Fractal Approach Research Articles

A Comparative Analysis of Fractal and Fractionalized Thermal Non-Equilibrium Model for Chaotic Convection Saturated by Porous Medium

The convective heat transfer is one of the most important mechanism of heat transference for controlling the chaotic characteristics in porous media. A comparative study of thermal non-equilibrium model is proposed for fractal porous under the consideration of chaotic convection. A novel chaos control is focused between fractal porous and fractional porous by means of newly proposed differential and integral techniques. The sensitivity analysis for chaos expansion and uncertainty quantification for the flow in heterogeneous media have been perceived to the problem of chaotic convection through numerical simulations. In order to approximate the propagation of chaos, two types of simulations have been carried out in terms of chaotic attractors through fractal and fractional approaches. For examining a variety of chaos under the numerical simulations in which fractal domain is varied and fractional domain is fixed, fractal domain is fixed and fractional domain is varied, and both fractal as well as fractional domain are varied. Finally, it is observed that the fractional and fractal memory effects have caused by interactions between uncertain parameters and disclosed the microstructures on the permeability of porous media.

Micromechanical properties and fractal homogenization of coal based on nanoindentation

Distinct from hard rock, coal is relatively soft and fragmented. It is not only challenging to prepare test coal samples that meet the requirements of standard mechanical experiments but also impossible to recycle them for repeated testing. There is an urgent need to explore new mechanical testing methods to enhance the study of the mechanical properties of coal. In this study, the micromechanical parameters of the coal matrix solid phase were acquired through targeted nanoindentation technology. The elemental composition, surface morphology, and pore structure characteristics of each indentation point were determined by energy dispersive spectrometer, optical microscope observation, and high-pressure mercury injection experiments. The fractal homogenization equation is deduced based on fractal geometry and the Mori–Tanaka method. The validity of the fractal homogenization approach is verified by integrating the micromechanical parameters and pore structure characteristics of coal, and the impact of the microstructural parameters on the macroscopic mechanical properties of coal is discussed. The results show that the proportion of clay minerals in the solid phase of the coal is the greatest (81.18%), with the main mineral components being kaolinite and illite. The elastic modulus is 1.974 ± 1.036 GPa, the hardness is 0.131 ± 0.108 GPa, and the ratio of upper and lower pore scales conforms to the fractal calibration rate. The macroscopic equivalent elastic modulus rises along with the increase in the fractal dimension. When the fractal dimension is constant, the macroscopic equivalent elastic modulus decreases with the increase in λmin/λmax and increases with the increase in solid phase elastic modulus.

FRACTAL APPROACH IN SOCIAL GOVERNANCE

At a time when the scope of social management in New Uzbekistan is expanding and its importance is increasing in various fields, the concept of a fractal approach to optimizing social management processes in the social sciences is widely studied on the basis of scientific analytical findings.

Enzymatic hydrolysis of highly concentrated substrates obtained from Miscanthus giganteus

This work is the first to study the enzymatic hydrolysis of four types of substrates obtained from Miscanthus giganteus of the KAMIS variety of Russian breeding. The study was conducting using the authors’ methodology based on a chemical pretreatment of substrates at atmospheric pressure with HNO3 and NaOH dilute solutions. A one-stage pretreatment of Miscanthus giganteus allows the polysaccharide content to be increased up to 90.4–90.8%, compared to 98.3–99.4% following a two-stage treatment. The experimental results of enzymatic hydrolysis of the four obtained substrates in the range of initial concentrations from 30 to 120 g/l are approximated using fractal kinetics approaches. An increase in the initial substrate concentrations in the specified range leads to an increase in the initial hydrolysis rate by 2.8–3.3 times and a decrease in the yield of reducing sugars by 12.4–13.1%. All four pretreatment types turned out to be extremely effective for Miscanthus giganteus, ensuring an increase in the reactivity to enzymatic hydrolysis by 34–36 times compared to the starting raw material. Lowered yields of reducing sugars are observed during enzymatic hydrolysis of the alkaline delignification product of Miscanthus giganteus, which is associated with the resistance of Miscanthus giganteus to treatment with sodium hydroxide. An increase in the initial concentration of substrates from 60 to 90 g/l does not lead to a significant decrease in the yield of reducing sugars. Therefore, enzymatic hydrolysis of highly concentrated substrates can be successfully used to produce biofuels and biochemicals.

A fractal approach to estimating the durability of critical parts

A fractal approach to estimating the durability of critical parts

Arbor vitae cerebelli: Fractal properties and their quantitative assessment by novel “contour scaling” fractal analysis method (an anatomical study)

BackgroundArbor vitae cerebelli (tree-like branching white matter of the cerebellum) has a complex spatial configuration that is challenging to assess using conventional morphometric methods. This study proposes a fractal approach to describe and quantify the anatomy of Arbor vitae cerebelli. For this purpose, a new “contour scaling” method for fractal analysis of cerebellar white matter was developed. Material and methodsThe cerebella of 100 cadavers (50 male and 50 female) who died from causes unrelated to brain pathology, aged 20–95 years, were examined. Mid-sagittal sections of the cerebellar vermis were studied. The fractal dimension values of the cerebellar white matter were determined using both the developed fractal analysis method and the conventional “box counting” method, along with measurements of non-fractal parameters including cerebellar weight, area and perimeter of the vermis cross-section, perimeter-to-area ratio, and circularity. ResultsConsidering the cerebellar white matter as a tree-like fractal, it was found to have 7 or 8 primary branches, which subdivide into 10-18 second-iteration branches, 19–38 third-iteration branches, and 34–53 fourth-iteration branches. Females more often had 8 primary branches compared to males, while males had a greater number of branches in the second to fourth iterations. The mean fractal (Hausdorff) dimension was 1.697 (1.721 in males, 1.674 in females, P = 0.01). The fractal dimension correlated most strongly with the perimeter and area of the vermis cross-section and had no significant relationship with age. ConclusionThe fractal (Hausdorff) dimension, determined using the novel “contour scaling” method, quantitatively assesses the degree of branching of the cerebellar white matter. An increase in the absolute size of the cerebellum leads to a higher degree of branching of its white matter and an increase in the number of its constitutive components – white matter branches and folia.

A Closed Burst Error Correcting Codes Cantor Fractal Approach

The nature of the errors depends on the behaviour of channel, there is a need to study different types of error pattern. This paper explores the new type of error called closed burst and obtained the possibilities of the existence of two types of block wise burst error correcting codes of length 3^N and 3N respectively with cantor fractal approach over GF(2). The code envisaged are meant to correct all the closed bursts of length b_i in the i^thiteration in the first and last sub-blocks of equal length l_i.

Inspection of numerical and fractional CMC and water-based hybrid nanofluid with power law and non-singular kernel: A fractal approach

A number of thermal devices might benefit from the usage of nanofluids in solar power. In this research, the idea of MHD mixed convective hybrid nanofluids including grapheme oxide (GO) and molybdenum disulfide (MoS2) nanoparticles with water (H2O) and Carboxymethyl Cellulose (CMC) as base fluids in a perpendicular channel to analyze the heat transfer of the flowing fluid with the help of recent definition of fractional derivatives namely Fractal fractional derivative. The problem is expressed as PDEs with beginning and boundary conditions, and it is analyzed analytically using the Laplace transform method. The velocity, temperature, and concentration measurements are also shown in series for their appropriate Laplace inverse. Delays in parameters like nanoparticle volume sharing rate have a significant influence on these techniques. Skin friction, Nusselt, and Sherwood numbers are computed for the longitudinal channel's left and right walls, and the necessary numerical results are presented in tabular format. As a result, it is discovered that the rate of heat transfer reduces as the volume percentage of nanoparticles and the Fractal time fractional value rise. Furthermore, when comparing nanofluids, water-based (H2O + GO + MoS2) hybrid nanofluids have a greater influence on governed model than (CMC + GO + MoS2)-based hybrid nanofluids.

Exploring groundwater patterns in Souss-Massa Mountainous Basin, Morocco: A fusion of fractal analysis and machine learning techniques on gravity data

Groundwater potential in Morocco’s Souss-Massa mountainous basin (SMMB) is being identified using geospatial tools and geological data. We deployed four mathematical models, namely Data-Driven Multi-index Overlay (DMIO), Geometric Average (GA), Support Vector Machine (SVM), and Logistic Regression (LR), to establish data-driven patterns among the nine influencing factors, primarily drainage density, permeability, slope, distance to rivers, elevation, lineament density, distance to lineaments, intersection node density, and rainfall. Based on the Concentration-Area (C-A) fractal approach, the findings of the four models were developed and classified into five levels of potentiality ranging from very low to very high. The regions designated as having high and very high potentialities for the DMIO, GA, SVM, and LR models, respectively, account for 22.44 %, 9.80 %, 19.36 %, and 26.77 % of the overall basin. We validated the models by calculating each model's area under the ROC curve (AUC). The estimated AUC values are more than 70 %, suggesting the model performs well. The four models' performance was compared, revealing that the SVM model outperforms the others. Gravimetric data shows that possible groundwater zones closely coincide with gravimetric lineaments. The findings of this study can provide valuable insights to decision-makers, allowing them to improve decision-making processes and develop holistic groundwater resource management in the Souss-Massa mountainous basin (SMMB).

A quantitative study of the microstructure of Indian Gondwana shale: a fractal and algebraic topology approach

This paper covers a novel micro-level application of image processing in understanding the topological and petrophysical properties of Indian Gondwana shale using X-ray computed microtomography images. The complexity and randomness in the pore system are explained through the concept of fractal dimension (FD). In this paper, a quantitative analysis of 2D and 3D fractal dimensions of pores, grains and interfaces was performed for Indian Gondwana shale, using the box-counting method. A pore network is formed by the connection of many subpore clusters, each with a different volume. Hence, an image segmentation algorithm was applied to label different subclusters, and subsequently an analysis of FD was carried out on such subclusters of pores and grains. We implemented a novel application of Betti numbers (B0, B1 and B2) and Euler characteristics on our sample and calculated the possible flow channels of the sample. The FD of grains was found to be greater than the FD of the pore–grain interfaces, while the FD of pores was found to have the smallest value. Consequently, we also observed how the FD of both pores and grains was majorly controlled by the largest subcluster, and during fluid intrusion we observed a significant decrease in the FD of pores. Finally, the pore network with a larger B0 and larger difference of B1 was proved to be best for the storage of hydrocarbons and for fluid movement along more flow channels.

Invasive weed optimization based compact hybridized fractal antenna design for RF energy harvesting and multifunctional wireless applications

This paper describes the optimal design and analysis of compact multiband Hybrid Fractal Antenna using Invasive Weed Optimization (HFAIWO). The configured structure involves the fusion of Minkowski, Sierpinski carpet and Giuseppe Peano in a coherent manner. The two-iterative conglomerated fractal antenna is realized physically by considering FR4 epoxy material (dielectric constant, εr = 4.4 and mass density = 1,900 kg/m3). The volumetric dimensions of the fabricated prototype are 36 x 36 x 1.6 mm3. In the designing process, the geometrical descriptors, namely, feedline width ‘WF’ and ground plane dimension ‘LG’ are optimized specifically using Invasive Weed Optimization (IWO) and Harmony Search Algorithm (HSA) strategies. The optimal solution is searched by changing the descriptor values under a set of practical constraints. The examined values of ‘WF’ and ‘LG’ using IWO and HSA are 3 and 31 mm, and 2.6 and 28.7 mm, respectively. Comparative results reveal that IWO offers superior solution quality and convergence than HSA. Afterwards, experimentation of the Projected HFAIWO is done to justify the recommended fractal hybridization approach. Measurements reveal that for VSWR ≤ 2, the fabricated structure produces nine resonance points (1.84, 3.99, 5.15, 5.55, 6.30, 6.58, 8.00, 9.29, and 12.01 GHz) with appreciable gain values. At the respective resonance points, the −10 dB impedance bandwidth is 3.9 %, 3.1 %, 2.1 %, 2.2 %, 1.4 %, 1.2 %, 6.9 %, 1.2 %, and 12.23 %. The provided radiation patterns are arbitrary bidirectional/omnidirectional. By applying the above-said approaches, the radiator size is reduced by 54 %. Importantly, the constructed structure covers two important bands i.e. 1.84 GHz (GSM 1800 band, downlink) and 5.55 GHz (WLAN (Lower) 5.150–5.725 GHz) associated with energy harvesting applications. The practical outcomes suggest that the introduced prototype is a proficient candidate for energy harvesting systems, Satellite communication for downlink, Long range tracking, Battlefield surveillance, Digital broadcast satellite service, Weather Radar, and Maritime navigation radar.

Analysing the surface morphology of annealed FTO/ZnS bilayer films: stereometric, fractal, and wettability approaches

The surface micromorphology and roughening of the thermal evaporation-coated FTO/ZnS bilayer thin films annealed at 300, 400, 500, and 550∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$550\\,^\\circ{\ ext{C}}$$\\end{document} for 1 h have been studied. AFM images of the prepared samples were analysed by the MountainsMap software, and the effects of the annealing temperature on the surface texture of the FTO/ZnS thin film’s surface were investigated. Stereometric and advanced fractal analyses showed that the sample annealed at 500∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$500\\,^\\circ{\ ext{C}}$$\\end{document} exhibited greater surface roughness and greater skewness and kurtosis. This film also has the most isotropic surface and exhibits the highest degree of heterogeneity. Also, despite the decrease in surface roughness with increasing temperature from 500 to 550∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$550 \\,^\\circ{\ ext{C}}$$\\end{document}, the fractal dimension tends to increase. The static water contact angle measurements indicate that the film annealed at 500∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$500 \\,^\\circ{\ ext{C}}$$\\end{document} exhibits higher hydrophobicity, which can be attributed to its greater topographic roughness. Our research indicates that the surface morphology of FTO/ZnS bilayer thin films is influenced by the annealing temperature. Changing factors such as roughness, fractality, and wettability parameters to help improve surface performance make the FTO/ZnS bilayer suitable for application in electronic and solar systems.

Chaotic behavior of geophysical logs for stratigraphic hiatuses: A case study from Upper Assam Shelf, India

We propose a novel fractal analysis-assisted approach for stratigraphic characterization to understand the in-situ subsurface geology of hydrocarbon reservoirs. By employing correlation dimension and multifractal detrended fluctuation analysis, we quantify the self-similarity and long-range dependencies in the geophysical logs, reflecting the unique sedimentation processes inherent in the stratigraphic formations of the Bhogpara oil field in the Upper Assam basin. The fractal properties of the logs associated with various stratigraphic units are used to establish a fractal-based stratigraphic signature. The hierarchy of the studied formations, based on the correlation dimension ranging from 1.98 to 1.13, is follows as: Girujan > Tipam > Barail > Kopili > Prang > Narpuh > Lakadong-Therria. Furthermore, the spectrum width values, was found to range from 0.70 to 2.04, reflecting the spatial correlation, geological complexity, and heterogeneity inherent in each formation as: Kopili > Prang > Narpuh > Barail > Girujan > Tipam > Lakadong-Therria. This method identifies common fractal patterns between wellbores and aids in determining the spatial continuity of stratigraphic units. Our approach effectively detects lateral variations in subsurface formations, linking well log fractality with depositional patterns through various transitional environments, such as lacustrine to shallow marine to fluvial, in presence of different fluids. The petroliferous formation exhibits lowest fractal dimension and weak multifractality. The research utilizes fractal analysis to improve stratigraphic correlation, enhancing subsurface characterization and reservoir delineation, particularly in complex geological environments, and enhancing reliability.

Simulated deep CT characterization of liver metastases with high-resolution filtered back projection reconstruction

Early diagnosis and accurate prognosis of colorectal cancer is critical for determining optimal treatment plans and maximizing patient outcomes, especially as the disease progresses into liver metastases. Computed tomography (CT) is a frontline tool for this task; however, the preservation of predictive radiomic features is highly dependent on the scanning protocol and reconstruction algorithm. We hypothesized that image reconstruction with a high-frequency kernel could result in a better characterization of liver metastases features via deep neural networks. This kernel produces images that appear noisier but preserve more sinogram information. A simulation pipeline was developed to study the effects of imaging parameters on the ability to characterize the features of liver metastases. This pipeline utilizes a fractal approach to generate a diverse population of shapes representing virtual metastases, and then it superimposes them on a realistic CT liver region to perform a virtual CT scan using CatSim. Datasets of 10,000 liver metastases were generated, scanned, and reconstructed using either standard or high-frequency kernels. These data were used to train and validate deep neural networks to recover crafted metastases characteristics, such as internal heterogeneity, edge sharpness, and edge fractal dimension. In the absence of noise, models scored, on average, 12.2% (α=0.012\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =0.012$$\\end{document}) and 7.5% (α=0.049)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =0.049)$$\\end{document} lower squared error for characterizing edge sharpness and fractal dimension, respectively, when using high-frequency reconstructions compared to standard. However, the differences in performance were statistically insignificant when a typical level of CT noise was simulated in the clinical scan. Our results suggest that high-frequency reconstruction kernels can better preserve information for downstream artificial intelligence-based radiomic characterization, provided that noise is limited. Future work should investigate the information-preserving kernels in datasets with clinical labels.

RESNET34 with Synchrosqueezing Transform for ADHD Disorder Detection Using EEG Signals

It is vital for the development of attention deficit hyperactivity disorders (ADHDs) diagnostic tools that help healthcare practitioners to have automated recognition of ADHDs. Recently, the detection of ADHD using EEG data has attracted a lot of interest due to its apparent rapidity in diagnosis and treatment. This is because the disease seems to be caused by hyperactivity and inattention. This paper presents the method for diagnosing ADHDs based on EEG data, with the nonlinear characteristics being retrieved via the Synchrosqueezing Transform (ST). The ST filter banks are used to break down the 16 channels of EEG signal information into the ideal number of time-frequency subbands. At each stage of the decomposition process, the distinctive feature vectors are assessed using CNN as well as the proposed nonlinear fractal dimensions approach. Using ResNet34, it was discovered that a modified CNN classifier that used a 10-fold cross-validation approach was an efficient classifier for differentiating between normal people and those with ADHD. The suggested method was able to successfully categorize ADHD and normal participants with the best accuracy, as shown by several performance indicators. The statistical study demonstrated that the CNN and the proposed nonlinear feature estimation techniques produce possible characteristics that are acceptable for the automated identification of ADHD. These features may be categorized with good accuracy, sensitivity and specificity. The technique that has been presented is capable of correctly differentiating between participants who have ADHD and those who do not have ADHD with an ultimate precision of 99.5%.

A DEM-based framework to optimize the gradation of concrete aggregate using fractal approach

A DEM-based framework to optimize the gradation of concrete aggregate using fractal approach

Prioritizing cervical cancer candidate genes using chaos game and fractal-based time series approach.

Cervical cancer is one of the most severe threats to women worldwide and holds fourth rank in lethality. It is estimated that 604, 127 cervical cancer cases have been reported in 2020 globally. With advancements in high throughput technologies and bioinformatics, several cervical candidate genes have been proposed for better therapeutic strategies. In this paper, we intend to prioritize the candidate genes that are involved in cervical cancer progression through a fractal time series-based cross-correlations approach. we apply the chaos game representation theory combining a two-dimensional multifractal detrended cross-correlations approach among the known and candidate genes involved in cervical cancer progression to prioritize the candidate genes. We obtained 16 candidate genes that showed cross-correlation with known cancer genes. Functional enrichment analysis of the candidate genes shows that they involve GO terms: biological processes, cell-cell junction assembly, cell-cell junction organization, regulation of cell shape, cortical actin cytoskeleton organization, and actomyosin structure organization. KEGG pathway analysis revealed genes' role in Rap1 signaling pathway, ErbB signaling pathway, MAPK signaling pathway, PI3K-Akt signaling pathway, mTOR signaling pathway, Acute myeloid leukemia, chronic myeloid leukemia, Breast cancer, Thyroid cancer, Bladder cancer, and Gastric cancer. Further, we performed survival analysis and prioritized six genes CDH2, PAIP1, BRAF, EPB41L3, OSMR, and RUNX1 as potential candidate genes for cervical cancer that has a crucial role in tumor progression. We found that our study through this integrative approach an efficient tool and paved a new way to prioritize the candidate genes and these genes could be evaluated experimentally for potential validation. We suggest this may be useful in analyzing the nucleotide sequences and protein sequences for clustering, classification, class affiliation, etc.

Non-Integer Dimensional Analysis of Ultrasonic Wave Propagation in Fractal Porous Media

This paper explores the acoustics of porous media characterized by fractal, or self-similar, structures. Employing a fractal approach, we use differential operators in non-integer dimensional spaces to address the fundamental equations of acoustics in such media. The primary aim is to examine the transmission of ultrasonic waves within a fractal porous medium. Our findings reveal that the fractal dimension significantly influences wave transmission. In fractal porous materials, waves travel along more complex and intricate paths, resulting in increased tortuosity and attenuation. We introduce the concept of an effective path length leff , which is dependent on the fractal dimension Dx , to describe the actual trajectory of wave propagation. Additionally, we define an effective tortuosity αDx , directly proportional to leff2 , to quantify the additional tortuosity brought about by the fractal structure. The insights gained from this study are crucial, as they enhance our understanding of wave behavior in self-similar porous media, which are prevalent in various natural settings and have multiple practical applications, including sound insulation and the design of acoustic materials. Furthermore, understanding the impact of fractal dimensions on wave behavior is vital for developing more efficient acoustic solutions. This research also sets the stage for further theoretical and experimental work on applying fractal geometry to analyze wave propagation in porous structures.

A fractal approach to ocean Ekman transport

This work examines ocean Ekman current dynamics in fractal dimensions based on the concept of product-like fractal measure introduced recently by Li and Ostoja-Starzewski in their formulation of anisotropic continuum media. We show that fractal dimensions of the fluid affects the amplitude and the shape of the velocity profile. It was observed that fast-moving current occurs for fractal dimensions much less than unity whereas slow-moving current arises for fractal dimensions close to unity. A large flow velocity leads to a decrease in the shear rate and an increase in the viscosity, a fact that has been observed in physical oceanography.

Features of the Formation of Fractal-Holographic Thinking of Students: Perceptual Challenges of the Digital

Introduction. The article examines the features of the formation of fractal-holographic thinking of students in the system of modern education, starting from kindergarten and ending with university, in the context of the methodology of transdisciplinary research, organically linked to the synergetic paradigm, the key point of which is the fractal approach. The purpose of the article is to consider the essence of fractal-holographic thinking of students and the features of its formation in the context of the perceptual challenges of the digital age. Methodology and methods of research. The methodological basis of the research is fractal and transdisciplinary approaches that allow us to consider the process of formation of fractal-holographic thinking of students, emphasizing the perceptual challenges of the digital era in the context of the interaction of trends in aestheticization and technologization. Building the scientific concept of “fractal-holographic thinking of students”, philosophical statements about man as a bio-psycho-socio-cultural-existential phenomenon are taken into account. The results of the study. For the first time, the authors explore the fractal-holographic thinking of man from the perspective of such fundamental concepts as the concept of “beauty of fractals”, expressing the laws of harmony of nature, the concept of T.V. Chernihovskaya “The universe is a work of Baroque art”, as well as the archetypes of the unconscious Jung. Special attention is paid to the mechanisms of formation of fractal-holographic thinking of students, which functions in the context of an aestheticized and technologized world. The content of the study describes fundamentally new approaches regarding the phenomenology of “perceptual challenge”, which make it possible to effectively form fractal-holographic thinking of students in the era of digitalization. For the first time, an attempt has been made to classify and describe the perceptual challenges underlying the formation of fractal-holographic thinking of students of the third millennium in the context of the interaction of aestheticization and technologization trends. Conclusion. When explaining the essence of fractal-holographic thinking, its relationship with holographic and synergetic thinking is shown, the role of fractal-holographic thinking in the hierarchy of human thinking types is determined, and the emphasis is on the importance of art, which among human activities has the highest degree of creativity.