Fractal Dimension Analysis Research Articles

Fractal dimension, lacunarity, and bone area fraction analysis of peri-implant trabecular bone after prosthodontic loading.

To assess the structural alterations in peri-implant bone occurring 5years after prosthodontic loading in panoramic radiography (PR). PR images of 44 mandibular and 33 maxillary implants along with 42 healthy control teeth taken before and 5years after prosthodontic loading were included. Two regions-of-interest (ROI) were selected from mesial and distal surrounding bone of each implant and tooth. Then, the selected ROIs were divided to obtain three sub-ROIs (coronal, middle, and apical) on each side. A total of eight ROIs and sub-ROIs from each implant and control tooth were used for the calculations of fractal dimension (FD), lacunarity, and bone area fraction (BA/TA). The paired-sample t test was used to compare measurements before and 5years after loading (p = 0.05). Overall evaluation of 77 implants showed that FD decreased at the middle and apical peri-implant bone levels 5years after loading (p < 0.05). In mandibular implants, BA/TA decreased after loading (p < 0.05). While FD decreased at the coronal level (p = 0.022), lacunarity increased at the middle level of mandibular implants (p < 0.05). In maxillary implants, FD decreased at the middle and BA/TA decreased at the coronal level (p < 0.05). On the other hand, BA/TA increased at the apical level of maxillary implants (p = 0.016) after loading. None of the parameters revealed any difference in the control group (p > 0.05). FD and BA/TA can be used to analyze structural changes in peri-implant bone after prosthodontic loading. Additionally, FD, lacunarity and BA/TA may provide useful information about changes occurring at different levels of peri-implant bone.

Research on Spatial Morphological Characteristics and Influencing Factors of Industrial Heritage: A Case Study of Nine Industrial Heritages in Guizhou Province

Industrial heritage, recognized as a significant aspect of historical and cultural heritage, has garnered considerable attention from scholars globally. To elucidate the spatial morphological characteristics and the underlying influencing factors of industrial heritage within karst regions, this study employs methods such as the interstice index, fractal dimension analysis, and spatial syntax. It conducts research on the spatial morphological characteristics of nine typical industrial heritages in Guizhou Province. The primary factors contributing to the variations in layout forms are the intricate karst topography and the functional requirements of production. The functional zoning of industrial heritage aligns with its layout, characterized by straightforward functional zones that have not developed into composite spaces. The overall connectivity of industrial heritage is relatively low, exhibiting weak integration, significant disparities in control values, low average depth values, and a deficiency in comprehensibility and diversity of options. This indicates that the internal connectivity of industrial heritage spaces is generally inadequate, with low accessibility, strong interrelations, average convenience, limited connectivity, and generally acceptable passage. The overall spatial, architectural, and roadway configurations of industrial heritage predominantly exhibit a uniform pattern. Importantly, industrial heritage reveals a highly variable overall spatial form, with an average fractal dimension of 1.57, complex architectural layouts (average fractal dimension of 1.50), and simplistic road network designs (average fractal dimension of 1.43), which collectively suggest high spatial complexity and irregular characteristics. This study can provide a reference for the analysis of spatial characteristics and influencing factors of other material cultural heritages, and it is of great significance for the systematic protection and revitalization of industrial heritage.

Curve smoothening for the analysis of fractal dimensions of blast-cleaned steel surface textures for tribological and adhesion interfaces

Abstract Fractal dimensions are increasingly used for the characterization of surface textures for tribological and adhesion applications. The resolution of 2D profiles acquired from various measurement methods can be adjusted via curve smoothing. It is still unclear whether curve smoothing would notably affect the estimated fractal dimensions. In this communication, 2D profiles of twelve blast-cleaned surface settings were derived by means of a data manipulation software, including a curve smoothing procedure. The fractal dimensions were estimated, and Design of Experiments was applied to analyze the relationships. Factors included abrasive type, preparation grade, roughness, and curve smoothing. Analysis of Variance indicated that the contribution of curve smoothing to the regression model was as low as 1.0%. Therefore, for blast-cleaned substrates, curve smoothing effects can be neglected with respect to the contributions of roughness and abrasive type, when estimating the fractal dimensions.

Genetic and phenotypic architecture of biventricular trabeculation

Abstract Introduction Cardiac trabeculae form a network of muscular strands that line the inner surfaces of the heart, and their development involves molecular pathways that regulate structural complexity. Excessive or hypertrabeculation occurs as part of normal variation in apparently healthy individuals, as an adaptation to altered loading conditions, and is observed in patients with cardiomyopathies (CMs) and heart failure (HF). Purpose In adults, trabeculation is not a prognostic factor independent of the underlying myocardial disease but may play a role in the natural history of ventricular remodelling. We sought to (i) understand the genetic and non-genetic determinants of trabeculation, (ii) understand its role in the causality of disease, and (iii) evaluate trabeculation as a biomarker for diagnosis and stratification. Methods We report genes with a burden of rare variants and novel common variant associations across the allele frequency spectrum for biventricular trabecular morphology in 47,803 participants of the UK Biobank using fractal dimension analysis of cardiac imaging (Figure 1). We assessed environmental modifiers of trabecular morphology, correlation with cardiac traits, phenome-wide association studies, and the relationship with the progression of CMs and HF. Results We identified a burden of trabeculation-associated rare variants in genes that regulate myocardial contractility and cardiac development and GWAS identified novel loci near genes implicated in CMs, conduction traits, and signalling pathways that define the early development of trabeculation. For example, we identified 56 genes with a burden of rare variants and 68 novel loci from GWAS (e.g., CASQ2, CACNA1C, MYBPC3, MYH7, NKX2-5, NOTCH1, TBX20) for the left ventricle. The strongest imaging relationships with trabeculation were with measures of volume and strain. Modifiers of trabeculation included African ancestry, alcohol intake, and physical activity. Carriers of CM-associated pathogenic variants had increased trabeculation. Of participants with CM reported after imaging, 25% had hypertrabeculation on imaging and hypertrabeculation was a risk factor for a subsequent diagnosis of HF (HR=1.3), mitral valve disorders (HR=1.4), bundle branch block (HR=1.2). Comparisons of biventricular trabeculation showed similarities in trabeculation across the ventricles in CM. Reduced right ventricular trabeculation and end-diastolic volume associated with Type-2 diabetes. Conclusions These data provide new insights into the mechanisms that regulate structural complexity in the heart. Changes in trabeculation may occur early in the pathogenesis of heart disease, can be modified by genes regulating pathways outside the sarcomere, and causality depends on the underlying cardiomyopathic substrate. Trabeculation progresses with cardiovascular disease, is a useful marker of remodelling, and identifies novel genetic modifiers of ventricular complexity.Figure 1

Electromagnetic wave-driven deep learning for structural evaluation of reinforced concrete strength

Monitoring the performance of reinforced concrete structures, particularly in terms of strength reduction, presents significant challenges due to the practical limitations of traditional detection methods. This study introduces an innovative framework that incorporates a non-destructive technique using electromagnetic waves (EM-waves) transmitted via Radio Frequency Identification (RFID) technology, combined with two-dimensional (2-D) Fourier transform, fractal dimension analysis, and deep learning techniques to predict reductions in structural strength. Experiments were conducted on three reinforced concrete beam (RCB) specimens exhibiting various levels of reinforcement corrosion. From these, a dataset of 1,800 EMwave images was generated and classified into “normal” and “reduced strength” categories. These categories were used to train and validate a Convolutional Neural Network (CNN), which demonstrated robust performance, achieving a high accuracy of 0.91 and an F1-score of 0.93 in classifying instances of reduced structural strength. This approach offers a promising solution for detecting strength reduction in reinforced concrete infrastructures, enhancing both safety and maintenance efficiency.

Fractal Dimension Analysis of the Tumor Microenvironment in Cutaneous Squamous Cell Carcinoma: Insights into Angiogenesis and Immune Cell Infiltration

The global incidence of cutaneous squamous cell carcinoma (cSCC), a prevalent and aggressive skin cancer, has risen significantly, posing a substantial public health challenge. This study investigates the tumor microenvironment (TME) of cSCC by focusing on the spatial distribution patterns of immune and vascular markers (CD31, CD20, CD4, and CD8) using fractal dimension (FD) analysis. Our analysis encompassed 141 cases, including 100 invasive cSCCs and 41 specimens with pre-invasive lesions exclusively, and the rest were peripheral pre-invasive lesions from the invasive cSCC class. The FD values for each marker were computed and compared between pre-invasive and invasive lesion classes. The results revealed significant differences in FD values between the two classes for CD20 and CD31 markers, suggesting distinct alterations in B cell distribution and angiogenic activity during cSCC progression. However, CD4 and CD8 markers did not exhibit significant changes individually. Still, the CD4/CD8 ratio showed a significant difference, suggesting a potential shift in the balance between T helper and cytotoxic T cell responses, impacting the immune landscape as lesions progressed from pre-invasive to invasive stages. These findings underscore the complexity and heterogeneity of the TME in cSCC and highlight the potential of FD analysis as a quantitative tool for characterizing tumor progression. Further research is needed to elucidate the implications of these differences in the clinical management of cSCC.

The relationship between radiomorphometric indices and fractal dimension analysis: a cone-beam computed tomography study.

The purpose of this study is to evaluate the relationship between radiomorphometric indices and fractal dimension (FD) analysis in jawbone radiographic density using Cone-Beam Computed Tomography (CBCT). The study included 87 CBCT datasets from dental patients aged 50-79. Four radiomorphometric indices (Computed Tomography Cortical Index (CTCI), Computed Tomography Mental Index (CTMI), Computed Tomography Index-Superior (CTI-S), and Computed Tomography Index-Inferior (CTI-I)) along with age, gender, remaining teeth, and mandibular bone height were evaluated. FD was assessed in trabecular bone near the mental foramen (ROI 1) and on the mandibular cortical bone (ROI 2). Relationships between indices and variables were analyzed using Pearson chi-square, Fisher's exact, one-way ANOVA, Kruskal-Wallis, and Spearman's rho tests. ANOVA showed significant differences in mandibular bone height (p = .004) and FD at ROI 2 (p = .000) across three mandibular cortex types (C1, C2, C3). Spearman's rho indicated significant correlations between FD at ROI 2 and CTMI, CTI-S, CTI-I (p = .000), and between mandibular bone height and CTMI (p = .010). The correlations of FD at ROI 2 ranged from strongest to weakest with CTCI, CTMI, CTI-S, and CTI-I. High-risk osteoporosis radiomorphometric indices are associated with FD analysis of cortical bone.

Exploring cortical morphology biomarkers of amnesic mild cognitive impairment using novel fractal dimension-based structural MRI analysis.

Amnestic mild cognitive impairment (aMCI) is considered as an intermediate stage of Alzheimer's disease, but no MRI biomarkers currently distinguish aMCI from healthy individuals effectively. Fractal dimension, a quantitative parameter, provides superior morphological information compared to conventional cortical thickness methods. Few studies have used cortical fractal dimension values to differentiate aMCI from healthy controls. In this study, we aim to build an automated discriminator for accurately distinguishing aMCI using fractal dimension measures of the cerebral cortex. Thirty aMCI patients and 30 health controls underwent structural MRI of the brain. First, the atrophy of participants' cortical sub-regions of Desikan-Killiany cortical atlas was assessed using fractal dimension and cortical thickness. The fractal dimension is more sensitive than cortical thickness in reducing dimensional effects and may accurately reflect morphological changes of the cortex in aMCI. The aMCI group had significantly lower fractal dimension values in the bilateral temporal lobes, right limbic lobe and right parietal lobe, whereas they showed significantly lower cortical thickness values only in the bilateral temporal lobes. Fractal dimension analysis was able to depict most of the significantly different focal regions detected by cortical thickness, but additionally with more regions. Second, applying the measured fractal dimensions (and cortical thickness) of both cerebral hemispheres, an unsupervised discriminator was built for the aMCI and healthy controls. The proposed fractal dimension-based method achieves 80.54% accuracy in discriminating aMCI from healthy controls. The fractal dimension appears to be a promising biomarker for cortical morphology changes that can discriminate patients with aMCI from healthy controls.

Fractal Dimension analysis at implant site on CBCT

Fractal Dimension analysis at implant site on CBCT

Resting-state EEG spectral and fractal features in dementia with Lewy bodies with and without visual hallucinations

ObjectiveComplex visual hallucinations (VH) are a core feature of dementia with Lewy bodies (DLB), though they may not occur in all patients. Power spectral density (PSD) analysis of resting-state EEG (rs-EEG) shows associations between some frequency bands (e.g., θ), individual alpha frequency (IAF) and VH. However, new tools that improve early differential diagnosis and symptom-based stratification with higher sensitivity and specificity, even within the DLB population, are desirable. We aimed to assess differences in rs-EEG data between DLB patients with VH (DLB-VH+) and without VH (DLB-VH-), comparing innovative non-linear approaches with more traditional linear ones. MethodsWe retrospectively analyzed rs-EEG recordings of DLB-VH+, DLB-VH-, Alzheimer’s disease patients and age-matched healthy controls. EEG was analyzed using the nonlinear Higuchi’s Fractal Dimension (FD) measure, and the results were compared with those of entropy and standard linear methods based on PSD and IAF. ResultsOnly the FD measure could discriminate between DLB-VH+ and DLB-VH-. ConclusionsIn conclusion, rs-EEG differences between DLB-VH+ and DLB-VH- are better characterized by FD analysis than by a more traditional power spectrum approach. SignificanceThis suggests that the presence of complex VH is associated with less complex brain dynamics at rest, as reflected by the FD measure.

Fractal dimension analysis of lightning discharges of various types based on a comprehensive literature review

In this study, photographic records of natural lightning flashes obtained from high-speed video camera observations are analyzed based on an extensive literature review. The purpose of this work is to estimate the fractal dimension of lightning discharges and to analyze and evaluate the effect of lightning type (downward and upward flashes during their propagation as well as return strokes) and lightning polarity (negative and positive). Three methods of fractal dimension estimation are employed namely the: (i) box-counting, (ii) sandbox, and (iii) correlation method, utilizing algorithms developed in MATLAB software. Appropriate image processing techniques are employed to guarantee precision in fractal dimension estimation. A thorough discussion is conducted by comparing the estimated fractal dimension values with those previously documented in the relevant literature based on field observations. The mean fractal dimension of downward negative leaders for the three methods (1.18, 1.31, 1.38) aligns well with previous studies, while positive downward leaders exhibit lower values (1.08, 1.15, 1.26), denoting a reduced branching behavior; upward leaders demonstrate slightly higher fractal dimensions than downward ones. Additionally, an attempt to correlate the lightning return stroke peak current with the fractal dimension is made. The outcomes of this research may assist in facilitating precise modeling of the lightning attachment phenomenon, thereby contributing to the development of safer lightning protection systems.

FRACTAL DIMENSION OF STAR CLUSTERS

Quantitative analysis of the structure of star clusters is crucial for understanding their formation and evolution. In this article, we explore the application of fractal dimension analysis to study the evolution of star clusters, also fractal dimension, a concept from fractal geometry, provides a quantitative measure of the complexity and self-similarity of geometric objects. By considering star clusters as complex networks, we employ the box covering method to calculate their fractal dimension. Our methodology combines the well-established Minimum Spanning Tree (MST) and Box-Covering (BC) methods and using these methods, the fractal structure of the clusters was determined. It was revealed that star clusters disintegrate at a fractal dimension of 1.3 and obey a power law. It should be noted that the obtained result was compared with the results of the McLuster.

Fractal Dimension and Lacunarity Analysis in the Dentulous and Edentulous Mandibular Posterior Region Using Cone-beam Computed Tomography: A Cross-sectional Retrospective Study.

This cross-sectional retrospective study was conducted to assess the differences in the microarchitecture of the trabecular bone of the posterior mandibular region at dentulous and edentulous sites with the help of fractal dimension (FD) and lacunarity using cone-beam computed tomography (CBCT). Ninety CBCT scans were analyzed for the purpose of the present study. Inclusion criteria included subjects with unilaterally missing mandibular molars or premolars and an with intact contralateral opposing tooth. The coronal view of the dentulous and edentulous sites was used, and the region of interest (ROI) was selected 2.6 mm below the apex of the tooth present. These images were then transferred to ImageJ Software, and fractal analysis was done using the box-counting method of the FracLac plug-in. A paired samples t-test was performed to compare the means of FD and lacunarity, and a Kendall correlation was performed to check correlations. A p-value less than 0.05 was considered to indicate statistical significance. Statistical analysis revealed that the mean FD of the edentulous side was significantly greater than that of the dentulous side (p-value = 0.011). Additionally, the mean lacunarity of the edentulous side was marginally significantly greater than that of the dentulous side (p-value = 0.089). A significant negative correlation was detected between the FD and lacunarity of the edentulous region (p-value = 0.017), and a marginally significant negative correlation was detected between edentulous lacunarity and dentulous lacunarity (p-value = 0.081). The differences in occlusal forces exerted in dentulous and edentulous regions can lead to a change in the trabecular pattern of the bone in these regions. This change in the microarchitecture of bones can be detected by FD and lacunarity, which can further help us assess changes pre- and post-implant. The advanced technology, the assessment of microarchitecture of the bone has been made easy, using FD and lacunarity, as done in the present study. This analysis can further aid us in both pre- and post-implant analysis to prevent failure of the implant. How to cite this article: Bhoraskar M, Denny C, Srikant N, et al. Fractal Dimension and Lacunarity Analysis in the Dentulous and Edentulous Mandibular Posterior Region Using Cone-beam Computed Tomography: A Cross-sectional Retrospective Study. J Contemp Dent Pract 2024;25(6):581-587.

Mechanisms of Proppant Transport in Rough Fractures of Offshore Unconventional Reservoirs: Shale and Tight Sandstone

After hydraulic fracturing, unconventional reservoirs frequently encounter challenges related to limited effective proppant support distance and suboptimal proppant placement. Due to the strong heterogeneity of offshore reservoirs, which causes varying fracture roughnesses depending on different lithologies, a systematic study of the relationship between roughness and proppant transport could optimize operational parameters. This study incorporates the box dimension method for fractal dimension analysis to quantify roughness in auto-correlated Gaussian distributed surfaces created by true triaxial tests. Combined with the numerical analysis of (computational fluid dynamics) CFD-DEM (discrete element method) for bidirectional coupling, the laws of proppant deposition and transport processes within fractures with different roughnesses are obtained through comparative verification simulations. The results show that for rougher fractures of shale, the proppants are transported farther, but at JRC_52, (joint roughness coefficient), where there may be plugging in curved areas, there is a risk of near-well blockages. Compared to the smooth model, fluctuations in JRC_28 (tight sandstone) drastically increase turbulent kinetic energy within the fracture, altering particle transport dynamics. Moreover, smaller proppants (d/w ≤ 0.3) exhibit better transport capacity due to gravity, but the conductivity of the proppant is limited when the particles are too small. A d/w of 0.4 is recommended to guarantee transport capacity and proppant efficiency near the well. Additionally, proppants injected sequentially from small to large in shale fractures offer optimal propping effects, and can take advantage of the better transport capacity of smaller proppants in rough fractures. The large proppant (d/w = 0.8) is primarily deposited by gravity and forms a sloping sand bed, which subsequently ensures the aperture of the fractures. This research provides a fresh perspective on the influence of fracture roughness on proppant transport in offshore unconventional reservoirs and offers valuable considerations for the order of proppant injection.

Exploring swine oviduct anatomy through micro-computed tomography: a 3D modeling perspective.

The oviduct plays a crucial role in the reproductive process, serving as the stage for fertilization and the early stages of embryonic development. When the environment of this organ has been mimicked, it has been shown to enhance in vitro embryo epigenetic reprogramming and to improve the yield of the system. This study explores the anatomical intricacies of two oviduct regions, the uterotubal junction (UTJ) and the ampullary-isthmic junction (AIJ) by using micro-computed tomography (MicroCT). In this study, we have characterized and 3D-reconstructed the oviduct structure, by measuring height and width of the oviduct's folds, along with the assessments of fractal dimension, lacunarity and shape factor. Results indicate distinct structural features in UTJ and AIJ, with UTJ displaying small, uniformly distributed folds and high lacunarity, while AIJ shows larger folds with lower lacunarity. Fractal dimension analysis reveals values for UTJ within 1.189-1.1779, while AIJ values range from 1.559-1.770, indicating differences in structural complexity between these regions. Additionally, blind sacs or crypts are observed, akin to those found in various species, suggesting potential roles in sperm sequestration or reservoir formation. These morphological differences align with functional variations and are essential for developing an accurate 3D model. In conclusion, this research provides information about the oviduct anatomy, leveraging MicroCT technology for detailed 3D reconstructions, which can significantly contribute to the understanding of geometric-morphological characteristics influencing functional traits, providing a foundation for a biomimetic oviduct-on-a-chip.

Prediction of Failure Due to Fatigue of Wire Arc Additive Manufacturing-Manufactured Product

Currently, the focus of production is shifting towards the use of innovative manufacturing techniques and away from traditional methods. Additive manufacturing technologies hold great promise for creating industrial products. The industry aims to enhance the reliability of individual components and structural elements, as well as the ability to accurately anticipate component failure, particularly due to fatigue. This paper explores the possibility of predicting component failure in parts produced using the WAAM (wire arc additive manufacturing) method by employing fractal dimension analysis. Additionally, the impact of manufacturing imperfections and various heat treatment processes on the fatigue resistance of 30CrMnSi steel has been investigated. Fatigue testing of samples and actual components fabricated via the WAAM process was conducted in this study. The destruction of the examined specimens and products was predicted by evaluating the fractal dimensions of micrographs acquired at different stages of fatigue testing. It has been established that technological defects are more dangerous in terms of fatigue failure than microstructural ones. The correctly selected mode of heat treatment for metal after electric arc welding allows for a more homogeneous microstructure with a near-complete absence of microstructural defects. A comparison of the fractal dimension method with other damage assessment methods shows that it has high accuracy in predicting part failure and is less labor-intensive than other methods.

Fractal dimension and its implication to mineral exploration: a case study from the Jonnagiri and Gadag gold deposits in India

Fractal dimensions characterize the spatial distribution pattern of mineral deposits, allowing the mineralization processes beneath and at the surface to be understood. This study considered a mineralized vein along the fracture/shear zone near the Dona Temple in the Jonnagiri gold deposit and borehole data from the Sangli Block in the Gadag gold deposit. The above-mentioned zones were considered using fractal dimensional analysis to constrain the fluid-flow pathways. The box-counting technique was used to measure the fractal dimension of the mineralized vein along the surface from a detailed to a regional scale. The fractal correlation integral method was used to provide the fractal dimension values from the gold assay (in g t −1 ). The box-counting fractal dimension values obtained varied from 1.07 to 1.36, whilst the fractal dimensions obtained from the fractal correlation integral method ranged from 0.03 to 1.97. Higher fractal values signify a fully matured interlinked fracture/fault network with steep fluid-flow pathways, while lower values indicate the converse condition. Further, the study showed that the fractal analysis of the mineralized vein along the fracture/shear zone appeared to correlate with the fault system rather than with the litho-contact. Economic gold deposition occurs mainly along a structure with a steep fractal gradient, which is the target area for economic gold exploration.

Efficacy of the CALM® Algorithm in Reducing Motion-Induced Artifacts in CBCT Imaging: A Fractal Dimension Analysis of Trabecular Bone.

The primary goal of this investigation was to ascertain the efficacy of the CALM® motion artifact reduction algorithm in diminishing motion-induced blurriness in Cone Beam Computed Tomography [CBCT] images. The assessment was conducted through Fractal Dimension [FD] analysis of the trabecular bone. A desiccated human mandible was subjected to Planmeca ProMax 3D® scanning under eight distinct protocols, marked by variations in motion presence [at 5, 10, and 15 degrees] and the deployment of CALM®. In every scan, five distinct regions of interest [ROIs] were designated for FD analysis, meticulously avoiding tooth roots or cortical bone. The FD was computed employing the box-counting method with Image-J 1.53 software. Our findings reveal that a 5-degree motion does not significantly disrupt FD analysis, while a 10-degree motion and beyond exhibit statistical differences and volatility among the sites and groups. A decreased FD value, signifying a less intricate or "rough" bone structure, correlated with amplified motion blurriness. The utilization of CALM® software seemed to counteract this effect in some instances, reconciling FD values to those akin to the control groups. Nonetheless, CALM®'s efficacy differed across sites and motion degrees. Interestingly, at one site, CALM® application in the absence of motion resulted in FD values considerably higher than all other groups. The study indicates that motion, particularly at 10 degrees or more, can considerably impact the FD analysis of trabecular bone in CBCT images. In some situations, the CALM® motion artifact reduction algorithm can alleviate this impact, though its effectiveness fluctuates depending on the site and degree of motion. This underscores the necessity of factoring in motion and the employment of artifact reduction algorithms during the interpretation of FD analysis outcomes in CBCT imaging. More research is necessary to refine the application of such algorithms and to comprehend their influence on different sites under varying motion degrees.

Fractal dimensional analysis to reveal traffic flow dynamics as organic metabolism

As urban areas face rapid population and vehicle growth, understanding system dynamics is crucial for managing transportation congestion effectively. Utilizing fractal and metabolic concepts offers fresh perspectives on the behavior and efficiency of complex urban transportation systems. To understand the dynamics of congested traffic flows, we conducted fractal analysis on the traffic pattern in Seoul city with chronic congestion worldwide and investigated its potential for evaluating metabolic efficiency. Our rank and size fractal analysis revealed that Seoul's fractal dimension ranges from 6.7060 to 7.6801. The fractal dimension's curve, when plotted against traffic congestion, shows a peculiar symmetrical relationship. The linear correlation between fractal dimension and metabolic indicators suggests that fractal dimension could potentially serve as a novel metric for evaluating traffic flow efficiency. This study introduces new insights by integrating fractal and metabolic principles to understand traffic system dynamics, marking the first use of fractal analysis in traffic pattern evaluation.

Analysis of fractal dimension of lymphocytes exposed to different doses of ionizing radiation through box counting method

Analysis of fractal dimension of lymphocytes exposed to different doses of ionizing radiation through box counting method