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105 results for “Fractal”
Data from: Fractal measures of spatial pattern as a heuristic for return rate in vegetative systems
Measurement of population persistence is a long-standing problem in ecology; in particular, whether it is possible to gain insights into persistence without long time-series. Fractal measurements of spatial patterns, such as the Korcak exponent or boundary dimension, have been proposed as indicators of the persistence of underlying dynamics. Here we explore under what conditions a predictive relationship between fractal measures and persistence exists. We combine theoretical arguments with an aerial snapshot and time series from a long-term study of seagrass. For this form of vegetative growth, we find that the expected relationship between the Korcak exponent and persistence is evident at survey sites where the population return rate can be measured. This highlights a limitation of the use of power-law patch-size distributions and other indicators based on spatial snapshots. Moreover, our numeric simulations show that for a single species and a range of environmental conditions that the Korcak–persistence relationship provides a link between temporal dynamics and spatial pattern; however, this relationship is specific to demographic factors, so we cannot use this methodology to compare between species.
Data from: Fractal geometry of a complex plumage trait reveals bird's quality
Animal coloration is key in natural and sexual selection, playing significant roles in intra- and interspecific communication because of its linkage to individual behaviour, genetics and physiology. Simple animal traits such as the area or the colour intensity of homogeneous patches have been profusely studied. More complex patterns are widespread in nature, but they escape our understanding because their variation is difficult to capture effectively by standard, simple measures. Here, we used fractal geometry to quantify inter-individual variation in the expression of a complex plumage trait, the heterogeneous black bib of the red-legged partridge (Alectoris rufa). We show that a higher bib fractal dimension (FD) predicted better individual body condition, as well as immune responsiveness, which is condition-dependent in our study species. Moreover, when food intake was experimentally reduced during moult as a means to reduce body condition, the bib's FD significantly decreased. Fractal geometry therefore provides new opportunities for the study of complex animal colour patterns and their roles in animal communication.
Data from: General models for the spectra of surface area scaling strategies of cells and organisms: fractality, geometric dissimilitude, and internalization
Surface areas and volumes of biological systems—from molecules to organelles, cells, and organisms—affect their biological rates and kinetics. Therefore, surface-area-to-volume ratios and the scaling of surface area with volume profoundly influences ecology, physiology, and evolution. The zeroth-order geometric expectation is that surface area scales with body mass or volume as a power law with an exponent of two-thirds, with consequences for surface-area-to-volume (SA:V) ratios and constraints on size; however, organisms have adaptations for altering the surface area scaling and SA:V ratios of their bodies and structures. The strategies fall into three groups: (i) fractal-like surface convolutions and crinkles; (ii) classic geometric dissimilitude through elongating, flattening, fattening, and hollowing; and (iii) internalization of surfaces. Here I develop general quantitative theory to model the spectra of effects of these strategies on SA:V ratios and surface area scaling, from exponents of less than two-thirds to superlinear scaling and mixed-power laws. Applying the theory to cells helps quantitatively evaluate the effects of membrane fractality, shape-shifting, vacuoles, vesicles, and mitochondria on surface area scaling, informing understanding of cell allometry, morphology, and evolution. Analysis of compiled data indicates that through hollowness and surface internalization eukaryotic phytoplankton increase their effective surface area scaling, attaining near-linear scaling in larger cells. This unifying theory highlights the fundamental role of biological surfaces in metabolism and morphological evolution.
Neuron Fractal Image Reading
<p>Seed along with few iterations of neuron fractal has been provided.</p>
Fractal geometry features of aerosol particle and its contribution to atmospheric optical property: development of Fractal Aerosol Cluster Model and its validation of atmospheric visibility during a heavy haze event
<p>-------------------------<br>Content of the dataset<br>-------------------------<br>****** the experiment case (EXP) ; the control case (CTR) ******</p> <p>1. Meteorological elements.tar contains observational and simulated data for T2, WS, RH, and PM2.5 time series, which can be used to plot Figure 4 and build Table 2</p> <p>2. Planar distribution.tar contains the horizontal spatial distribution data of aerosol extinction coefficients simulated by CTR and EXP for the four typical moments selected in this paper, which can be used to plot Figures 5, 6, and 7</p> <p>3. PM.rar contains the vertical profile data of simulated Particulate Matter concentrations by CTR and EXP during the study period in the paper, which can be utilized for drawing Fig. 11.</p> <p>4. Timeseries.tar contains observational and simulated data for time series of atmospheric visibility and surface shortwave radiation, which can be used to plot Figures 5, 6, 7, 8, S1, and build Table 3</p> <p>5. wrfbiochemi.rar contains the biogenic emissions data for simulation both for CTR and EXP.</p> <p>6. wrffirechemi.rar contains the biomass burning emissions data for simulation both for CTR and EXP.</p> <p>7. wrfchemi.rar contains the Anthropogenic emissions data for simulation both for CTR and EXP.</p> <p>8. The file module_optical_averaging.F contains the main code of the improved visibility model, the Fractal Aerosol Cluster Model</p> <p>(FACM), which is coupled to WRF-Chem and used by EXP. It is located in the chem/ directory and called by optical_driver.F.</p> <pre> </pre> <p> </p> <p>-------------------------</p> <p>Contact information</p> <p>-------------------------</p> <p> </p> <p>Zhenxin Liu</p> <p>liuzhenxin@nuist.edu.cn</p> <p> </p> <p> </p>
Geometry and Opacity Data for Fractal Aggregates
<p>In a previous version of this archive, geometry data and tables of opacity calculations were given that could be used to calculate the radiative pressure and absorption on fractal dust grains under Asymptotic Giant Branch (AGB) conditions (with a peak stellar wavelength of ~ 1 micron) for aggregates containing up to 256 primary particles. Because the focus of that work was on radiative pressure from a stellar spectrum peaking at approximately 1 micron, these data only covered the wavelength range from 0.3 to 30 microns. In this updated archive the wavelength range of the data has been expanded to allow calculation of the emission of the grains at longer wavelengths. Data are calculated for three common dust materials: forsterite, (Mg2SiO4), olivine, (Mg_(2x)Fe_(2(1-x))SiO4) with x=0.5, and 'astronomical silicate' (B.T. Draine and H.M. Lee, Optical Properties of Interstellar Graphite and Silicate Grains, Astrophysical Journal, 1984). In this updated version the range of aggregate sizes (number of primary particles in the aggregate) of some of these materials has also been increased from a maximum of 256 to 1024 constituent particles.<br> <br>Example fractal aggregates were generated using the Diffusion Limited Aggregation (DLA) code as described in Wozniak M., Onofri F.R.A., Barbosa S., Yon J., Mroczka J., Comparison of methods to derive morphological parameters of multi-fractal samples of particle aggregates from TEM images, Journal of Aerosol Science 47: 12–26 (2012) and Onofri F.R.A., M. Wozniak, S. Barbosa, On the Optical Characterization of Nanoparticle and their Aggregates in Plasma Systems, Contributions to Plasma Physics 51(2-3):228-236 (2011). Aggregates were generated with a constant prefactor, kf=1.3, and two fractal dimensions (Df), representing open, porous (Df=1.8) aggregates and more compact (Df=2.8) aggregates.<br> <br>The geometry files were produced with the DLA software. An example run using this software is shown for aggregates with 256 primary particles and a fractal dimension of 2.8 in the file 'dla_example.png'<br> <br>For the fractal dimension=1.8 data, the number of primary particles in the aggregate, N, was increased up to 1024 from the previous maximum of 256 for all three dust materials investigated. In addition, the data for MgFeSiO4 with a fractal dimension of 2.8 was increased from 256 to 1024. As in the previous archive, 12 instances of each aggregate size were generated with primary particles having a radius of 0.5. These geometry data are given in:<br>aggregates_kf1.3_df1.8.zip --> Geometry for a prefactor of 1.3 and fractal dimension 1.8<br>aggregates_kf1.3_df2.8.zip --> Geometry for a prefactor of 1.3 and fractal dimension 2.8<br> <br>An example file name for an aggregate is 'N_00000032_Agg_00000008.dat' where the first number is the number of primary particles in the aggregate (N=32) and the second number is the instance number (e.g. 8 of 12). The radius of each primary particle in an aggregate is 0.5. The geometry files have 4 columns: the x, y and z coordinates of each primary particle followed by the primary particle radius. In each zip file there is also a pdf document that describes the geometry data and shows an image of each geometry file.</p> <p> <br>These geometry data were then used to calculate the opacity of the aggregates using the Multiple Sphere T-Matrix code (MSTM v 3.0) developed by Daniel Mackowski (D.W. Mackowski, M.I. Mishchenko, A multiple sphere T-matrix Fortran code for use on parallel computer clusters, Journal of Quantitative Spectroscopy and Radiative Transfer, Volume 112, Issue 13, 2011). Data were generated using the first 10 instances of each aggregate size, and the geometry data were appropriately scaled to calculate the opacity data for primary particle radii ranging from 0.001 - 1.0 microns. As noted earlier, an earlier version of this archive was focused on radiative pressure on these aggregates and only covered the spectrum of a typical AGB star (0.3 to 30 microns wavelength). In this updated version this wavelength range has been increased to the longer wavelength limits of the optical data. By default, MSTM calculations are made along the z-axis of the geometry data. Additional calculations were made along the x and y axes for each aggregate. Therefore the final data set is the average of 30 values (10 instances each in the x,y,z directions).<br> <br>The opacity data files are given in:</p> <p>astronomical_silicate_df1.8.zip --> astronomical silicate aggregates with fractal dimension 1.8<br>astronomical_silicate_df2.8.zip --> astronomical silicate aggregates with fractal dimension 2.8<br>forsterite_df1.8.zip --> forsterite aggregates with fractal dimension 1.8<br>forsterite_df2.8.zip --> forsterite aggregates with fractal dimension 2.8<br>olivine_df1.8.zip --> olivine aggregates with fractal dimension 1.8<br>olivine_df2.8.zip --> olivine aggregates with fractal dimension 2.8</p> <p>In the previous version of this archive, only the table files with the averages of the 10 instances were provided. In this updated version each of the individual opacity files used to create these tables is now also provided. These opacity files are numbered similar to the geometry files. For example, the opacity calculations for N=32, instance=5, angle=3 is given by <br>'opacity_results_N000032_I05_A03_file.dat.' Each file begins with a short header describing the data. For example, the astronomical silicate header for this N=32, instance=5, angle=3 file is:</p> <p>#############################################################################################<br># Number of primary particles in aggregate: 32 <br># Geometry Instance Number: 5 <br># Geometry File Name: N_00000032_Agg_00000005.dat <br># Rotation Angles: 90.000 90.000 0.000 <br># Number of radius values: 30 <br># Minimum and maximum radius values in microns: 1.00000e-003 1.00000e+000 <br># Number of wavelength values: 92 <br># Minimum and maximum wavelength values in microns: 3.00000e-001 1.00000e+004 <br>#############################################################################################</p> <p>Afterwards the columns list the line number, the primary particle radius (microns), the wavelength (microns), the extinction efficiency factor, the absorption efficiency factor, the scattering absorption efficiency factor, the asymmetry factor and the radiation pressure efficiency factor. These efficiency factors are based on the effective radius of the aggregate described later in this document.</p> <p>Within each of these zipped folders is a file that contains the averages of these individual opacity files. For example 'astronomical_silicate_df1.8.dat' is the averaged data for the astronomical silicate aggregates with a fractal dimension 1.8. As in the previous archive, the first lines of these table files are a header starting with the '#' character describing the table and the source of the optical data used.<br> <br>After the header, the first line of data in the table has the following nine values giving the range for the data table and number of samples in N, (aggregate size), primary particle radius (microns) and wavelength (microns). These are:<br> Minimum aggregate size<br> Maximum aggregate size<br> Number of Aggregate samples<br> Primary Particle Minimum Radius (microns)<br> Primary Particle Maximum Radius (microns)<br> Number of Primary Particle radii samples<br> Wavelength minimum (microns)<br> Wavelength maximum (microns)<br> Number of Wavelength samples <br> <br>Subsequent lines contain 13 columns. These columns give the efficiency factors and asymmetry factor for aggregates. These efficiency factors are based on the effective radius of the aggregate given by:<br> a_eff = a_primary*N^(1/3)<br>where a_primary is the primary particle radius and N is the number of primary particles in the aggregate.<br> <br>For example, the absorption opacity of an aggregate would then be = pi*a_eff^2 * Q_abs.<br>The values in each column are:<br> Column 1: Primary particle radius in microns<br> Column 2: Wavelength in microns<br> Column 3: Number of primary particles in aggregate<br> Column 4: Mean Q_ext, mean extinction efficiency factor<br> Column 5: Standard Deviation of Mean Q_ext <br> Column 6: Mean Q_abs, mean absorption efficiency factor<br> Column 7: Standard Deviation of Mean Q_abs<br> Column 8: Mean Q_sca, mean scattering efficiency factor<br> Column 9: Standard Deviation of mean Q_sca<br> Column 10: Mean g_cos, mean asymmetry factor<br> Column 11: Standard Deviation of mean asymmetry factor<br> Column 12: Mean Q_pr, mean radiation pressure efficiency factor<br> Column 13: Standard Deviation of mean </p>
A group of images used for fractal analysis in Grading Evaluation of Marbling in Wagyu Beef Using Fractal Analysis.
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Figure 2 from: Amosu A, Mahmood H, Ofoche P (2018) Estimating the Permeability of Carbonate Rocks from the Fractal Properties of Moldic Pores using the Kozeny-Carman Equation. Research Ideas and Outcomes 4: e24430. https://doi.org/10.3897/rio.4.e24430
Figure 2 Figure showing the application of the pigeonhole fractal model to the pore spaces in the thin-section photomicrograph.
Figure 2 in Fractal analysis of structural differences of otolith microrelief in closely related and distant Baikal ichthyotaxa
Figure 2. Otoliths of T. baicalensis (a), L. leuciscus (b), L. kesslerii (c), and P. knerii (d): macroforms.
Fractal images of mountain entrepreneurship in the analyzed countries
<p><strong><span>Fractal images of mountain entrepreneurship in the analyzed countries</span></strong></p>
Seasonal frozen soil electrical resistance estimation based on capillary fractal model
<p>This project code is provided by the article "Seasonal frozen soil electrical resistance estimation based on capillary fractal model".</p> <p>The experimental sample data for this study is supplemented by supporting information. The validation of experimental samples demonstrated in this study, sen-sitivity calculations, field experiment applications, and visualization code are all completed using Matlab and are publicly available via the following link.</p> <ol> <li> <p><em>The validation of experimental samples</em>: [Sample_test1.m] to [Sample_test6.m] and the plot file [Sample_plot.m] The samples dataset: [perturecalculation.txt]</p> </li> <li> <p><em>Sensitivity calculations</em>: [sensitivitytest.m]</p> </li> <li> <p><em>Field experiment applications</em>: [model_application01m.m] and [model_application07m.m]</p> </li> </ol>
Figure 4 from: Musarella CM, Cano-Ortiz A, Pinar Fuentes JC, Navas-Urena J, Pinto Gomes CJ, Quinto-Canas R, Cano E, Spampinato G (2018) Similarity analysis between species of the genus Quercus L. (Fagaceae) in southern Italy based on the fractal dimension. PhytoKeys 113: 79-95. https://doi.org/10.3897/phytokeys.113.30330
Figure 4 Value of the medians for each homogeneous group. Fractal dimensions (mean values) of the studied species where Quercusilexsubsp.ilex and Quercussuber have an FD < 1.6 and the marcescent Quercus has a FD > 1.6.
Figure 2 from: Musarella CM, Cano-Ortiz A, Pinar Fuentes JC, Navas-Urena J, Pinto Gomes CJ, Quinto-Canas R, Cano E, Spampinato G (2018) Similarity analysis between species of the genus Quercus L. (Fagaceae) in southern Italy based on the fractal dimension. PhytoKeys 113: 79-95. https://doi.org/10.3897/phytokeys.113.30330
Figure 2 a RGB colour image b 8-bit greyscale image and c binary selection of an image of a Quercuscrenata leaf.
Data from: Breathing frequency bias in fractal analysis of heart rate variability
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Data from: Three-dimensional surface parameters and multi-fractal spectrum of corroded steel
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Data from: Improving the signal subtle feature extraction performance based on dual improved fractal box dimension eigenvectors
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Data from: Fractal geometry of a complex plumage trait reveals bird's quality
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Data from: Fractal measures of spatial pattern as a heuristic for return rate in vegetative systems
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Data from: General models for the spectra of surface area scaling strategies of cells and organisms: fractality, geometric dissimilitude, and internalization
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Biomimetic fractal topography enhances podocyte maturation in vitro
GEO Series GSE298416. Mus musculus. 17 samples. Type: Expression profiling by high throughput sequencing.
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Allen Brain Atlas
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ABODe is a University of Edinburgh DataShare dataset for behavior classification in group-housed mice using home-cage video, identities, bounding boxes, ground-plate positions, and annotator labels.
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