1). Results: By D(sub f), venous and arterial densities were 1.370 +/- 0.006 and 1.329 +/- 0.016 for early NPDR, compared to 1.318 +/- 0.012 and 1.320 +/- 0.036 for control. The space filling capacity in early NPDR measured by D(sub f), a sensitive parameter, therefore demonstrated a pronounced increase for veins, but not for arteries. Mas receptor mRNA in CACs was increased in diabetics without DR but reduced with onset of NPDR, indicating possible loss of compensation of protective RAS during early DR. Migratory dysfunction of CD34+ cells was further associated with DR. Conclusions: As assessed by the fractal dimension in our preliminary study, the space-filling capacity of veins, but not arteries, was greater in early NPDR than in control. Larger patient populations will be examined as we complete our ongoing longitudinal study. Results further suggest the protective RAS axis within diabetic CACs is lost early in DR and is associated with increased vascular remodeling as evidenced by VESGEN analysis.
Graphite's resilience to high temperatures and neutron damage makes it vital for nuclear reactors, yet irradiation alters its microstructure, degrading key properties. We used small- and wide-angle X-ray scattering to study neutron-irradiated fine-grain nuclear graphite (Grade G347A) across varied temperatures and fluences. Results show significant shifts in internal strain and porosity, correlating with radiation-induced volume changes. Notably, porosity volume distribution (fractal dimensions) follows non-monotonic volume changes, suggesting a link to the Weibull distribution of fracture stress.
ABSTRACT Characterization of the interface between explosive product gases and ambient air in an explosion is a complicated task due to the turbulent mixing and inherently three‐dimensional expansion of the interface. This study aims to quantify the evolution of the interface as a temporally varying Hausdorff dimension. Two test series were conducted with Composition C‐4 charges with masses of 105 and 880 g. Imaging data were collected from the time of detonation until shock wave detachment using ultra‐high‐speed cameras. Gas cloud profiles were extracted using automated image processing algorithms, and the Hausdorff dimension of these two‐dimensional slices of the gas cloud was then estimated using boxcounting algorithms. When scaled with standard gas dynamic nondimensional scalings, the Hausdorff dimension of all explosive events appears to collapse towards a single curve. The fireball was initially nonfractal and began to develop fractal properties as the shock wave separated from the detonation products. Artificial perturbation of the charged surface had no detectable impact on the evolution of the Hausdorff dimension in the early development of the fireball outside of error, despite visible phenomenological differences in the early development of mixing on the fireball surface.