Fractal Analysis Method Research Articles

Fractal analysis of the medical insurance market: Theoretical and practical aspects

The latest experience obviously reflects that social-economic systems increasingly demonstrate an unforecastable behaviour. Financial markets are characterised by extremely guick change and crisis phenomena. Use of traditional modelling methods (in particular, the effective market hypothesis) provides no opportunity to obtain efficient forecasts about state and development of financial markets. One of promising methods in researching and modelling financial markets is the fractal analysis. Various natural and social phenomena posess fractality properties, namely there are similar structures on different scales. Generality of the fractal analysis methods allows their applying to study systems of any nature – from physical to economic and social ones. Fractality attributes of time series provide its dynamics pre-forecast and assess the time series predictability. The fractal analysis consists in establishing the extent of time series similarity to the fractal ones and defining a relation between the trend line and fractal dimension. The Hurst exponent assessment (persistence or anti-persistence of time series) predicts the further process development on the preliminary data basis. The fractal analysis efficiency during the unstable market periods is applicable for studying different social-economic systems (in particular, the Ukrainian medical insurance market). The research object is time series of gross insurance rewards on the Ukrainian medical insurance market. The research topic is the time series fractal analysis. The paper deals with peculiarities of the time series fractal analysis, the R/S analysis for time series of gross insurance rewards on the Ukrainian medical insurance market (via the MS Excel software). The Statistica 10.0.228.2 application generated the ARIMA model to predict dynamics of the gross insurance rewards on the Ukrainian medical insurance market. The obtained results may be used to conduct the R/S analysis of financial time series. In particular, that concerns those time series that describe the insurance market. Also, dynamics of the financial time series may be forecasted via these results as well.

Pencirian Isyarat Data Muzik yang Terhasil dari Alat Muzik Tradisional Menggunakan Ciri Fraktal

Musical instruments are usually distinguished by their sound produced through human perception which may lead to misinterpretation due to auditory perception bias and other disturbances. Therefore, recognition using music signals is carried out to help characterize signals from different musical instruments. Fractal analysis is a mathematical tool used to study complex and irregular patterns in various systems. In this study, fractal analysis was used to study and analyze musical notes signal data from different instruments. The fractal analysis method used is the box counting method. The traditional musical instruments involved in this study are the seruling, cak lempong, kompang, and gambus. Matlab software was used to analyze the musical data signal. First, the fractal dimension of the music data signal in the form of time domain is calculated. Then, the mean and standard deviation of the fractal dimension values were determined to recognize different musical instruments. Additionally, different image resolutions and box sizes are also used to calculate the fractal dimension of musical instrument from the time domain data. The error of best fit line, E will also be calculated to ensure the reliability of box counting dimensions using leastsquares regression method. The results show that the value of the fractal dimension for all 18 data is between 1.2636 to 1.7543. In terms of musical instrument recognition, the recognition of seruling and kompang using mean fractal dimension is successful. However, this method is less suitable for identification for cak lempong and gambus due to the high standard deviation. By using different image resolutions and box sizes, the accuracy of fractal dimension values will be affected. Increasing these parameters increases the accuracy of the results. The results of the study show that an image with a resolution of 1024 x 1024 pixels and a scaling factor of 9 is suitable to analyze the fractal characteristics of musical instrument data signals by using the box counting method.

Evaluating Street Character Using the 3D Fractal Analysis Method: Lefkoşa

The aim of this article is to reveal the mathematical dimension behind the complex structure of architectural fabric through a three-dimensional analysis. Given that the architectural character, which has evolved under the influence of various cultures over time, is crucial for urban integrity and sustainability, understanding the mathematical dimension underlying this character is of great importance for new designs and interventions in existing urban fabric. Therefore, streets in the Arabahmet neighbourhood of Lefkoşa Suriçi, which best represents the traditional fabric, were examined using a three-dimensional fractal analysis method. The analyses indicate that, in general, the fractal dimension values of the residential fabric-created streets are above 2.52, demonstrating a high level of character and complexity in these streets. Additionally, the fractal dimension values of these streets are close to each other, supporting the spatial and mass consistency of different streets within the same neighbourhood.

Fractal and geography: Fractal scanning in three different urban areas of Elazığ

The study of systems' ability to self-organize, internal structural balance, and space partitioning is the focus of a larger body of theories produced by mathematicians in the second half of the twenty-first century, which includes fractal theory and analysis. These theories focus on how the distribution of forms and urban functions within an urban agglomeration, the sequencing of the settlement system, the choice of a specific style of localization, or the evolution of urban sprawl is influenced by a region with inhomogeneous characteristics. The study's objective is to quantify how urban macro-forms reflect urban space. It is aimed to use fractal analysis, one of the methods that examine the structure of urban areas, as a measurement technique and to increase the recognition of this method in the community. When performing fractal analysis, the study area is generally evaluated holistically. Determining the place of the parts that make up this whole within the analysis is another aim of the study. The most basic method used in the study is the Fractal Analysis method. In order to make a relevant evaluation, Fractalyse 3.0 program was used. Two bases were created for the urban spots to be used in the program. While one of these bases is the parcels of Elazığ city center, the other one is buildings. In order to measure the parts of the whole mentioned as one of the aims of the study, three different regions of the city were identified and fractal analyzes were carried out separately for those regions. The study field covers all the central 42 neighborhoods where Elazığ city develops. According to the results obtained from the analysis, the Fractal dimension value of the city was 1.62. This value is a very interesting result as it is considered a transition criterion for cities to be fringed and compact. Accordingly, Elazığ city is a fringed city in the process of becoming compact. In the analysis of three different sections containing the parts that make up the whole, the fractal value of Doğukent neighborhood, located in the easternmost part of Elazığ city, was calculated as 1.70. This area, which has a compact structure, presents a positive response against the urban sprawl. The sample taken from the central part of the city, called the Center, showed a high value of 1.89 in fractal dimension. The fractal dimension value of the sample selected from the south of the city showed a high fringed result of 1.32.

Detection of lung pathology using the fractal method

<span lang="EN-US">Currently, the detection of pathology of lung cavities and their digitalization is one of the urgent problems of the healthcare industry in Kazakhstan. In this paper, the method of fractal analysis was considered to solve the task set. Diagnosis of lung pathology based on fractal analysis is an actively developing area of medical research. Conducted experiments on a set of clinical data confirm the effectiveness of the proposed methodology. The results obtained show that fractal analysis can be a useful tool for early detection of lung pathologies. It allows you to detect even minor changes in the structure and texture of lung tissues, which may not be obvious during visual analysis. The article deals with images of pathology of the pulmonary cavity, taken from an open data source. Based on the analysis of fractal objects, they were pre-assembled. Software algorithms for the operation of the information system for screening diagnostics have been developed. Based on the information contained in the fractal image of the lungs, mathematical models have been developed to create a diagnostic rule. A reference set of information features has been created that allows you to create algorithms for diagnosing the lungs: healthy and with pathologies of tuberculosis. </span>

Traffic injury as a medical and sanitary consequence of a man-made emergency in Ukraine. Report one: clinical and epidemiological characteristics

Background. Road traffic injuries remain one of the main causes of death in Ukraine even during the war. The Code of Civil Protection of Ukraine (Article 2, Clause 6) recognizes a traffic accident as a type of emergency. The purpose of the study: to form a comprehensive characterization of a traffic injury as a medical and sanitary consequence of a man-made emergency. Materials and methods. Typical territorial formations of Ukraine, namely cities with a population of more than 1,000,000 people, a typical regional center and rural areas, were included in the general research model. These components were chosen in compliance with the law of large numbers, regarding the requirements of typicality and the scope of the study. To meet these requirements, we selected a total of 1,696 victims of road traffic accidents who were included in the research array from the array of 21,000 victims using the random number method, while maintaining the component proportionality criterion. This study was conducted using the methods of epidemiological natural modeling, formal logic, fractal analysis, clinical standardization and medical statistics. Results. The specific weight of men injured in road accidents is 66.86 %, which is twice the number of women injured in road accidents. A significant effect of gender on the survival rate of victims was found: men survive in 88.71 %, and women in 91.99 % of cases. In the general array, majority of patients are persons of the most working age — 21–50 years old (63.33 %). In general, there is a tendency to decrease the specific weight of road accident victims starting from the age of 21, as the age factor increases. The highest rate of survival was recorded in the group of 21–30 years — 93.81 %, and the lowest — in people over 71 years of age — 75.27 %. Pedestrians have the largest specific weight in the total array, almost 40 %, and passengers have the lowest one — 24.65 %. In general, active road users make up 75.35 % of the total number. In the array of drivers who died, the specific weight of men is 90.32 %, and the fatality rate is 5.32 %. At the same time, the mortality rate for women is 3.95 %. The specific gravity of deceased male pedestrians is 70.64 %, while the fatality rate is 18.16 %, and among women this rate is 12.75 %. In all age groups, there is a different nature of the distribution of the negative outcome of traumatic process based on participation in the movement. At the same time, in all age groups, most victims who died are pedestrians. It was found that the age has a significant influence on the occurrence of a fatal outcome in traffic participants, with its greatest influence in victims older than 50 years. Conclusions. The clinical and epidemiological characteristics of victims of road accidents in Ukraine, as a medical and sanitary consequence of a man-made emergency, indicates that road traffic injuries are a significant medical and social problem in our country. This is due to the fact that they predominantly affect the most economically active segment of the population, which contributes significantly to the national product. The clinical and epidemiological characteristics of road traffic injuries in Ukraine have certain aspects, unlike other countries of the world, as a reflection of the peculiarities of life of population in our country. All clinical and epidemiological signs are risk-creating factors for the occurrence of a negative outcome of traumatic process due to the presence of a probable influence on this result and require verification of risks.

Quantifying Spatial Complexity of Settlement Plans Through Fractal Analysis

In this paper, I investigate the possibilities and limitations of fractal analysis methods applied to archaeological and synthetic settlement plans, with the goal of providing quantitative measures of spatial randomness or noise, as well as potential tools for automated culture-historical attribution of settlement plans and socio-economic intra-site differentiation. The archaeological sample is made from Linear Pottery settlements in south-west Slovakia and Trypillia settlements in the Southern Bug—Dnieper interfluve in central Ukraine, all based upon high-quality geomagnetic site plans. Synthetic plans are constructed as geometrically ideal versions of the archaeological ones, with varying degrees of added spatial noise. A significant correlation between fractal dimension and noise level is revealed for synthetic settlement plans, independently of size, density, house-size distribution and basic layout. However, several methodological challenges persist, and further systematic exploration on larger samples is needed before these results may be generalised. All analysis is performed in the R language and the script is made freely available in order to facilitate further development.

Examination of old-new building harmony in the historical environment with 3D fractal analysis method: Safranbolu example

Geleneksel dokular toplumların kültürlerinin somut yansımalarıdır. Toplumların-sürdürülebilirlik açısından- bu dokuları korumak, gelecek kuşaklara aktarmak ve onlardan çıkarımlar yapmak gibi sorumlulukları vardır. Ancak ilerleyen zamana karşın değişen yaşam koşulları ve artan ihtiyaçlar doğrultusunda yeni mekânlara ve binalara gereksinim duyulmaktadır. İki unsur arasındaki dengeyi kurabilmek için geleneksel dokuların çevresinde onlara uyumlu, sürdürülebilir yapıları planlamak, inşa etmek gereklidir. Bu amaç doğrultusunda geçmişten bugüne tabi ki nitel ve nicel çeşitli yöntemler ve kurallar geliştirilmiştir. Dolayısıyla uygulanan yöntem ve kuralların sonuçlarının nesnel değerlendirilmesine de her zaman ihtiyaç duyulmuştur. Buna karşılık olarak kullanılabilecek değerlendirme araçlarından birisi de doğadaki çeşitli dokuların analizinde kullanılan, mimari analizlerde de değerlendirilen ve somut çıkarımlar sunan fraktal boyut uygulamalarıdır. Bu çalışmada da bu yöntemle, tarihi çevre içinde ya da çevresinde uygulanan yapıların çevresiyle uyumluluklarının sınanması amaçlanmıştır. Bunun için, diğer çalışmalardan farklı olarak üç boyutlu fraktal yaklaşımla, kültürel miras kenti Safranbolu’da Babasultan Mahallesi’nde seçilen tescilli eski ve yeni inşa edilen binaların doku analizleri yapılarak ve birbirleriyle tutarlılıkları ölçülmüştür. Bu şekilde, hem bu tarihi çevredeki yeni yapı yaklaşımlarıyla ilgili bir durum tespiti hem de bu tekniğin sayısal çıktıları üzerinden eski ve yeni yapıların yorumlaması yapılmıştır. Analizlerde yeni yapılarda farklı yaklaşımlarla birlikte, özellikle biçimsel doku bakımından, bir dil birliğinin olduğu tespit edilmiştir.

Quantitative characterization of age-related atrophic changes in cerebral hemispheres: A novel “contour smoothing” fractal analysis method

BackgroundQuantitatively assessing age-related atrophic changes in cerebral hemispheres remains a crucial challenge, particularly in distinguishing between normal and pathological brain atrophy caused by neurodegenerative diseases. In this study, we introduced a new fractal analysis algorithm, referred to as the “contour smoothing” method, to quantitatively characterize age-related atrophic changes in cerebral hemispheres. Materials and methodsMRI scans from 100 healthy individuals (44 males, 56 females), aged 18–86 (mean age 41.72 ± 1.58), were analyzed. We used two fractal analysis methods: the novel “contour smoothing” method (with stages: 1–6, 1–5, 2–6, 1–4, 2–5) and the classical “box-counting” method to assess cerebral cortex pial surface contours. ResultsFractal dimensions obtained using the “box-counting” method showed weak or statistically insignificant correlations with age. Conversely, fractal dimensions derived from the “contour smoothing” method exhibited significant age-related correlations. The “contour smoothing” method with 1–4 stages proved more suitable for quantifying atrophic changes. The average fractal dimension for 1–4 coronal sections was 1.402 ± 0.005 (minimum 1.266, maximum 1.490), and for all five tomographic sections, it was 1.415 ± 0.004 (minimum 1.278, maximum 1.514). These fractal dimensions exhibited the strongest correlations with age: r = −0.709 (p < 0.001) and r = −0.669 (p < 0.001), respectively. ConclusionThe “contour smoothing” fractal analysis method introduced in this study can effectively examine cerebral hemispheres to detect and quantify age-related atrophic changes associated with normal or pathological aging. This method holds promise for clinical application in diagnosing neurodegenerative disorders, such as Alzheimer's disease.

Advancing dentistry: fractal assessment of bone health in pediatric patients with celiac disease using dental images.

To assess the effects of a gluten-free diet on bone structure in children with celiac disease using fractal analysis on panoramic radiographs. A total of 49 patients with celiac disease aged 6-13 years, separated into 2 groups as previously and newly diagnosed, and a control group of 32 healthy individuals were evaluated. In previously and newly diagnosed patients with celiac disease, body mass index (BMI) Z-scores were calculated, calcium, alkaline phosphatase, vitamin D3, and parathormone levels were measured and bone mineral density (BMD) Z-scores obtained from dual energy X-ray absorptiometry. In all patients, the fractal dimensions (FD) of the right and left temporomandibular condyles were evaluated with the fractal analysis method on panoramic radiographs. The mean values of serum biomarker levels and the BMI and BMD Z-scores for both celiac groups were within the normal reference range. No statistically significant difference was determined between right and left condyle FD values in the 3 groups examined. In terms of both right and left condyle FD values, there was a statistically significant difference between groups. The highest FD values were determined in the previously diagnosed group. Differences in FD values were observed among patients with celiac disease following the gluten-free diet. Utilizing fractal analysis on panoramic radiographs can prove valuable for dentists in evaluating BMD due to its cost-effectiveness, easy accessibility, and reduced radiation exposure for patients, enabling them to provide comprehensive oral health care and potential early interventions for patients with celiac disease.

Determination of dielectric performance and surface heteromorphology in single-walled carbon nanotube/vinylester polymer composites by fractal approaches

This study aims to establish a relationship between the dielectric characteristics and fractal parameters of single walled carbon nanotube reinforced vinylester based nanocomposites manufactured by sheet molding compound process. The complex dielectric permittivity was analyzed and interpreted using electric modulus formalism. The topography of both unfilled and single-walled carbon nanotube reinforced nanocomposites has been investigated using scanning electron microscopy (SEM) to provide correlation between experimental dielectric data and fractal theory. The self-similar microstructure was observed in micro photos for both materials. The superficial particle and cluster coverage ratio were calculated with the application of the scaling theory. Additionally, critical exponent and the fractal dimensions that determine the environment-area relationship have been determined by Slit Island Method (SIM) which is used to process 2-dimensional digital microscopic images. Fractal dimensions estimated with SIM were compared with the fractal dimensions computed obtained by box counting method for reliable results. It has been revealed that the surface of the composite consists of amorphous clusters with different sizes independent of each other and the structure is self-affine. In addition, the superficial area and cluster size have been shown to have a significant effect on the fractal dimension. As a result, the relationship between the dielectric permittivity of the material, determined by the electrical module formalism, and the morphological surface formation defined by the fractal analysis method and the SIM method, were determined and the results were compared with similar studies in the literature in this article.

Фрактальна параметризація щільності розподілу включень в структурі металу зварних швів

One of the modern proposed methods actively used for diagnosing metal structures is the method of fractal analysis. This method seeks to find the conjunction between the fractal dimension of individual components of the metal structure and its mechanical properties. The comprehensive use of microanalysis and fractal analysis allows not only for comparing structural characteristics but also for finding a numerical parameterization of the elements of this structure. The problem of advance the mechanical properties of welded joints in metal structures remains relevant due to the constant increase in high-strength low-alloy steels used in welded structures. As known, the mechanical properties of welded joints are determined by their structural components, including non-metallic inclusions. A purely qualitative assessment based on the DSTU 8966:2019 standard does not provide an opportunity for a thorough analysis of such an important characteristic as the distribution of inclusions by size and the character of their distribution in the metal matrix. Existing knowledge is based on the peculiarities of the influence of non-metallic inclusions on the mechanical properties of steel welded joints, which requires constant expansion and deepening cognitions, as this work aims to do. The method of fractal analysis allows considering non-metallic inclusions as voids in the metal matrix, which enables parameterization of the inclusion characteristics in the metal structure. The paper describes a methodology that takes into account the distance between inclusions as well as the size of inclusions, which differently affect the mechanical characteristics of the samples. In particular, this article is a continuation of the work [1], which describes an approach to finding relationships between fractal dimensions and mechanical properties. This work focuses on the impact of proposed inoculants on mechanical properties through the distribution of inclusions throughout the metal sample. Keywords: fractal, inclusion, microstructure, inoculants, distribution

New library of phase-change materials with their selection by the Rényi entropy method

The secret to the successful and widespread deployment of solar energy for thermal applications is effective and affordable heat storage. The ability to provide a high energy storage density and the capacity to store heat at a constant temperature corresponding to the phase transition temperature of the heat storage material (phase-change material or PCM) make latent heat storage one of the most alluring methods of heat storage. Today, it can be challenging to obtain all the published data on PCM qualities, including relevant non-thermodynamic properties in addition to thermodynamic ones. The developed new PCM library contains various types of PCMs which possess broad range of operation temperatures. This new library consists of 500 substances along with nine associated properties such as phase change temperature, solidification temperature, maximum operation temperature, density, latent heat and specific heat capacity, thermal conductivity, cycleability and ignition temperature. Furthermore, a new PCM selection method, based on calculating the Rényi entropy for a given set of selection criteria, has been proposed. The newly developed selection method requires no subjective judgements. The idea of the method is inspired by earlier applications of fractal analysis methods in many areas of research.

Investigation of Fractal Characteristics of Karman Vortex for NACA0009 Hydrofoil

A Karman vortex is a phenomenon of fluid flow that can cause fluctuation and vibration. As a result, it leads to fatigue damage to structures and induces safety accidents. Therefore, the analysis of the shedding law and strength of the Karman vortex is significant. To further understand the laws of turbulent Karman vortex shedding and strength, this study conducts a numerical vorticity simulation of a Karman vortex at the trailing edge of a hydrofoil based on the two-dimensional simplified model of the NACA0009 hydrofoil under different Reynolds numbers. Combined with image segmentation technology, the fractal characteristics of a turbulent Karman vortex at the trailing edge of a hydrofoil are extracted, the number and total area of vortex cores are calculated, and the fractal dimension of the vortex is obtained. The results show that the fractal dimension can characterize the change in vortex shape and strength under different Reynolds numbers, and that the fractal analysis method is feasible and effective for the shedding analysis of a turbulent Karman vortex.

Changes in the level of consolidation of the fatty acid profile of Hermetia illucens larvae grown on a substrate contaminated with heavy metals

We conducted a comparative investigation to examine the alterations in the composition and content of the fatty acid complex in the larvae of the Black Lion fly (Hermetia illucens) as they were reared under different concentrations and combinations of heavy metals. The use of the method of mass spectrometric analysis of the obtained biomass showed that linoleic, lauric and oleic fatty acids predominated in the composition of the larvae. The use of the mathematical method of fractal analysis based on the data on the profile distribution of fatty acid components in the insect body according to the experimental variants showed that samples with metal concentrations of 20 mg of cadmium, 800 mg of cobalt and Mix (200 mg of copper, 20 mg cadmium, 200 mg cobalt, 20 mg aluminium and 50 mg lead) per kilogram of dry food. The variation in the values of the indices of the biosystemic consolidation of acids, based on the conversion to their molar masses, ranged from 0.41 to 0.82.

An approach to detecting anomalies in a self-similar network traffic

Aim. The effects of cyber attacks cause failures of network elements, theft of information and other unlawful actions. Cyber attacks are often accompanied by untypical traffic activity and anomalies. The paper aims to develop an approach to detecting anomalies in network traffic by identifying the degree of self-similarity of the traffic using fractal analysis and statistical methods. Methods. The paper uses methods of mathematical statistics, mathematical analysis, fractal analysis. Results. The paper suggests an approach to identifying anomalies in network traffic by evaluating self-similarity and using statistical methods for improving the accuracy of cyber attack detection. At the first stage, the Hurst exponent is calculated for the reference traffic. At the second stage, actual traffic is divided into optimal time intervals; for each interval, the Hurst exponent is calculated. If the identified value of the Hurst exponent differs from the one obtained for the reference traffic, it is decided that there is an anomaly. At the final stage, statistical analysis is used in order to precisely localise the anomaly. The authors analysed fractal and statistical methods that resulted in the identification of more efficient methods to be used as part of the proposed approach. For fractal analysis, the DFA method was proposed, while for statistical analysis, the ARFIMA method was proposed. Conclusion. The suggested approach allows identifying cyber attacks in real time or near-real time.

Применение метода вариации Аллана при исследовании физико-химических процессов на поверхности твердого тела

The Allan variation method is being effectively used to study stability of frequency generators and noise characteristics of the dynamic processes of various physical nature presented in the form of time series. At the same time, the methods of nonlinear dynamics, in particular, of the fractal analysis, are used both in processing the time series and in studying irregularities in profiles or surfaces. By analogy with this, the possibility of introducing the Allan variance method to analyze alterations in the solid body surface during chemical and thermal treatment was evaluated. Introduction of the Allan variance method makes it possible to quantify the roughness components corresponding to the surface defects of a certain size. Alterations in the surface of grounded and polished quartz glass plates were studied, as well as the melted rods during chemical dissolution of the surface layer. The presented graphs and calculated Allan variations for the profiles of various surfaces clearly demonstrate that alterations in the surface relief standard deviation during chemical etching of the quartz plates and bars is associated with the surface defects size. The results of studying the surface stay in good agreement with the estimates made by the fractal analysis method. Introduction of the Allan variance method makes it possible to optimize both the mechanical and the chemical surface treatment mode of various parts during their manufacture

Determining the limits of traditional box-counting fractal analysis in leaf complexity studies

Fractal-based measures have widespread applications in the characterization of complex biological structures. Box-counting is one of the most widely used methods of fractal analysis. However, the utility of traditional box-counting fractal analysis in complexity studies is limited. We discuss the shortfalls of traditional fractal dimension (D) approaches in leaf complexity studies. Mature and healthy flat leaves of 61 plant species were collected from Trivandrum, Kerala, India. Digital images of these leaves were analyzed using the ImageJ software. No significant variations in D were seen in the results that could differentiate the leaf forms. We present the limitations and biases affecting accurate D analysis. Fractal properties of plant leaves are restricted over a limited scale, causing the failure of the linear regression-based D estimates. Arbitrary grid placement and miscounting the boxes of a specific size to cover the leaves are also subject to quantization errors. Since traditional fractal analysis depends on the bulk and boundary of the leaves, some D errors result from the potential bias of this area dependency. The traditional box-counting analysis also fails to capture the lacunarity observed in leaf images. Hence an accurate estimation of D is challenging using conventional methods. Considering the broad utility of fractal methods, plant researchers must be sensitized about the uncertainties in traditional box-counting approaches in complexity studies.

Fractal Analysis of Fuel Nozzle Surface Morphology Based on the 3D-Sandbox Method.

The dual oil circuit centrifugal fuel nozzle is made of martensitic stainless steel, which has complex morphological characteristics. The surface roughness characteristics of the fuel nozzle directly affect the degree of fuel atomization and the spray cone angle. The surface characterization of the fuel nozzle is investigated by the fractal analysis method. A sequence of images of an unheated treatment fuel nozzle and a heated treatment fuel nozzle are captured by the super-depth digital camera. The 3-D point cloud of the fuel nozzle is acquired by the shape from focus technique, and its three-dimensional (3-D) fractal dimensions are calculated and analyzed by the 3-D sandbox counting method. The proposed method can characterize the surface morphology well, including the standard metal processing surface and the fuel nozzle surface, and the experiments show that the 3-D surface fractal dimension is positively correlated with the surface roughness parameter. The 3-D surface fractal dimensions of the unheated treatment fuel nozzle were 2.6281, 2.8697, and 2.7620, compared with the heated treatment fuel nozzles dimensions of 2.3021, 2.5322, and 2.3327. Thus, the 3-D surface fractal dimension value of the unheated treatment is larger than that of the heated treatment and is sensitive to surface defects. This study indicates that the 3-D sandbox counting fractal dimension method is an effective method to evaluate the fuel nozzle surface and other metal processing surfaces.

Morphologic Mandibular Bone Changes on Panoramic Radiographs of Children and Adolescents with Congenital Heart Disease

Congenital heart disease (CHD) has effects on growth and development. However, information on how the structure of the mandibular bone is affected is limited. In the present study, we aim to compare mandibular bone structures of children affected with CHD and healthy ones through the fractal analysis method and radiomorphometric indices based on panoramic radiographs. The study consisted of 80 children (20 with cyanotic CHD, 20 with acyanotic CHD, 40 control) who were diagnosed with CHD and were treated through interventional therapy or followed up through medical therapy. Fractal dimension (FD) was performed in three different areas (angulus, corpus, and interdental bone) on 80 panoramic radiographs. Additionally, we assessed various radiomorphometric indices: mandibular cortical width (MCW), panoramic mandibular index (PMI), mandibular cortical index (MCI), and simple visual estimation (SVE). p < 0.05 was accepted as statistically significant in the analysis. Values of mean MCW, PMI, MCI, SVE, and FD measurements in children affected with CHD were found to be similar to the control group, regardless of whether they were cyanotic or acyanotic (p > 0.05). In this study, fractal analysis and radiomorphometric indices revealed no trabecular structure and mineral density changes in mandibular bone of children and adolescents with CHD compared to healthy subjects.