scholarly journals Heterogeneity in catchment properties: a case study of Grey and Buller catchments, New Zealand

2002 ◽  
Vol 6 (2) ◽  
pp. 167-184 ◽  
Author(s):  
U. Shankar ◽  
C. P. Pearson ◽  
V. I. Nikora ◽  
R. P. Ibbitt
Keyword(s):  
New Zealand ◽  
Fractal Dimensions ◽  
Affine Scaling ◽  
Stream Networks ◽  
Ecological Processes ◽  
Spectral Parameters ◽  
Scaling Behaviour ◽  
Multifractal Spectra ◽  
Box Counting Method ◽  
Landscape Patches

Abstract. The scaling behaviour of landscape properties, including both morphological and landscape patchiness, is examined using monofractal and multifractal analysis. The study is confined to two neighbouring meso-scale catchments on the west coast of the South Island of New Zealand. The catchments offer a diverse but largely undisturbed landscape with population and development impacts being extremely low. Bulk landscape properties of the catchments (and their sub-basins) are examined and show that scaling of stream networks follow Hack’s empirical rule, with exponents ∼0.6. It is also found that the longitudinal and transverse scaling exponents of stream networks equate to νl ≈0.6 and νw≈ 0.4, indicative of self-affine scaling. Catchment shapes also show self-affine behaviour. Further, scaling of landscape patches show multifractal behaviour and the analysis of these variables yields the characteristic parabolic curves known as multifractal spectra. A novel analytical approach is adopted by using catchments as hydrological cells at various sizes, ranging from first to sixth order, as the unit of measure. This approach is presented as an alternative to the box-counting method as it may be much more representative of hydro-ecological processes at catchment scales. Multifractal spectra are generated for each landscape property and spectral parameters such as the range in α (Holder exponent) values and maximum dimension at α0, (also known as the capacity dimension Dcap), are obtained. Other fractal dimensions (information Dinf and correlation Dcor) are also calculated and compared. The dimensions are connected by the inequality Dcap≥Dinf≥Dcor. Such a relationship strongly suggests that the landscape patches are heterogeneous in nature and that their scaling behaviour can be described as multifractal. The quantitative parameters obtained from the spectra may provide the basis for improved parameterisation of ecological and hydrological models. Keywords: fractal, multifractal, scaling, landscape, patchiness

scholarly journals Modeling of the emulsion stability using fractal dimensions

2008 ◽  
Vol 14 (3) ◽  
pp. 153-158 ◽  
Author(s):  
Snezana Pasalic ◽  
Predrag Jovanic
Keyword(s):  
Emulsion Stability ◽  
Fractal Dimensions ◽  
Ccd Camera ◽  
Stability Evaluation ◽  
Stable States ◽  
Water Emulsion ◽  
Box Counting Method ◽  
The Stability ◽  
The Moment ◽  
Life Circle

There are many developed strategies in the emulsion stability evaluation, for purpose of determining the life circle of emulsions. Most of them are based on the reological properties of the emulsions. There are very few which relay on the direct emulsion observations. In this paper we present the developed method for the emulsion stability evaluation by the direct observation of optical properties. As the stability quantification measure we propose the fractal dimension approach. The method is based on the measure of the emulsion transmittance properties, which are directly dependent on the emulsion stability at the moment of measurement. As the test emulsion the oil in the water emulsion was used. The system is classified as the stable emulsion and our intention was to find the moment when the emulsion starts to break. The emulsion transmittance properties were measured using an acquisition system, consisting of a CCD camera and a fast PC configuration equipped with the capturing software. The fractal dimensions were determined by the so called box counting method. The experimental emulsions were measured continuously within the period of 1200 h, from the moment of the emulsion creation. The changes of fractal dimensions were observed which indicates that the emulsion changed its state and therefore the stability during the time. Three regions of the emulsion life circle were divided according to the fractal dimensions measurement, which can be connected with the stable, unstable, and meta-stable states of the emulsion life circle. In the end, the model of the emulsion behavior was developed for the purpose of quantifying the changes in the experimental emulsion.

Mathematical Model Incorporated Fractal Geometry and Permeability of Compressed Peanut and Sesame for Oil Extraction

2012 ◽  
Vol 550-553 ◽  
pp. 676-681
Author(s):  
Xiao Zheng ◽  
Jing Zhou Wang ◽  
Guo Xiang Lin ◽  
Zhi Xian Sun ◽  
Don Ping He
Keyword(s):  
Mathematical Model ◽  
Fractal Dimension ◽  
Applied Pressure ◽  
Fractal Dimensions ◽  
Image Analyzer ◽  
Fractal Characteristic ◽  
Pore Size Distributions ◽  
The Difference ◽  
Sesame Cake ◽  
Box Counting Method

Considering the fractal characteristic of oilseed cake, the relationship between the permeability and the pore fractal dimension of peanut and sesame cake has been investigated. The microstructures of peanut and sesame cake under five applied pressures are measured by using stereo light microscope and Image-pro image analyzer. Using the box-counting method, the fractal dimensions of pore size distributions are measured. A mathematical model incorporated fractal dimension and permeability has been developed to predicate the permeability of compressed peanut and sesame under cold condition based upon combining Hagen-Poiseulle equation with Darcy’s law for flow of fluid through porous media. There is a prediction of permeability of peanut and sesame cake. Thus, a measurement is carried out for validation. The values of mean relative errors are 19.4% and 11.4 respectively. A fairly good agreement is obtained in the case of high applied pressure. And there exists a tendency that the value of the difference between the theoretical calculation and the permeability measurement decrease significantly with the increase of applied pressure.

scholarly journals Study on the Fractal Dimension and Growth Time of the Electrical Treeing Degradation at Different Temperature and Moisture

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Youping Fan ◽  
Dai Zhang ◽  
Jingjiao Li
Keyword(s):  
Fractal Dimension ◽  
Tree Growth ◽  
Fractal Dimensions ◽  
Moisture Level ◽  
Growth Time ◽  
Counting Method ◽  
Box Counting ◽  
Electrical Trees ◽  
Box Counting Method ◽  
Electrical Treeing

The paper aims to understand how the fractal dimension and growth time of electrical trees change with temperature and moisture. The fractal dimension of final electrical trees was estimated using 2-D box-counting method. Four groups of electrical trees were grown at variable moisture and temperature. The relation between growth time and fractal dimension of electrical trees were summarized. The results indicate the final electrical trees can have similar fractal dimensions via similar tree growth time at different combinations of moisture level and temperature conditions.

scholarly journals Postnatal Development of the Retina in Rats Exposed to Hyperoxia: A Fractal Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Anne Claudia Ştefănuţ ◽  
Ştefan Ţălu ◽  
Viorel Miclăuş ◽  
Adriana Mureşan ◽  
Remus Moldovan ◽  
...  
Keyword(s):  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Control Group ◽  
Newborn Rats ◽  
Vascular Abnormalities ◽  
Retinal Layers ◽  
Fractal Analyses ◽  
Group 10 ◽  
Box Counting Method ◽  
Experimental Group

Purpose. The aim of this study was to investigate and quantify changes in the newborn rats retinal layers during the hyperoxia (80% O2) exposure using fractal analysis. Materials and Methods. This study was conducted on two groups of 20 newborn rats: a control (normal) group (10 rats) and an experimental group (10 rats). The control group was composed of 10 newborn rats, which were placed at 12 hours after birth, in a pediatric incubator, together with their mother, in conditions of normoxia for 21 days. The experimental group consisted of 10 newborn rats, which were placed at 12 hours after birth, in a pediatric incubator with their mother, in conditions of normoxia for 7 days, then 7 days of hyperoxia (80% O2) for 22.5 hours/day, and then 7 days in conditions of normoxia. Slaughtering of the rats was performed on day 21 and the eye globes were harvested in order to perform histopathological examinations. The fractal analyses of the retinal digital images were performed using the fractal analysis software Image J, and the fractal dimensions were calculated using the standard box-counting method. Results. Microscopic examination revealed a normal development of the retina in the control group. In the experimental group, all the animals exposed to hyperoxia revealed both structural and vascular abnormalities on entire retina. Conclusions. The results showed that the fractal analysis is a valuable tool to quantify histoarchitectural changes in the newborn rats retinal layers during the hyperoxia (80% O2).

scholarly journals FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY

2011 ◽  
Vol 19 (1) ◽  
pp. 45 ◽  
Author(s):  
Ian Parkinson ◽  
Nick Fazzalari
Keyword(s):  
Fractal Dimension ◽  
Trabecular Bone ◽  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Box Counting ◽  
Cell Tissue ◽  
Image Analyser ◽  
Model Independent ◽  
Box Counting Method ◽  
Image Orientation

A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge). The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm) and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals), with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.

Abstract 17136: Pulmonary Arterial and Venous Fractal Dimension as a Marker of Pulmonary Arterial Hypertension

Circulation ◽  
2020 ◽  
Vol 142 (Suppl_3) ◽  
Author(s):  
Andrew Tsao ◽  
Pietro Nardelli ◽  
Eileen Harder ◽  
Gonzalo Vegas Sanchez-Ferrero ◽  
James C Ross ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Mean Pulmonary Arterial Pressure ◽  
Box Counting ◽  
Wilcoxon Rank Sum Test ◽  
History Of ◽  
Pulmonary Arterial ◽  
Box Counting Method ◽  
Definition Of ◽  
Vascular Trees

Introduction: PAH is characterized by a loss of pulmonary vascular complexity. In this study, total, arterial, and venous vasculatures of patients with PAH and with ePAH were analyzed using fractal analysis and compared against controls Methods: Data from 1514 consecutive right heart catheterizations from 4/27/2011 to 10/2/2018 representing subjects referred to our dyspnea center were searched for availability of imaging. 388 CT angiography (CTA) scans were identified (used given retrospective availability of thin slice reconstructions). Three initial cohorts (no overlap) were identified from individuals in this set. Control patients had normal resting and exercise hemodynamics and no history of cardiopulmonary disease. The second group met the current definition of PAH (resting mean pulmonary arterial pressure >20mmHg, pulmonary vascular resistance >3 Wood Units, pulmonary capillary wedge pressure <15mmHg). The third group (ePAH) had normal resting hemodynamics but age adjusted evidence of PAH with exercise. Pulmonary vascular trees were reconstructed; total, arterial, and venous trees were separated; and fractal dimensions were measured using a 3D box counting method for each tree. Comparisons were made using the Wilcoxon Rank Sum test (R 3.5). Results: Venous fractal dimensions of controls (2.10±0.07) were higher than those of PAH (2.03±0.08; p=3e-6) and of ePAH (2.04±0.13; p=0.008). Total fractal dimension also yielded higher values for controls (2.30±0.05) compared against PAH (2.28±0.07; p=0.009) and ePAH (2.26±0.10; p=0.04). No significant differences were found between arterial fractal dimensions of controls (2.17±0.04) against those of PAH (2.16±0.07; p=0.15) and of ePAH (2.15±0.10; p=0.14). Conclusions: Fractal dimension allows for non-invasive characterization of pulmonary vascular complexity. Using this method, patients with PAH or ePAH were found to have lower total and venous vascular complexities than controls without PAH or ePAH.

Multifractals Defined by Nonlinear Cellular Automata

1998 ◽  
Vol 08 (02) ◽  
pp. 259-280 ◽  
Author(s):  
Burton Voorhees
Keyword(s):  
Cellular Automata ◽  
Fractal Dimensions ◽  
Space Time ◽  
Equivalence Classes ◽  
Conserved Quantity ◽  
Substitution System ◽  
Multifractal Spectra

It is known that the space-time output patterns of additive cellular automata may be scaled to yield fractals. In this paper, nonadditive cellular automata rules are grouped into equivalence classes, each class defined in terms of a characteristic nonadditive rule. This rule defines a multifractal uniquely associated to each class. It is shown that these multifractals can be generated by a form of matrix substitution system, called concatenation substitution. This allows easy computation of fractal dimensions. It is likely that the multifractal spectra for each class does not possess the usual inverted U shape. A conserved quantity is found to be associated with the concatenation substitution system, and is shown to play a role similar to Langton's λ-parameter.

Image Reconstruction and Analysis of Three-Dimensional Fracture Surfaces Based on the Stereo Matching Method

2004 ◽  
Vol 261-263 ◽  
pp. 1593-1598
Author(s):  
M. Tanaka ◽  
Y. Kimura ◽  
A. Kayama ◽  
L. Chouanine ◽  
Reiko Kato ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Image Reconstruction ◽  
Fracture Surface ◽  
Fractal Analysis ◽  
Stereo Matching ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Matching Method ◽  
Fracture Surfaces ◽  
Box Counting Method

A computer program of the fractal analysis by the box-counting method was developed for the estimation of the fractal dimension of the three-dimensional fracture surface reconstructed by the stereo matching method. The image reconstruction and fractal analysis were then made on the fracture surfaces of materials created by different mechanisms. There was a correlation between the fractal dimension of the three-dimensional fracture surface and the fractal dimensions evaluated by other methods on ceramics and metals. The effects of microstructures on the fractal dimension were also experimentally discussed.

FRACTAL ANALYSIS OF DENDRITIC ARBORISATION PATTERNS OF STALKED AND ISLET NEURONS IN SUBSTANTIA GELATINOSA OF DIFFERENT SPECIES

Fractals ◽  
2007 ◽  
Vol 15 (01) ◽  
pp. 1-7 ◽  
Author(s):  
NEBOJŠA T. MILOŠEVIĆ ◽  
DUŠAN RISTANOVIĆ ◽  
JOVAN B. STANKOVIĆ ◽  
RADMILA GUDOVIĆ
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Islet Cells ◽  
Fractal Dimensions ◽  
Substantia Gelatinosa ◽  
Neuronal Populations ◽  
Box Counting ◽  
Morphological Descriptor ◽  
The Mean ◽  
Box Counting Method

Through analysis of the morphology of dendritic arborisation of neurons from the substantia gelatinosa of dorsal horns from four different species, we have established that two types of cells (stalked and islet) are always present. The aim of the study was to perform the intra- and/or inter-species comparison of these two neuronal populations by fractal analysis, as well as to clarify the importance of the fractal dimension as an objective and usable morphological parameter. Fractal analysis was carried out adopting the box-counting method. We have shown that the mean fractal dimensions for the stalked cells are significantly different between species. The same is true for the mean fractal dimensions of the islet cells. Still, no significant differences were found for the fractal dimensions of the stalked and islet cells within a particular species. The human species has shown as the only exception where fractal dimensions of these two types of cells differ significantly. This study shows once more that the fractal dimension is a useful and sensitive morphological descriptor of neuronal structures and differences between them.

The Comparison of Fractal Dimensions of Cracks on Reinforced Concrete Beam

2011 ◽  
Vol 291-294 ◽  
pp. 1126-1130 ◽  
Author(s):  
Hong Quan Sun ◽  
Jun Ding
Keyword(s):  
Fractal Dimension ◽  
Reinforced Concrete ◽  
Concrete Beam ◽  
Research Result ◽  
Fractal Dimensions ◽  
Reinforce Concrete ◽  
Reinforced Concrete Beam ◽  
Linear Relationships ◽  
Practical Engineering ◽  
Box Counting Method

In the paper, fractal geometry is used to study the crack evolving process of reinforce concrete beams. The fractal dimensions on surface of the reinforced concrete beam and the mechanical properties of the beam have the linear relationships perfectly. In order to compare the accuracy of the fractal dimensions, box counting method and the digital image box method in practical engineering are used to calculate the fractal dimension separately. The advantages and the disadvantages of these methods are analyzed. And the calculating conditions of these two methods are obtained. The research result gives a better way for determining the fractal dimension of the cracks on the reinforced concrete beam.

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