Fractal Analysis Research Articles

Correlation Fractal Dimension Analysis Mountainous Traditional Village Settlement Spatial Form –Case Study of Qiandongnan in Guizhou

Objective: A study carried out in the traditional villages of Qiandongnan in Guizhou province, located in China, to portray 409 traditional villages’ spatial distribution and fractal charicteristic, as well as its implications for the preservation of the group of traditional villages. Theoretical framework: From previous research, traditional village quantitative research on spatial area focuses on the statistics of mathematical models and spatial analyses of GIS, which indirectly reflect the complexity of the spatial patterns of traditional villages. Therefore, applying fractal theory to the spatial complexity of villages can provide a relatively objective and direct assessment for studying traditional villages with different formation backgrounds. Method: Data were collected in Google Earth map data and spatial data were obtained, which were synthesized and analyzed using spatial, statistical and mathematics analysis to verify the distribution factors and know about villages’ spatial fractal characteristics. Results and conclusion: The mountain settlements in Qiandongnan are concentrated in Leishan based on the Miao national group and “Liping-Congjiang-Rongjiang” based on the Dong national group. The q values of the explanatory power of each factor for the spatial distribution of traditional villages in the Qiandongnan area are, in descending order, intangible cultural heritage > GDP > distance from roads > height > the proportion of ethnic minorities > urbanization rate > average annual temperature > average annual precipitation > distance to rivers. Research implications: Villages contribute significantly to the enhancement of traditional Chinese culture, especially the preservation of historical buildings and distinctive local cultures. Furthermore, Knowing the factors of traditional village centralized contiguous protection mode and rural planning based on the policy of rural revitalization in China. Originality/value: Collected traditional villages’ distribution data from the official website and marked on the Google Earth map. Spatial analysis distribution of villages and emphasizes the importance of spatial correlation analysis in understanding the relationship between land use and rural population distribution.

Study of fractality nature in VO2 films and its influence on metal-insulator phase transition

The mechanisms underlying the origin of fractal shape of inclusions of a new phase in VO2 films during metal-insulator phase transition are discussed. The obtained results show that hysteresis of the temperature dependence of resistance R(T) significantly depends on the film morphology and texture. Moreover, some fractal features are observed. To determine the fractal dimension D of the structural elements of the studied films from their images, different fractal analysis approaches were preliminary compared and discussed. As a result of the film image treatments, the boundaries of the structural elements were found to have fractal dimensions of 1.3 to 1.5 or higher and to correlate with the shape of R(T). The fractal boundaries indicate the dominant role of elastic stress on the phase transition of films, which is confirmed by numerical modeling. Based on these results, an analytical model is proposed that relates the free energy of a film to the fractal dimension of its constituents. Depending on the ratio of the elastic and interface specific energies, the position of the free energy minimum F corresponds to a certain fractal dimensionality D. A small interface energy leads to a higher fractal dimension making the initial phase more stable. This conclusion explains well all the effects observed experimentally in VO2. The obtained results provide a better understanding of the influence of structure and morphology on other properties of the studied films.

Anatomical assessment of the trabecular structure of the alveolar bone in periodontal disease by fractal analysis method.

Early diagnosis and treatment of periodontitis, which can cause loss of bone support of the teeth, is of great importance. The use of fractal analysis method is being investigated in order to differentiate periodontal disease radiographically. Fractal analysis presents the degree of complexity in the structure of fractal objects as a numerical data, and has been used to measure changes in trabecular bone. The aim of this study was to compare the trabecular bone fractal dimension (FD) values of patients with periodontitis and gingivitis using panoramic radiographs, and to evaluate the possible relationship between age and gender with fractal dimension. Panoramic radiographs of 64 patients with gingivitis and 64 patients with periodontitis were evaluated retrospectively in the study. Using the radiographs of the patients, FD values measured from the trabecular bone were calculated with the box-counting method in the Image J programme. The FD values of both groups were compared. In addition, the relationship between age and gender parameters and FD values was evaluated within the groups. According to the results of the study, the calculated average FD value of the patients in the gingivitis group was 1.195, while the calculated average FD value of the patients in the periodontitis group was 1.196. No statistically significant difference was observed between the FD values of the gingivitis group and the periodontitis group (p > 0.05). No statistically significant correlation was observed between FD values and age and gender (p > 0.05). No statistically significant results were obtained for the calculated mean FD values of the patients in the gingivitis and periodontitis groups.

The impact of digital transformation on enterprise performance: An empirical analysis based on China's manufacturing export enterprises.

Currently, countries worldwide are embracing digital strategies, enabling enterprises to utilize digital technology, digital supply chains, blockchain, and additional digital measures to increase their competitiveness. This paper analyzed the correlation between the digital transformation of manufacturing export enterprises and their business and export performance, focusing on China's manufacturing export enterprises through empirical analysis. The study investigated the influence of digital transformation on enterprise performance. Using the Resource Based View theory and Trade theory, hypotheses were proposed and regression models were developed to analyze a sample of 1007 enterprises listed on the Shanghai and Shenzhen Stock markets from 2012 to 2019. The study conducted regression analysis, intermediate effect test, robustness test, stage lag, and heterogeneity analysis. The study found that (1) Manufacturing export enterprises listed in the stock market implemented digital transformation, leading to a significant positive impact on their overall performance. (2) Digital transformation led to cost reduction, improved R&D intensity, and enhanced human resources, among other benefits for enterprise performance. (3) According to the fractal analysis, non-state-owned enterprises exhibited more favorable effects on enterprise performance, and the digital transformation of manufacturing export companies in developed regions had a more significant impact on their performance. Finally, the study's empirical results yielded pertinent proposals for digital transformation.

River networks evolution under multiple stresses: A geometric and structural fractal perspective

Accurately quantifying changes in river networks is essential for studying and assessing the environmental effects of such changes. The fractal method has become a popular and effective tool for describing and capturing river network changes. However, it is usually limited to the geometric fractal dimension (Dg), whereas the structural fractal dimension (Ds) is rarely used. Despite this, the Ds could capture crucial structural information, which the Dg does not, such as interconnections among rivers and the overall basin connectivity. In this study, we examined the evolution of Dg and Ds in the Qinhuai River Basin from the 1960s to 2016, revealing the changes in river networks under natural and anthropogenic stresses from both the traditional geometric and novel structural fractal analysis perspective. We also determined the key factors causing fractal variation and their contributions. The results showed that river networks possess both structural and geometric fractality, with values ranging from 1.484 to 1.287 and 1.615–1.514, respectively. The values of Dg and Ds both declined, with Ds declining at a higher rate, suggesting that the river network weakened and deteriorated. The variances of Dg and Ds attributed to urbanization were 0.3139 and 0.3103, respectively, more than thirty times and almost twice as much as the variance attributed to precipitation features. Urbanization was identified as the most significant factor influencing fractal dynamics. These findings advance the understanding of river network evolution from a novel fractal perspective and provide support for integrating river restoration with urban planning practices.

Research on the surface characteristics of 42CrMo alloy steel pulse electrochemical machining

Electrochemical processing, due to its unique material removal mechanism compared to mechanical processing, often results in significantly different micro-morphologies. It is widely used in areas such as aerospace component processing, surface finishing, passivation, micro-structure mold processing, etc. The complexity of alloy steel composition makes uniform etching difficult to achieve, and the post-etch micro-morphology is also complex, making it challenging to describe and analyze. Therefore, it is difficult to analyze the surface morphology of electrochemical etching under different parameters. In this study, a self-developed electrochemical etching device with adjustable DC voltage, pulse width voltage, and pulse width positive and negative voltage output was used. Different parameters of pulse voltage were used to etch the surface of 42CrMo alloy steel. Due to the strong relationship between surface roughness parameters and the chosen measurement scale, as well as the surface morphology and waviness errors introduced by specimen preparation and etching processes, a wavelet filtering method was used to remove the low frequency components in the surface morphology, and only the surface roughness part was retained for fractal parameter calculation and analysis. The research showed that fractal analysis can also be applied to analyze the surface morphology after electrochemical etching. Pulse voltages with characteristic voltages, characteristic pulse frequencies, and duty ratios can achieve better surface quality during positive pulse etching. Positive and negative pulse etching can obtain better surface morphology than positive pulse etching, but the etching amount is lower, making it suitable for precision finishing.

A Study on Planar Complexity and Order in Residential Projects by Steven Holl

This article examines that planar complexity of residential work by Steven Holl with fractal analysis. It is suggested that his architectural design has order from his discourse expressions. This study aims to verify planar characteristics in residential design in terms of order and randomness. This study contributes to clarify design methodology of planar expression with analysing fractal. The evaluation of characteristics is assessed by fractal dimension and clustering. The results indicate that the residential planar has 4 types of character by the figures of fractal dimension. The results are based on the scale of order and randomness for the planar form of the interior and outline.

Subsea jumper damage detection based on fractal analysis and modal characteristics

Subsea jumpers play a critical role in subsea oil and gas production. Structural damage such as cracks is inevitable in subsea jumpers due to the harsh marine environment (internal fluid flow corrosion, high temperature and pressure, etc.). However, the current research on damage detection and evaluation of subsea jumpers is limited, particularly in cases of slight damage. This study thus proposes a method to identify cracks in subsea jumpers based on the modal characteristics and fractal theory. The accuracy of the method is verified by comparing the finite element simulation method via APDL and the analytical method via MATLAB. In addition, the sensitivity of the method to noise is investigated. The results indicate that the method accurately identifies cracks (single and multiple) with a minimum depth of 0.2 mm in various locations on subsea jumpers. This study may hold significant reference value for improving the safety and reliability of subsea jumpers.

Differing patterns of cortical grey matter pathology identified by multifractal analysis in UMN-predominant ALS patients with and without corticospinal tract hyperintensity

The pathological hallmarks of amyotrophic lateral sclerosis (ALS) are degeneration of the primary motor cortex grey matter (GM) and corticospinal tract (CST) resulting in upper motor neuron (UMN) dysfunction. Conventional brain magnetic resonance imaging (MRI) shows abnormal CST hyperintensity in some UMN-predominant ALS patients (ALS-CST+) but not in others (ALS-CST–). In addition to the CST differences, we aimed to determine whether GM degeneration differs between ALS-CST+ and ALS-CST– patients by cortical thickness (CT), voxel-based morphometry (VBM) and fractal dimension analyses. We hypothesized that MRI multifractal (MF) measures could differentiate between neurologic controls (n = 14) and UMN-predominant ALS patients as well as between patient subgroups (ALS-CST+, n = 21 vs ALS-CST–, n = 27). No significant differences were observed in CT or GM VBM in any brain regions between patients and controls or between ALS subgroups. MF analyses were performed separately on GM of the whole brain, of frontal, parietal, occipital, and temporal lobes as well as of cerebellum. Estimating MF measures D (Q = 0), D (Q = 1), D (Q = 2), Δf, Δα of frontal lobe GM classified neurologic controls, ALS-CST+ and ALS-CST– groups with 98% accuracy and > 95% in F1, recall, precision and specificity scores. Classification accuracy was only 74% when using whole brain MF measures and < 70% for other brain lobes. We demonstrate that MF analysis can distinguish UMN-predominant ALS subgroups based on GM changes, which the more commonly used quantitative approaches of CT and VBM cannot.

Three-dimensional characteristics of separation vortex generated by crossing shock/boundary layer interaction

Three-dimensional characteristics of separation vortex generated by crossing shock/boundary layer interaction

Study on freeze-thaw deterioration model of new-to-old concrete based on pore surface fractal characteristics

New-to-old concrete (NTOC) structures are widely used in engineering practice, the adhesive interface as a weak part is easily damaged under freeze-thaw environment. At present, most of NTOC deterioration models are grounded in the empirical summary of experiment data. In this paper, the bonding and durability of NTOC adhesive interface under different freeze-thaw cycles were investigated by splitting tensile test and ultrasonic nondestructive test, and the pore distribution characteristics of adhesive interface were obtained by mercury intrusion porosimetry. Based on the S-N equation and the constitutive relationship of damaged concrete, the phenomenological freeze-thaw damage model of NTOC was established. According to the fractal analysis of the effective bearing area of the pores, the freeze-thaw deterioration model of NTOC adhesive interface was further established, which was named PDM model. The splitting tensile strength (macroscopic mechanical properties) and ultrasonic wave velocity (microscopic defects) of the concrete repaired by four kinds of alkali activated slag-fly ash were used to verify PDM model. The results showed that PDM model could reflect the change of bonding properties and the defects of NTOC adhesive interface under freeze-thaw conditions. The microscopic pore evolution characteristics reflected the macroscopic mechanical properties. With a restricted number of monitoring sites, the PDM model could n forecast the changing trend of the whole freeze-thaw degradation process of NTOC.

Petrophysical insights into pore structure in complex carbonate reservoirs using NMR data

The study delves into pore structure attributes within the complex Eocene carbonate of an Indian offshore field, encompassing pore throat, radius and their characteristics. Nuclear Magnetic Resonance (NMR) experimental data reveals crucial insights into pore structures and fluid states. This study compares the NMR T2 distribution curve with capillary pressure data from the Mercury Injection Capillary Pressure (MICP) technique, deriving linear and nonlinear conversion coefficients to transform NMR T2 spectra into equivalent pore radius distribution. Pore radius-dependent porosity partitioning, linked to permeability and the distribution of irreducible water, is conducted utilizing NMR-derived data. Following the T2 cut-off analysis, a two-segment fractal analysis of NMR T2 distribution is also carried out. This analysis unveils associations between fractal dimensions and various petrophysical parameters, including permeability, porosity, T2LM, irreducible water saturation and R50. The NMR-derived pore radius distribution is mostly unimodal, occasionally slightly bimodal. Six different pore size classes (less than 0.05 μm to more than 5 μm) are analysed in relation to permeability, porosity and irreducible water. Small pores (<1 μm) contribute more to irreducible water with low porosity and permeability. The fractal dimension of large pores correlates strongly with porosity, permeability, T2LM, irreducible water and R50 suggesting significant impact on reservoir seepage capacity. In addition to porosity partitioning, the current study demonstrates effectiveness in modelling modified permeability and correlating it with in situ permeability when applied to field NMR log data from the study area. While numerous studies focus on sandstone, our study marks the pioneering attempt at a comprehensive analysis on complex carbonate reservoirs.

Comparison of periapical radiography, panoramic radiography, and CBCT in the evaluation of trabecular bone structure using fractal analysis.

The aim of this study is to compare imaging techniques to evaluate trabecular bone structure using Fractal Analysis (FA). Fifteen sheep hemimandibles were used for this study. Digital images were obtained using periapical radiography, panoramic radiography, and cone-beam computed tomography (CBCT). CBCT imaging was performed in standard (STD) and high-resolution (HR) modes. FA was conducted using ImageJ 1.3 software with the box-counting method on the images. The fractal dimension (FD) values were analyzed by the statistical software Jamovi 1.6.23. Statistical significance was accepted as p < 0.05. The highest mean FD value was the FD on digital periapical radiographs (PaFD) (1.28 ± 0.04), and the lowest mean FD value was the FD on standard resolution cone-beam computed tomography images (STD-CBCTFD) (1.12 ± 0.10). Although there was no statistically significant difference between the PaFD and the FD on digital panoramic radiographs (PanFD) (p = 0.485), the PaFD was found to be significantly higher than STD-CBCTFD (p < 0.001), and the FD on high-resolution cone-beam computed tomography images (HR-CBCTFD) (p = 0.007). The PanFD was found to be significantly higher than the STD-CBCTFD (p = 0.004). According to our results, in the evaluation of trabecular bone structure using FA, periapical radiographs and panoramic radiographs have similar image quality for assessment of the FD. On the other hand, CBCT results did not correlate with results from any of the other techniques in this study.

Method for phase space reconstruction to estimate the short-term future behavior of pressure signals in pipelines

In this study, we propose a method based on phase space reconstruction to estimate the short-term future behavior of pressure signals in pipelines. The pressure time series data were obtained from an IoT experimental model conducted in the laboratory. The proposed hydraulic system demonstrated the presence of traces of weak chaos in the time series of the pressure signal. Fractal dimension analysis revealed a complex fractal structure in the data, indicating the existence of nonlinear dynamics. Similarly, Lyapunov coefficients, divergent trajectories, and autocorrelation analysis confirmed the presence of weak chaos in the time series. The results demonstrated the existence of apparently chaotic patterns that follow the theory proposed by Kolmogorov for deterministic dynamic systems that exhibit apparently random behaviors. Phase space reconstruction allowed us to show the dynamic characteristics of the signal so that short-term predictions were stable. Finally, the study of strange attractors in pipeline pressure time series can have significant contributions to anomaly detection.•A methodology is proposed for the reconstruction of the phase space to estimate the short-term future behavior of pressure signals in pipelines in real time.•The analysis of the proposed hydraulic system revealed some indications of weak chaos in the time series of the pressure signal obtained experimentally.•The methodology implemented and the results of this study showed that the short-term predictions were very accurate and consistent; Chaotic patterns were also identified that support the theory proposed by Kolmogorov.

Do Habitat MRI and Fractal Analysis Help Distinguish Triple-Negative Breast Cancer From Non-Triple-Negative Breast Carcinoma.

Purpose: To determine whether multiparametric MRI-based spatial habitats and fractal analysis can help distinguish triple-negative breast cancer (TNBC) from non-TNBC. Method: Multiparametric DWI and DCE-MRI at 3T were obtained from 142 biopsy- and surgery-proven breast cancer with 148 breast lesions (TNBC = 26 and non-TNBC = 122). The contrast-enhancing lesions were divided into 3 spatial habitats based on perfusion and diffusion patterns using K-means clustering. The fractal dimension (FD) of the tumour subregions was calculated. The accuracy of the habitat segmentation was measured using the Dice index. Inter- and intra-reader reliability were evaluated with the intraclass correlation coefficient (ICC). The ability to predict TNBC status was assessed using the receiver operating characteristic curve. Results: The Dice index for the whole tumour was 0.81 for inter-reader and 0.88 for intra-reader reliability. The inter- and intra-reader reliability were excellent for all 3 tumour habitats and fractal features (ICC > 0.9). TNBC had a lower hypervascular cellular habitat and higher FD 1 compared to non-TNBC (all P < .001). Multivariate analysis confirmed that hypervascular cellular habitat (OR = 0.88) and FD 1 (OR = 1.35) were independently associated with TNBC (all P < .001) after adjusting for rim enhancement, axillary lymph nodes status, and histological grade. The diagnostic model combining hypervascular cellular habitat and FD 1 showed excellent discriminatory ability for TNBC, with an AUC of 0.951 and an accuracy of 91.9%. Conclusions: The fraction of hypervascular cellular habitat and its FD may serve as useful imaging biomarkers for predicting TNBC status.

The fractal turbulent–non-turbulent interface in the atmosphere

Abstract. With their constant increase in size, wind turbines are reaching unprecedented heights. Therefore, at these heights, they are influenced by wind conditions that have not yet been studied in detail. With increasing height, a transition to laminar conditions becomes more and more likely. In this paper, the presence of the turbulent–non-turbulent interface (TNTI) in the atmosphere is investigated. Three different on- and offshore locations are investigated. Our fractal scaling analysis leads to typical values known from ideal laboratory and numerical studies. The height distribution of the probability of the TNTI is determined and shows a frequent occurrence at the height of the rotor of future multi-megawatt turbines. The indicated universality of the fractality of the TNTI allows the use of simplified models in laboratory and numerical investigations.

Development of a Powder Analysis Procedure Based on Imaging Techniques for Examining Aggregation and Segregation Phenomena.

In this manuscript, a method that utilizes classical image techniques to assess particle aggregation and segregation, with the primary goal of validating particle size distribution determined by conventional methods, is presented. This approach can represent a supplementary tool in quality control systems for powder production processes in industries such as manufacturing and pharmaceuticals. The methodology involves the acquisition of high-resolution images, followed by their fractal and textural analysis. Fractal analysis plays a crucial role by quantitatively measuring the complexity and self-similarity of particle structures. This approach allows for the numerical evaluation of aggregation and segregation phenomena, providing valuable insights into the underlying mechanisms at play. Textural analysis contributes to the characterization of patterns and spatial correlations observed in particle images. The examination of textural features offers an additional understanding of particle arrangement and organization. Consequently, it aids in validating the accuracy of particle size distribution measurements. To this end, by incorporating fractal and structural analysis, a methodology that enhances the reliability and accuracy of particle size distribution validation is obtained. It enables the identification of irregularities, anomalies, and subtle variations in particle arrangements that might not be detected by traditional measurement techniques alone.

Multifractal information on reading eye tracking data

The study of the multifractal characteristics of physiological processes attracted wide interest in recent decades, since evidence has been found that the presence of certain alterations in these processes is reflected in the variability of their dynamics. However, neurocognitive processes have not been so widely studied from this perspective. We aim to provide new insights regarding the alterations that dyslexia produces in eye movements during reading. For this reason, we performed fractal and multifractal analysis of eye movements of children with and without dyslexia. This investigation showed that disorders in the cognitive process of reading, such as the one caused by dyslexia, induce slight alterations in the variability of eye movements usually found in neurotypical subjects. In particular, we found differences in the dynamics of fixations and saccades presented by children with dyslexia, a fact that is reflected in the long-range correlation behavior of the recorded eye-tracking data. This finding may provide hints about the neurocognitive organization of the reading process and how it is altered in dyslexic subjects, and also an inexpensive and non-invasive means to detect the condition in its early stages.

Bone Trabecular Pattern Analysis in Odontogenic Cysts Using Cone Beam Computed Tomography: A Clinical Retrospective Study.

Introduction The cysts of the maxillofacial region account for one of the most common pathologies of the head and neck region after the mucosal pathologies. Radiography provides an essential clue in early diagnosis and triaging, but it continues further as it is used to evaluate the post-treatment outcome. However, manual analysis is prone to errors. In this scenario, fractal analysis (FA) in radiographs uses mathematical methods to analyse the changes in grey scales in a given radiographic image. FA in odontogenic cysts is used to characterise their complexity, uncover hidden patterns, monitor treatment response, and potentially provide prognostic information. This paper aimed to assess the fractal characteristics of the radicular cyst (RC), dentigerous cyst (DC), and odontogenic keratocyst (OKC) using cone beam computed tomography (CBCT). The objective was to calculate fractal dimension (FD) values expressed in each of these cysts, which could prove to be a radiological adjunct in diagnosing the above cysts. Materials and methods As this is a retrospective study, the archives of CBCT images from June 2021 to December 2023 were obtained from patients diagnosed and confirmed with a histopathological diagnosis with RC, DC, and OKC. The FA was performed using Image J Software(Ver 1.51, National Institute ofHealth Bethesda, Fiji). The cortical and cancellous bones were segmented using thresholding techniques and converted to binary images. The mean FD of the three planes was then compared to establish the distinctive fractal characteristic for the specific odontogenic cysts. A one-way ANOVA was performed using the Statistical Product and Service Solutions (SPSS) (version 23.0; IBM SPSS Statistics for Windows, Armonk, NY) to determine the difference between FD values of RC, DC, and OKC with a significance level less than 0.05. Results The FD values of DC, RC, and OKC were 1.33 ± 0.17, 1.08 ± 0.16, and 1.65 ± 0.12, respectively. The results indicated that OKC had higher FD values than DC and RC, which means that OKC had lesser bone destruction compared to DC and RC. Inferential statistics showed that the one-way ANOVA was used to compare the means of the three groups of FD data. When calculated for the three groups, the F-statistic value was at 7.29, which yielded a P value of 0.03, making it statistically significant for a 95% confidence interval (p<0.05). Conclusion Our CBCT study on bone trabecular pattern analysis using FD and FAin odontogenic cysts reveals distinct alterations in bone parameters among different cyst types. The probability of higher FD values in OKC is because of lesser cortical bone destruction in OKC compared to the other cyst types. These findings have potential implications for diagnosing, treating, and prognosticating odontogenic cysts.

Older adults and individuals with Parkinson's disease control posture along suborthogonal directions that deviate from the traditional anteroposterior and mediolateral directions.

A rich and complex temporal structure of variability in postural sway characterizes healthy and adaptable postural control. However, neurodegenerative disorders such as Parkinson's disease, which often manifest as tremors, rigidity, and bradykinesia, disrupt this healthy variability. This study examined postural sway in young and older adults, including individuals with Parkinson's disease, under different upright standing conditions to investigate the potential connection between the temporal structure of variability in postural sway and Parkinsonism. A novel and innovative method called oriented fractal scaling component analysis was employed. This method involves decomposing the two-dimensional center of pressure (CoP) planar trajectories to pinpoint the directions associated with minimal and maximal temporal correlations in postural sway. As a result, it facilitates a comprehensive assessment of the directional characteristics within the temporal structure of sway variability. The results demonstrated that healthy young adults control posture along two orthogonal directions closely aligned with the traditional anatomical anteroposterior (AP) and mediolateral (ML) axes. In contrast, older adults and individuals with Parkinson's disease controlled posture along suborthogonal directions that significantly deviate from the AP and ML axes. These findings suggest that the altered temporal structure of sway variability is evident in individuals with Parkinson's disease and underlies postural deficits, surpassing what can be explained solely by the natural aging process.